Number System and Arithmetic
[UPSC CSAT PYQ last 11 years(2014-2024)]
For a charity show, the total tickets sold were 420. Half of these tickets were sold at the rate of Rs 5 each, one-third at the rate of Rs 3 each and the rest for Rs 2 each. What was the total amount received? [2014]
Rs 900
Rs 1,540
Rs 1,610
Rs 2,000
If Sohan, while selling two goats at the same price, makes a profit of 10% on one goat and suffers a loss of 10% on the other [2014]
he makes no profit and no loss.
He makes a profit of 1%.
he suffers a loss of 1%.
he suffers a loss of 2%.
Five persons fire bullets at a target at an interval of 6, 7, 8, 9 and 12 seconds respectively. The number of times they would fire the bullets together at the target in an hour is [2014]
(a) 6
(b) 7
(c) 8
(d) 9
4. A bell rings every 18 minutes. A second bell rings every 24 minutes. A third bell rings every 32 minutes. If all the three bells ring at the same time at 8 o’clock in the morning, at what other time will they all ring together? [2014]
(a) 12 : 40 hrs
(b) 12 : 48 hrs
(c) 12 : 56 hrs
(d) 13 : 04 hrs
5. As per agreement with a bank, a businessman had to refund a loan in some equal installments without interest. After paying 18 installments he found that 60 percent of his loan was refunded. How many instalments were there in the agreement ? [2014]
(a) 22
(b) 24
(c) 30
(d) 33
6. In a town, 45% of the population read magazine A, 55% read magazine B, 40% read magazine C, 30% read magazines A and B, 15% read magazines B and C, 25% read magazines A and C; and 10% read all the three magazines. What percentage do not read any magazine? [2015]
(a) 10%
(b) 15%
(c) 20%
(d) 25%
7. Two equal glasses of the same type are respectively 1/3 and 1/ 4 full of milk. They are then filled up with water and the contents are mixed in a pot. What is the ratio of milk and water in the pot? [2015]
(a) 7 : 17
(b) 1 : 3
(c) 9 : 21
(d) 11 : 23
8. The monthly incomes of Peter and Paul are in the ratio of 4 : 3. Their expenses are in the ratio of 3 : 2. If each saves Rs 6,000 at the end of the month, their monthly incomes respectively are in Rs) [2015]
(a) 24,000 and 18,000
(b) 28,000 and 21,000
(c) 32,000 and 24,000
(d) 34,000 and 26,000
9. A cow costs more than 4 goats but less than 5 goats. If a goat costs between Rs 600 and Rs 800, which of the following is a most valid conclusion? [2015]
(a) A cow costs more than Rs 2,500.
(b) A cow costs less than Rs 3,600.
(c) A cow costs between Rs 2,600 and Rs 3,800.
(d) A cow costs between Rs 2,400 and Rs 4,000.
10. Candidates in a competitive examination consisted of 60% men and 40% women. 70% men and 75% women cleared the qualifying test and entered the final test where 80% men and 70% women were successful. Which of the following statements is correct? [2015]
(a) Success rate is higher for women.
(b) Overall success rate is below 50%.
(c) More men cleared the examination than women.
(d) Both (a) and (b) above are correct.
11. The sum of the ages of 5 members comprising a family, 3 years ago, was 80 years. The average age of the family today is the same as it was 3 years ago, because of the addition of a baby during the intervening period. How old is the baby ? [2016]
(a) 6 months
(b) 1 year
(c) 2 years
(d) 2 years and 6 months
12. The total emoluments of two persons are the same, but one gets allowances to the extent of 65% of his basic pay and the other gets allowances to the extent of 80% of his basic pay. The ratio of the basic pay of the former to the basic pay of the latter is: [2016]
(a) 16 : 13
(b) 5 : 4
(c) 7 : 5
(d) 12 : 11
A person is standing on the first step from the bottom of a ladder. If he has to climb 4 more steps to reach exactly the middle step, how many steps does the ladder have? [2016]
(a) 8
(b) 9
(c) 10
(d) 11
14. AB is a vertical trunk of a huge tree with A being the point where the base of the trunk touches the ground. Due to a cyclone, the trunk has been broken at C which is at a height of 12 meters,broken part is partially attached to the vertical portion of the trunk at C. If the end of the broken part B touches the ground at D which is at a distance of 5 meters from A, then the original height of the trunk is: [2016]
(a) 20 m
(b) 25 m
(c) 30 m
(d) 35 m
15. Ram and Shyam work on a job together for four days and complete 60% of it. Ram takes leave then and Shyam works for eight more days to complete the job. How long would Ram take to complete the entire job alone? [2016]
(a) 6 days
(b) 8 days
(c) 10 days
(d) 11 days
16. If R and S are different integers both divisible by 5, then which of the following is not necessarily true? [2016]
(a) R – S is divisible by 5
(b) R + S is divisible by 10
(c) R × S is divisible by 25
(d) R2 + S2 is divisible by 5
17. How many numbers are there between 100 and 300 which either begin with or end with 2? [2016]
(a) 110
(b) 111
(c) 112
(d) None of the above
18. We can do 25% of the work-in 30 days, X can do 1/4 of the work in 10 days, Y can do 40% of the work in 40 days and Z can do 1/3 of the work in 13 days. Who will complete the work first? [2016]
(a) W
(b) X
(c) Y
(d) Z
19. The average monthly income of a person in a certain family of 5 is Rs 10,000. What would be the average monthly income of a person in the same family if the income of one person increased by Rs 1,20,000 per year? [2016]
(a) Rs 12,000
(b) Rs 16,000
(c) Rs 20,000
(d) Rs 34,000
20. In a race, a competitor has to collect 6 apples which are kept in a straight line on a track and a bucket is placed at the beginning of the track which is a starting point. The condition is that the competitor can pick only one apple at a time, run back with it and drop it in the bucket. If he has to drop all the apples in the bucket, how much total distance he has to run if the bucket is 5 meters from the first apple and all other apples are placed 3 meters apart? [2016]
