TOPIC:- NUMBER SYSTEM

GENERAL QUESTIONS

Q1. 