(a) 40 m
(b) 50 m
(c) 150 m
(d) 75 m
21. A round archery target of diameter 1 m is marked with four scoring regions from the centre outwards as red, blue, yellow and white. The radius of the red band is 0.20 m. The width of all the remaining bands is equal. If archers throw arrows towards the target, what is the probability, that the arrows fall in the red region of the archery target? [2016]
(a) 0.40
(b) 0.20
(c) 0.16
(d) 0.04
22. A person allows a 10% discount for cash payment from the marked price of a toy and still he makes a 10% gain. What is the cost price of the toy which is marked Rs 770? [2016]
(a) Rs 610
(b) Rs 620
(c) Rs 630
(d) Rs 640
23. A class starts at 11:00 am and lasts till 2:27 pm. Four periods of equal duration are held during this interval. After every period, a rest of 5 minutes is given to the students. The exact duration of each period is: [2016]
(a) 48 minutes
(b) 50 minutes
(c) 51 minutes
(d) 53 minutes
24. 30g of sugar was mixed in 180 ml water in a vessel A, 40 g of sugar Was mixed in 280 ml of water in vessel B and 20 g of sugar was mixed in 100 ml of water in vessel C. The solution in vessel B is : [2016]
(a) sweeter than that in C
(b) sweeter than that in A
(c) as sweet as that in C
(d) less sweet than that in C
25. In aid of charity, every student in a class contributes as many rupees as the number of students in that class. With the additional contribution of Rs 2 by one student only, the total collection is Rs 443. Then how many students are there in the class? [2016]
(a) 12
(b) 21
(c) 43
(d) 45
26. Anita’s mathematics test had 70 problems carrying equal marks i.e., 10 arithmetic, 30 algebra and 30 geometry. Although she answered 70% of the arithmetic, 40% of the algebra and 60% of the geometry problems correctly, she did not pass the test because she got less than 60% marks. The number of more questions she would have to answer correctly to earn a 60% passing marks is: [2016]
(a) 1
(b) 5
(c) 7
(d) 9
27. In the class, there are 18 very tall boys. If these constitute three-fourths of the boys and the total number of boys is two-thirds of the total number of students in the class, what is the number of girls in the class? [2016]
(a) 6
(b) 12
(c) 18
(d) 21
28. The monthly average salary paid to all the employees of a company was Rs 5000. The monthly average salary paid to male and female employees was Rs 5200 and Rs 4200 respectively. Then the percentage of males employed in the company is:[2016]
(a) 75%
(b) 80%
(c) 85%
(d) 90%
29. Two numbers X and Y are respectively 20% and 28% less than a third number Z. By what percentage is the number Y less than the number X ? [2016]
(a) 12%
(b) 10%
(c) 9%
(d) 8%
30. What is the total number of digits printed, if a book containing 150 pages is to be numbered from 1 to 150 [2017]
(a) 262
(b) 342
(c) 360
(d) 450
31. If there is a policy that 1 / 3rd of a population of a community has migrated every year from one place to some other place, what is the leftover population of that community after the sixth year, if there is no further growth in the population during this period? [2017]
(a) 16/243rd part of the population
(b) 32/243rd part of the population
(c) 32 / 729th part of the population
(d) 64/ 729th part of the population
32. There are three pillars, X, Y and Z of different heights. Three spiders A, B and C start to climb on these pillars simultaneously. In one chance. A climbs on X by 6cm but slips down 1 cm. B climbs on Y by 7 cm but slips down 3 cm. C climbs on Z by 6.5 cm but slips down 2 cm. If each of the requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar? [2017]
(a) 161 cm
(b) 163 cm
(c) 182 cm
(d) 210 cm
33. Gopal bought a cell phone and sold it to Ram at 10% profit. Then Ram wanted to sell it back to Gopal at 10% loss. What will be Gopal’s position if he agreed? [2017]
(a) Neither loss nor gain
(b) Loss 1%
(c) Gain 1%
(d) Gain 0.5%
34.Suppose the average weight of 9 persons is 50 kg. The average weight of the first 5 persons is 45 kg, whereas the average weight of the last 5 persons is 55 kg, Then the weight of the 5th person will be [2017]
45 kg
47.5 kg
50 kg
52.5 kg
35. A watch loses 2 minutes in every 24 hours. while another watch gains 2 minutes in every 24 hours. At a particular instant, the two watches showed an identical time. Which of the following statements is correct if 24-hour clock is followed? [2017]
(a) The two watches show the identical time again on completion of 30 days.
(b) The two watches show the identical time again on completion of 90 days.
(c) The two watches show the identical time again on completion of 120 days.
(d) None of the above statements is correct.
36. In a city, 12% of households earn less than Rs 30,000 per year, 6% households earn more than Rs 2,00,000 per year, 22% households earn more than Rs1,00,000 per year and 990 house- holds earn between Rs 30,000 and Rs 1,00,000 per year. How many households earn between Rs 1,00,000 and Rs 2,00,000 per year? [2017]
(a) 250
(b) 240
(c) 230
(d) 225
37. A clock strikes once at 1 o’clock, twice at 2 o’clock and thrice at 3 o’clock, and so on. If it takes 12 seconds to strike at 5 o’clock, what is the time taken by it to strike at 10 o’clock? [2017]
(a) 20 seconds
(b) 24 seconds
(c) 28 seconds
(d) 30 seconds
38. There are thirteen 2-digit consecutive odd numbers. If 39 is the mean of the first five such numbers, then what is the mean of all the thirteen numbers? [2017]
(a) 47
(b) 49
(c) 51
(d) 45
39. There is a milk sample with 50% water in it. If 1/3rd of this milk is added to equal amount of pure milk, then water in the new mixture will fall down to [2017]
(a) 25%
(b) 30%
(c) 35%
(d) 40%
40. There are 4 horizontal and 4 vertical lines, parallel and equidistant to one another on a board. What is the maximum number of rectangles and squares that can be formed? [2017]
(a) 16
(b) 24
(c) 36
(d) 42
41. Certain 3-digit numbers have the following characteristics:
1. All the three digits are different.
2. The number is divisible by 7.
3. The number on reversing the digits is also divisible by 7.
How many such 3-digit numbers are there? [2017]
(a) 2
(b) 4
(c) 6
(d) 3
42. How many numbers are there between 99 and 1000 such that the digit 8 occupies the unit’s place? [2017]
(a) 64
(b) 80
(c) 90
(d) 104
43. If for a sample data [2017]
Mean < Median < Mode then the distribution is
(a) symmetric
(b) skewed to the right
(c) neither symmetric nor skewed
(d) skewed to the left
44. The age of Mr. X last year was the square of a number and it would be the cube of a number next year. What is the least number of years he must wait for his age to become the cube of a number again? [2017]
(a) 42
(b) 38
(c) 25
(d) 16
45. P works thrice as fast as Q, whereas P and Q together can work four times as fast as R. If P, Q and R together work on a job, in what ratio should they share the earnings? [2017]
(a) 3 : 1 : 1
(b) 3 : 2 : 4
(c) 4 : 3 : 4
(d) 3 : 1 : 4
46. There are certain 2-digit numbers. The difference between the number and the one obtained on reversing it is always 27. How many such maximum 2-digit numbers are there? [2017]
(a) 3
(b) 4
(c) 5
(d) None of the above
47. A 2-digit number is reversed. The larger of the two numbers is divided by the smaller one. What is the largest possible remainder [2017]
(a) 9
(b) 27
(c) 36
(d) 45
48. The monthly incomes of X and Y are in the ratio of 4 : 3 and their monthly expenses are in the ratio of 3 : 2. However, each saves Rs 6,000 per month. What is their total monthly income? [2017]
(a) Rs 28,000
(b) Rs 42,000
(c) Rs 56,000
(d) Rs 84,000
49. Two walls and a ceiling of a room meet at right angles at a point P. A fly is in the air 1 m from one wall, 8 m from the other wall and 9 m from the point P. How many meters is the fly from the ceiling? [2017]
(a) 4
(b) 6
(c) 12
(d) 15
50. A lift has the capacity of 18 adults or 30 children. How many children can board the lift with 12 adults? [2018]
(a) 6
(b) 10
(c) 12
(d) 15
51. A person bought a refrigerator worth Rs 22,800 with 12.5% interest compounded yearly. At the end of first year he paid Rs 8,650 and at the end of second year Rs 9,125. How much will he have to pay at the end of third year to clear the debt? [2018]
(a) Rs 9,990
(b) Rs 10,000
(c) Rs 10,590
(d) Rs 11 ,250
52. If x – y = 8, then which of the following must be true?
1. Both x and y must be positive for any value of x and y.
2. If x is positive, y must be negative for any value of x and y.
3. If x is negative, y must be positive for any value of x and y.
Select the correct answer using the code given below. [2018]
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d Neither 1 nor 2 nor 3
53. A shopkeeper sells an article at Rs 40 and gets X% profit. However, when he sells it at Rs 20, he faces the same percentage of loss. What is the original cost of the article? [2018]
Rs 10
Rs 20
(c) Rs 30
(d) Rs 40
54. There are 24 equally spaced points lying on the circumference of a circle. What is the maximum number of equilateral triangles that can be drawn by taking sets of three points as the vertices? [2018]
(a) 4
(b) 6
(c) 8
(d) 12
55. A number consists of three digits of which the middle one is zero and their sum is 4. If the number formed by interchanging the first number itself by 198, then the difference between the first and last digits is [2018]
(a) 1
(b) 2
(c) 3
(d) 4
56. A bookseller sold ‘a’ number of Geography textbooks at the rate of Rs x per book, ’a + 2’ number of History textbooks at the rate of Rs (x + 2) per book and ‘a – 2’ number of mathematics textbooks at the rate of Rs (x –2) per book. What is his total sale in Rs? [2018]
(a) 3x + 3a
(b) 3ax + 8
(c) 9ax
(d) x3 a3
57. A student has to get 40% marks to pass in an examination. Suppose he gets 30 marks and fails by 30 marks, then what are the maximum marks in the examination? [2018]
(a) 100
(b) 120
(c) 150
(d) 300
58. 19 boys turn out to play hockey. Of these, 11 are wearing hockey shirts and 14 are wearing hockey pants. There are no boys without shirts and/or pants. What is the number of boys wearing full uniform? [2018]
(a) 3
(b) 5
(c) 6
(d) 8
59. If X is between – 3 and – 1, and y is between – 1 and 1, then X2 – Y2 is in between which of the following? [2018]
(a) – 9 and 1
(b) – 9 and – 1
(c) 0 and 8
(d) 0 and 9
60. X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number? [2018]
(a) XY
(b) X /Y
(c) Y / X
(d) (X + Y) / XY
61. Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is [2019]
(a) 13 units
(b) 15 units
(c) 16 units
(d) 30 units
62. An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible? [2019]
(a) 2
(b) 3
(c) 4
(d) 6
63. A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00 p.m. on Wednesday, what is the correct time? [2019]
(a) 5:36 p.m.
(b) 5:30 p.m.
(c) 5:24 p.m.
(d) 5:18 p.m.
64. In a group of 15 people; 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is [2019]
(a) 10
(b) 9
(c) 5
(d) 4
65. A family has two children along with their parents. The average of the weights of the children and their mother is 50 kg. The average of the weights of the children and their father is 52 kg. If the weight of the father is 60 kg, then what is the weight of the mother? [2019]
(a) 48 kg
(b) 50 kg
(c) 52 kg
(d) 54 kg
66. Number 136 is added to 5B7 and the sum obtained is 7A3, where A and B are integers. It is given that 7A3 is exactly divisible by 3. The only possible value of B is [2019]
(a) 2
(b) 5
(c) 7
(d) 8
67. The number of times the digit 5 will appear while writing the integers from 1 to 1000 is [2019]
(a) 269
(b) 271
(c) 300
(d) 302
68. A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A? [2019]
(a) 60 %
(b) 45.5 %
(c) 40 %
(d) 37.5 %
69. In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football? [2019]
(a) 4
(b) 8
(c) 10
(d) 12
70. Raju has Rs 9000 with him and he wants to buy a mobile handset; but he finds that he has only 75% of the amount required to buy the handset. Therefore, he borrows Rs 2000 from a friend. Then [2019]
(a) Raju still does not have enough amount to buy the handset.
(b) Ruju has exactly the same amount as required to buy the handset.
(c) Ruju has enough amount to buy the handset and he will have Rs 500 with him after buying the handset.
(d) Ruju has enough amount to buy the handset and he will have Rs 1000 with him after buying the handset.
71. In 2002, Meenu’s age was one-third of the age of Meera, whereas in 2010, Meenu’s age was half the age of Meera. What is Meenu’s year of birth? [2019]
(a) 1992
(b) 1994
(c) 1996
(d) 1998
72. Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent Rs1300 and Rajesh spent Rs 1500. If each racket costs three times a ball does, then what is the price of a racket ? [2019]
(a) Rs70
(b) Rs90
(c) Rs 210
(d) Rs 240
73. In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct?
1. At least 30 Indian participants are vegetarian.
2. At least 10 Indian participants are non-vegetarian.
Select the correct answer using the codes given below : [2019]
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
All members of the club went to Mumbai and stayed in a hotel. On the first day, 80% went shopping and 50% went sightseeing, whereas 10% took a rest in the hotel.
Which of the following conclusion(s) can be drawn from the above data?
1. 40% members went shopping as well as sightseeing.
2. 20% of the members went for only shopping.
Select the correct answer using the code given below : [2019]
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
75. The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7.The number of such pairs is [2019]
(a) 5
(b) 4
(c) 3
(d) 2
76. In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored? [2019]
(a) 360
(b) 380
(c) 400
(d) 420
77. If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct? [2019]
(a) x is greater than y
(b) (y – x) is greater than 15
(c) (y – x) is less than or equal to 15
(d) (x + y) is greater than or equal to 65
78. Ena was born 4 years after her parents’ marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena’s father get married? [2019]
(a) 22 years
(b) 23 years
(c) 24 years
(d) 25 years
Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered a very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered? [2019-II]
15%
(b) 20%
(c) 25%
(d) 30%
80. The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are [2019]
(a) 39
(b) 39.7
(c) 40
(d) 40.3
81. Two Statements are given followed by two Conclusions: [2020]
Statements:
All numbers are divisible by 2.
All numbers are divisible by 3.
Conclusion-I: All numbers are divisible by 6.
Conclusion-II: All numbers are divisible by 4.
Which of the above Conclusions logically follows/follow from the two given Statements?
(a) Only Conclusion-I
(b) Only Conclusion-II
(c) Neither Conclusion-I nor Conclusion-II
(d) Both Conclusion-I and Conclusion-II
82. How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4? [2020]
(a) 5
(b) 11
(c) 12
(d) 13
83. The average age of a teacher and three students is 20 years. If all the three students are of the same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher? [2020]
(a) 25 years
(b) 30 years
(c) 35 years
(d) 45 years
84. A person bought a car and sold it for Rs 3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car? [2020]
(a) Rs 3,60,000
(b) Rs 3,65,000
(c) Rs 3,70,000
(d) Rs 3,75,000
85. Two Statements S1 and S2 are given below followed by a Question: [2020]
S1: n is a prime number.
S2: n leaves a remainder of 1 when divided by 4.
Question: If n is a unique natural number between 10 and 20, then what is n?
Which one of the following is correct in respect of the above Statements and the Question?
(a) S1 alone is sufficient to answer the Question.
(b) S2 alone is sufficient to answer the Question.
(c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
(d) S1 and S2 together are not sufficient to answer the Question.
86. Two Statements S1 and S2 are given below with regard to two numbers followed by a Question:[2020]
S1: Their product is 21.
S2: Their sum is 10.
Question:
What are the two numbers?
Which one of the following is correct in respect of the above Statements and the Question?
(a) S1 alone is sufficient to answer the Question.
(b) S2 alone is sufficient to answer the Question.
(c) S1 and S2 together are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.
(d) S1 and S2 together are not sufficient to answer the Question.
87. In the sum @ + 1 @ + 5 @ + @@ + @1 = 1@@ for which digit does the symbol @ stand? [2020]
(a) 2
(b) 3
(c) 4
(d) 5
88. If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length you can measure? [2020]
(a) 0.05 foot
(b) 0.25 foot
(c) 1 foot
(d) 3.25 feet
89. A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, … results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence? [2020]
(a) 34
(b) 36
(c) 38
(d) 40
90. Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D? [2020]
(a) 1
(b) 2
(c) 3
(d) 4
Consider the following data:
What is the value of x in the above table? [2020-II]
(a) 7.8
(b) 7.6
(c) 7.4
(d) 7.2
92. How many zeroes are there at the end of the following product? [2020]
1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60
10.
12
(c) 14
(d) 15
93. Let XYZ be a three-digit number, where (X+ Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by [2020]
(a) 3
(b) 9
(c) 37
(d) (X+ Y + Z)
Let p, q, r and s be natural numbers such that p – 2016 = q + 2017 = r – 2018 = s + 2019
Which one of the following is the largest natural number? [2020]
(a) p
(b) q
(c) r
(d) s
95. How many pairs of natural numbers are there such that the difference of whose squares is 63? [2020]
(a) 3
(b) 4
(c) 5
(d) 2
96. Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3,3/4,4/5 and 5/6? [2020]
(a) 2/3
(b) 3/4
(c) 4/5
(d) 5/6
97. A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4? [2020]
(a) 2n
(b) 3n
(c) 2n + 4
(d) 3n + 1
A frog tries to come out of a dried well 4.5 m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. What is the number of jumps required for the frog to come out of the well? [2020]
(a) 28
(b) 29
(c) 30
(d) 31
99. A bottle contains 20 litres of liquid A., 4 litrs of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture? [2020]
(a) 4 : 1
(b) 5 : 1
(c) 16 : 9
(d) 17 : 8
100. The average score of a batsman after his 50th innings was 46.4. After 60th innings, his average score increases by 2.6. What was his average score in the last ten innings? [2020]
(a) 122
(b) 91
(c) 62
(d) 49
101. As a result of a 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for Rs1,200. What was the original price of rice per kg. [2020]
(a) Rs 30
(b) Rs 40
(c) Rs 50
(d) Rs 60
102. What is the greatest length x such that 312 m and 834 m are integral multiples of x ? [2020]
(a) 112 m
(b) 113 m
(c) 134 m
(d) 314 m
103. The recurring decimal representation 1.272727 … is equivalent to [2020]
(a) 13/11
(b) 14/11
(c) 127/99
(d) 137/99
104. What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case? [2020]
(a) 1012
(b) 1022
(c) 1122
(d) 1222
105. In the adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers? [2020]
(a) 3317 %
(b) 34%
(c) 3427 %
(d) 35%
106. What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100? [2020]
(a) 50
(b) 25
(c) 5
(d) 1
107. A sum of Rs 2,500 is distributed among X, Y and Z in the ratio 1/2:3/4:5/6. What is the difference between the maximum share and the minimum share? [2020]
(a) Rs 300
(b) Rs 350
(c) Rs 400
(d) Rs 450
108. For what value of n, the sum of digits in the number (10n + 1) is 2? [2020]
(a) For n = 0 only
(b) For any whole number n
(c) For any positive integer n only
(d) For any real number n
109. In a class, there are three groups, A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight for the students of the class? [2020]
(a) It increases.
(b) It decreases.
(c) It remains the same.
(d) No conclusion can be drawn due to insufficient data.
110. A shop owner offers the following discount options on an article to a customer: [2020]
1. Successive discounts of 10% and 20%, and then pay a service tax of 10%.
2. Successive discounts of 20% and 10%, and then pay a service tax of 10%.
3. Pay a service tax of 10% first, then successive discounts of 20% and 10%.
Which one of the following is correct?
(a) 1 only is the best option for the customer.
(b) 2 only is the best option for the customer.
(c) 3 only is the best option for the customer.
(d) All the options are equally good for the customer.
111. What is the largest number among the following? [2020]
(a) (1/2)-6
(b) (1/4)-3
(c) (1/3)-4
(d) (1/6)-2
112. There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22.Four students are shifted from Class-A to Class-B. [2021]
Consider the following statements :
The average score of Class-B will definitely decrease.
The average score of Class-A will definitely increase.
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
113. A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5:6:7:8:9: 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks ?[2021]
(a) 2
(b) 3
(c) 4
(d) 5
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10? [2021]
(a) 6
(b) 7
(c) 8
(d) 9
115. If 32019 is divided by 10, then what is the remainder? [2021]
1
3
7
9
116. The number 3798125P369 is divisible by 7.What is the value of the digit P? [2021]
(a) 1
(b) 6
(c) 7
(d) 9
117. A biology class at high school predictor that a local population of animals will double in size every 12 years. The population at the beginning of the year 2021 was estimated to be 50 animals.If P represents the population after n years, then which one of the following equations represents the model of the class for population?[2021]
(a) P=12+50n
(b) P=50+12n
(c) P=50x(2)12n
(d) P=50X (2) n/12
The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54
Consider the following statements : [2021]
1.The sum of the two digits of the number can be determined only if the product of the two digits is known.
2. The difference between the two digits of the number can be determined.
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
119. X said Y, “At the time of your birth I was twice as old as you are at present.” If the present age of X is 42 years, then consider the following statements:[2021]
8 years ago, the age of X was five times the age of Y.
After 14 years, the age of X would be two times the age of Y.
Which of the above statements is/are correct ?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
120. If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price?[2021]
(a) 0%
(b) 5% increase
(c) 5% decrease
(d) Insufficient data
121. When a certain number is multiplied by 7, the product entirely comprises ones only (1111…).What is the smallest such number ? [2021]
(a) 15713
(b) 15723
(с) 15783
(d)15873
122. A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is fürther increased by 50%?.[2021]
24
b. 21
c. 18
d. 15
There are three Points P, Q and R on a straight line such that PQ: QR= 3:5. If n is the number of possible values of PQ: PR, then what is n equal to ? [2021]
1
2
3
4
124. Consider the following statements: [2021]
The sum of 5 consecutive integers can be 100.
The product of three consecutive natural numbers can be equal to their sum.
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
125. An amount of money was distributed among A, B and C in the ratio p: q: r.
Consider the following statements : [2021]
A gets the maximum share if p is greater than (q + r).
C gets the minimum share if r is less than (p + q).
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
126. Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store, If Jay bought 3 pens and 5 pencils, and Vijay bought 2 pens and 7 pencils, then which one of the following is correct? [2021]
(a)A pencil costs more than a pen
(b)The price of a pencil is equal to that of a pen
(c)The price of a pen is two times the price of a pencil
(d)The price of a pen is three times the Price of a pencil
127. P scored 40 marks more than Q in an examination. If Q scored10% less marks than P, then how much did Q score ? [2021]
a. 360
b. 380
c. 400
d. 420
128. A person P asks one of his three friends X as to how much money he had. X replied, “If Y gives me Rs 40, then Y will have half of as much as Z, but if Z gives me Rs 40, then three of us will have equal amount.” What is the total amount of money that X, Y and Z have ? [2021]
（a）Rs 420
（b）Rs 360
(c) Rs 300
（d）Rs 270
129. In an objective type test of 90 questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attempting all the 90 questions, a student got a total of 387 marks. what is the number to incorrect responses ? [2021]
(a) 9
(b) 13
(c) 27
(d) 43
130. Consider the following addition problem:[2021]
3P+ 4P + PP + PP= RQ2; where P, Q and R are different digits.
What is the arithmetic mean of all such possible sums ?
(a) 102
(b) 120
(c) 202
(d) 220
131. Consider the following multiplication problem:[2021]
(PQ) × 3 = RQQ, where P, Q and R are different digits and R is not equal to 0.What is the value of (P + R) / Q?
(a) 1
(b) 2
(c) 5
(d) insufficient data
132. An Identity Card has the number ABCDEFG, not necessarily in that order, where each letter represents a distinct digit (1, 2, 4, 5, 7, 8, 9 only). The number is divisible by 9. After deleting the first digit from the right the resulting number is divisible by 6. After deleting two digits from the right of the original number, the resulting number is divisible by 5. After deleting three digits from the right of the original number, the resulting number is divisible by 4. After deleting four digits from the right of the original number, the resulting number is divisible by 3. After deleting five digits from the right of the original number. the resulting number is divisible by 2. Which of the following is a possible value for the sum of the middle three digits of the number? [2022]
(a) 8
(b) 9
(c) 11
(d) 12
133. A bill for Rs 1,840 is paid in the denominations of Rs 50, Rs 20 and Rs 10 notes. 50 notes in all are used. Consider the following statements:[2022]
25 notes of Rs 50 are used and the remaining are in the’ denominations of Rs 20 and Rs10.
35 notes of 720 are used and the remaining are in the denominations of Rs 50 and Rs 10.
20 notes of 710 are used and the remaining are in the
denominations of Rs 50 and Rs 20.
Which of the above statements are not correct?
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
134. Which number amongst 240, 321, 418 and 812 is the smallest?[2022]
(a) 240
(b) 321
(c) 418
(d) 812
135. Consider the question and two statements given below:
Question: Is x an integer?[2022]
Statement-1: x/3 is not an integer.
Statement-2: 3x is an integer.
Which one of the following is correct in respect of the question and then statements?
Statement-l alone is sufficient to answer the Question
Statement-2 alone is sufficient to answer the Question
Both Statement-l and Statement-2 are sufficient to answer the Question
Both Statement-l and Statement-2 are not sufficient to answer the Question
136. The increase in the price of a certain item was 25%, Then the price was decreased by 20% and then again increased by 10%, What is the resultant increase in the price?[2022]
5%
10%
12.5%
15%
137. On one side of a 1.01 km long road, 101 plants are planted at equal distance from each other. What is the total distance between 5 consecutive plants?[2022]
(a) 40 m
(b) 40.4 m
(c) 50 m
(d) 50.5 m
138. A has some coins. He gives half of the coins and 2 more to B.B gives half of the coins and 2 more to C. C gives half of the coins and 2 more ta D. The number of coins D has now’, is the smallest two digit number. How many coins does A have in the beginning? [2022]
(a) 76
(b) 68
(c) 60
(d) 52
139. How many seconds in total are there in x weeks, x days, x hours, x minutes and seconds?[2022]
(a) 11580x
(b) 11581x
(c) 694860x
(d) 694861x
140. Five friends P, Q, X, Y and Z purchased some notebooks. The relevant information is given below : [2022]
Z purchased 8 notebooks more than X did.
P and Q together purchased 21 notebooks.
Q purchased 5 notebooks less than P did.
X and Y together purchased 28 notebooks.
P purchased 5 notebooks more than X did.
If each notebook is priced Rs 40, then what is the total cost of all the notebooks?
（a）Rs 2,600
（c）Rs 2,360
（b）Rs 2,400
（d) Rs 2,320
141. A person X wants to distribute some pens among six children A, B, C, D, E, and F. Suppose A gets twice the number of pens received by B, three times that of C, four times that of D, five times that of E and six times that of F. What is the minimum number of pens X should buy so that the number of pens each one gets is an even number? [2022]
(a) 147
(b) 150
(c) 294
(d) 300
142. Consider the Question and two Statements given below Question: What is the age of Manisha? [2022]
Statement-1 : Manisha is 24 years younger than her mother
Statement-2: 5 years later, the ages of Manisha and her mother will be in the ratio 3: 5.
Which one of the following is correct in respect of the question and then statements?
(a) Statement-1 alone is sufficient to answer the question.
(b) Statement-2 alone is sufficient to answer the question.
(c) Both statement-1 and statement-2 are sufficient to answer the question.
(c) Both statement-l and statement-2 are not sufficient to answer the question.
143. Let A. B and C represent distinct non zero digits. Suppose x is the sum of all possible 3-digit numbers formed by A, B and C without repetition.
Consider the following statements:
The 4-digit least value of x is 1332.
The 3-digit greatest value of x is 888.
Which of the above statements is/are correct? [2022]
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
144. What is the remainder when 91 x 92 x 93 x 94 x 95 x 96 x 97 x 98 x 99 is divided by 1261? [2022]
(a) 3
(b) 2
(c) 1
(d) 0
145. When 70% of a number x is added to another number y, the sum becomes 165% of the value of y. When 60% of the number x is added to another number Z, then the sum becomes 165% of the value of z. Which one of the following is correct? [2022]
(a) z < x < y
(b) x < y < z
(c) y < x < z
(d) z< y <x
146. Two candidates X and Y contested an election. 80% of voters cast their vote and there were no invalid votes. There was no NOTA (None of the above) option. X got 56% of the votes cast and won by 1440 votes. What is the total number of voters in the voters list? [2022]
(a) 15000
(b) 12000
(c) 9600
(d) 5000
147. What is the smallest number greater than 1000 that when divided by anyone of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3? [2022]
(a) 1063
(b) 1073
(c) 1083
(d) 1183
148. Let p be a two-digit number and q be the number consisting of the same digits written in reverse order. If p * q = 2430, then what is the difference between p and q? [2022]
(a) 45
(b) 27
(c) 18
(d) 9
149. Consider the following statements in respect of two natural numbers p and q such that p is a prime number and q is a composite number:[2022]
1. p x q can be an odd number.
2. q/ p can be a prime number.
3. p + q can be a prime number.
Which of the above statements are correct?
1 and 2 only
2 and 3 only
1 and 3 only
1,2 and 3
There are two contents X and Y. X contains 100 ml of milk and y contains 100 ml of water. 20 ml of milk from X is transferred to Y. After mixing well, 20 ml of the mixture in Y is transferred back to X. If m denotes the proportion of milk in X and n denotes the proportion of water in Y, then which oneof the following is correct?[2022]
(a) m =n
(b) m > n
(c)m < n
(d) Cannot be determined due to insufficient data
151. The sum of three consecutive integers is equal to their product.How many such possibilities are there?[2022]
Only one
Only two
(c) Only three
(d) No such possibility is there
152. What is the number of numbers of the form 0.XY, where X and Y are distinct non-zero digits? [2022]
(a) 72
(b) 81
(c) 90
(d) 100
153. The average weight of A, B, C is 40 Kg, the average weight of B, D, E is 42 kg and the weight of F is equal to that of B.What is the average weight of A, B, C, D, E and F?[2022]
40.5 kg
40•8 kg
41 kg
Cannot be determined as data inadequate
154. If 15 × 14 x 13 x …. x 3 x 2 x 1 = 3m x n where m and n are positive integers, then what is the maximum value of m?[2022]
(a) 7
(b) 6
(c) 5
(d) 4
155. What is the remainder when 85 × 87 x89 x91 x95 x96 is divided by 100?[2023]
(a) 0
(b) 1.
(c) 2
(d) 4
156. What is the unit digit in the expansion of (57242)9*7*5*3*1?[2023]
(a) 2
(b) 4
(c) 6
(d) 8
157. If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits such that ABC + DEP = 1111, then what is the value of A + B + C+D +E+F?[2023]
(a) 28
(b) 29
(c) 30
(d) 31
158. D is a 3-digit number such that the ratio of the number to the sum of its digits is least. What is the difference between the digit at the hundred’s place and the digit at the unit’s place of[2023]
(a) 0
(b) 5
(c) 6
(d) 8
159. Three of the five positive integers p,q,r,s, t are even and two of them are odd (not necessarily in order) Consider the following:[2023]
p+ q+r-s – t is definitely even.
2p + q + 2r – 2s + t is definitely odd.
Which of the above statements is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
160. A 3-digit number ABC, on multiplication with D gives 37DD.where A, B, C and D are different non-zero digits. What is the value of A + B + C? [2023]
(a) 18
(b) 16
(c) 15
(d) Cannot be determined due to insufficient data
161. For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by :[2023]
(a) 7 and 11 only
(c) 7 and 13 only
(b) 11 and 13 only
(d) 7, 11 and 13
162. Let x be a positive integer such that 7x + 96 is divisible by x.How many values of x are possible?[2023]
(a) 10
(c) 12
(b) 11
(d) Infinitely many
163. If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p + q)(r+ s) ?[2023]
(a) 230
(b) 225
(c) 224
(d) 221
164. A number N is formed by writing 9 for 99 times, What is the remainder if N is divided by 13?[2023]
(a) 11
(b) 9
(c) 7
(d) 1
165. Each digit of a 9-digit number is 1. It is multiplied by itself.What is the sum of the digits of the resulting number?[2023]
(a) 64
(b) 80
(c) 81
(d) 100
166. What is the sum of all digits which appear in all the integers from 10 to 100? [2023]
(a) 855
(b) 856
(c) 910
(d) 911
167. A principal P becomes Q in 1 year when compounded half-yearly with R% annual rate of interest. If the same principal P becomes Q in 1 year when compounded annually with S% annual rate of interest, then which one of the following is correct? [2023]
(a) R = S
(b) R > S
(c) R < S
(d) R ≤ S
168. How many natural numbers are there which give a remainder of 31 when 1186 is divided by these natural numbers? [2023]
(a) 6
(b) 7
(c) 8
(d) 9
169. Let pp, qq and rr be 2-digit numbers where p < q<r. If pp+qq + rr = tt0, where til is a 3-digit number ending with zero,consider the following statements :[2023]
The number of possible values of p is 5.
The number of possible values of q is 6.
Which of the above statements is/are correct ?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
170. There are three traffic signals. Each signal changes colour from green to red and then from red to green. The first signal takes 25 seconds, the secónd signal takes 39 seconds and the third signal takes 60 seconds to change the colour from green to red. The durations for green and red colours are same. At 2:00 p.m, they together turn green. At what time will they change to green next, simultaneously?[2023]
(a) 4:00 p.m.
(b) 4:10 p.m.
(c) 4:20 p.m.
(d) 4:30 p.m.
171. Question: Is p greater than q?[2023]
Statement-1: p x q is greater than zero.
Statement-2: p2 is greater than q2?.
Which one of the following is correct in respect of the above Question and the Statements ?
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
The Question can be answered by using either Statement alone.
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
The Question cannot be answered even by using both the Statements together.
172 . Question: Is (p + q – r) greater than (p – q + r), where p, q and r are integers ? [2023]
Statement-1: (p-q) is positive.
Statement-2: (p-r) is negative.
Which one of the following is correct in respect of the above Question and the Statements ?
The Question can be answered by using one of the Statements alone. but cannot be answered using the other Statement alone.
The Question can be answered by using either Statement alone.
The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
The Question cannot be answered even by using both the Statements together.
173. Consider a 3-digit number.[2023]
Question: What is the number?
Statement – 1: The sum of the digits of the numbers equal to the product of the digits.
Statement – 2: The number is divisible by the sum of the digits of the number.
Which one of the following is correct in respect of the above Question and the Statements?
The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
(b) The Question can be answered by using either Statement alone.
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement Alone.
d) The Question cannot be answered even by using both the Statements together.
174. In a party, 75 people took tea, 60 people took coffee and 15 people took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.
[2023] Question: How many people attended the party?
Statement-1: 50 persons took milk.
Statement -2: Number of persons who attended the party is five times the number of persons who took milk only.
Which one of the following is correct in respect of the above Question and the Statements ?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
(b) The Question can be answered by using either Statement alone.
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
(d) The Question cannot be answered even by using both the Statements together.
175. For five children with ages a < b <c <d <e; any two successive ages differ by 2 years.[2023]
Question: What is the age of the youngest child?
Statement-1: The age of the eldest in 3 times the youngest.
Statement-2: The average age of the children is 8 years.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone.
(b) The Questions can be answered by using either Statement alone.
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
(d) The Question cannot be answered even by using both the Statements together.
176. What is the remainder if 2192 is divided by 6? [2023]
(a) 0
(b) 10
(c) 2
(d) 4
AB and CD are 2-digit numbers, Multiplying AB with CD results in a 3-digit number DEF. Adding DEF to another 3-digit number GHI results in 975. Further A, B, C, D, E, F, G, H, l are distinct digits. If E = 0, F = 8, then what is A + B + C equal [2023]
(a) 6
(b) 7
(c) 8
(d) 9
178. Consider the following in respect of prime number p and composite number c.
can be even [2023]
(p+c)/(p-c) can be even
2p + c can be odd
p x c can be odd.
Which of the statements given above are correct?
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
179. In the expression 5 * 4* 3* 2* 1, * is chosen from +, -, × each at most two times. What is the smallest non-negative value of the expression? [2024]
(a) 3
(b) 2
(c) 1
(d) 0
180. How many consecutive zeros are there at the end of the integer obtained in the product 1^2 × 2^4 × 3^6 × 4^8 ×…. × 25^50? [2024]
(a) 50
(b) 55
(c) 100
(d) 200
181. On January 1st, 2023, a person saved Rs 1. On January 2nd, 2023, he saved Rs. 2 more than that on the previous day. On January 3rd, 2023, he saved Rs. 2 more than that on the previous day and so on. At the end of which date was his total savings a perfect square as well a perfect cube? [2024]
(a) 7th January, 2023
(b) 8th January, 2023
(c) 9th January, 2023
(d) Not possible
182. 222333 + 333222 is divisible by which of the following numbers ? [2024]
(a) 2 and 3 but not 37
(b) 3 and 37 but not 2
(c) 2 and 37 but not 3
(d) 2, 3 and 37
183. What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey ?[2024]
(a) 20%
(b) 10%
(c) 5%
(d) 4%
184. 421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1 ? [2024]
(a) 1
(b) 2
(c) 3
(d) 4
185. A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible? [2024]
(a) 3
(b) 4
(c) 5
(d) 6
186. Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers each less than 10.
1. The unit digit of S can be 0.
2. The unit digit of S can be 9.
3. The unit digit of S can be 5.
Which of the statements given above are correct? [2024]
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
187. Two persons P and Q enter into a business. P puts ₹ 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P’s share is ₹ 400 more than Q’s share out of the total profit of ₹ 2,000, what is the capital contributed by P? [2024]
(a) ₹ 30,000
(b) ₹ 26,000
(c) ₹ 24,000
(d) ₹ 20,000
188. P’s salary is 20% lower than Q’s salary which is 20% lower than R’s salary. By how much percent is R’s salary more than P’s salary? [2024]
(a) 48.75%
(b) 56.25%
(c) 60.50%
(d) 62.25%
189. A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?[2024]
(a) 25%
(b) 50%
(c) 72.75%
(d) 93.75%
190. In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject? [2024]
(a) 15%
(b) 20%
(c) 25%
(d) 35%
191. A father said to his son, “n years back I was as old as you are now. My present age is four times your age n years back”. If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages? [2024]
(a) 30 years
(b) 32 years
(c) 34 years
(d) 36 years
192. Consider the following : [2024]
1. 1000 litres = 1m3
2. 1 metric ton = 1000 kg
3. 1 hectare = 10000 m2
Which of the above are correct?
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
193. Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X + Y) is the greatest two-digit number, then what is the number of possible values of X?[2024]
(a) 2
(b) 4
(c) 6
(d) 8
194. Consider the following : Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women. If the average weight of the women is 63 kg, then what is the average weight of the boys? [2024]
(a) 40 kg
(b) 42 kg
(c) 45 kg
(d) 63 kg
195. Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements : [2024]
1. (p-r)^2 x(qs) is even.
2. (q-s)xq^2 s is even.
3. (q + r)^2 x (p + s) is odd.
Which of the statements given above are correct?
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
196. What is the number of fives used in numbering a 260-page book? [2024]
(a) 55
(b) 56
(c) 57
(d) 60
197. What is the sum of the first 28 terms in the following sequence? [2024]
1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2,……
(a) 83
(b) 84
(c) 85
(d) 86
198. A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P? [2024]
(a) ₹ 1,000
(b) ₹ 1,200
(c) ₹ 1,250
(d) ₹ 1,350
199. If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A? [2024]
(a) 9
(b) 8
(c) 7
(d) Cannot be determined due to insufficient data
200. Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible? [2024]
(a) One triplet
(b) Two triplets
(c) Three triplets
(d) Four triplets
201. The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples. Consider the following statements : [2024]
1. The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples.
2. The total cost of one orange and one mango is equal to the cost of one apple.
Which of the statements given above is/are correct?
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
202. 32^5 + 2^27 is divisible by [2024]
(a) 3
(b) 7
(c) 10
(d) 11
203. Let p and q be positive integers satisfying p<q and p+q=k. What is the smallest value of k that does not determine p and q uniquely?[2024]
(a) 3
(b) 4
(c) 5
(d) 6
204. A Question is given followed by two Statements I and II. Consider the Questions and the Statements. [2024]
Question : What are the values of m and n, where m and n are natural numbers?
Statement-I : m + n > mn and m > n.
Statement-II : The product of m and n is 24.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
205. A question is given followed by two Statements I and II. Consider the Question and then Statements. [2024]
Question : What are the unique values of x and y, where x, y are distinct natural numbers? Statement-I : x/y is odd.
Statement-II : xy = 12
Which one of the following is correct in respect of the above Question and the Statements?
(a) The question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
206. A Question is given followed by two Statements I and II. Consider the Question and then Statements. A certain amount was distributed among X, Y and Z. [2024]
Question : Who received the least amount?
Statement-I : X received 4/5 of what Y and Z together received.
Statement-II: Y received 2/7 of what X and Z together received.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
207. A Question is given followed by two Statements I and II. Consider the Question and the Statements. [2024]
Question : If the average marks in a class are 60, them what is the number of students in the class?
Statement-I : The highest marks in the class are 70 and the lowest marks are 50.
Statement-II : Exclusion of highest and lowest marks from the class does not change the average.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
208. A Question is given followed by two Statements I and II. Consider the Question and the Statements. [2024]
There are three distinct prime numbers whose sum is a prime number.
Question : What are those three numbers?
Statement-I : Their sum is less than 23.
Statement-II : One of the numbers is 5.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
209. A Question if given followed by two Statements I and II. Consider the Question and the Statements. [2024]
Question : Is (x+y) an integer?
Statement-I : (2x+y) is an integer.
Statement-II : (x+2y) is an integer.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
210. A Question is given followed by two Statements I and II. Consider the Question and the Statements. A person buys three articles p, q and r for ₹50. The price of the article q is ₹16 which is the least. [2024]
Question : What is the price of the article p?
Statement-I : The cost of p is not more than that of r.
Statement-II : The cost of r is not more than that of p.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
211. A Question is given followed by two Statements I and II. Consider the Question and the Statements. P, Q, R and S appeared in a test. [2024]
Question : Has P scored more marks than Q ?
Statement-I : The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S.
Statement-II : The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.
Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
212. Question is given followed by two Statements I and II. Consider the Question and the Statements. [2024]
Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.
Question : What is the difference of their ages?
Statement-I : The age of P is greater than the age of Q.
Statement-II : The sum of their ages is 11/6 times their difference. Which one of the following is correct in respect of the above Question and the Statements?
(a) The Question can be answered by using one of the Statements alone, but cannot be answered using the other Statement alone
(b) The Question can be answered by using either Statement alone
(c) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone
(d) The Question cannot be answered even by using both the Statements together
Answer Key:
Updated syllabus not given by CBSE for 2026-27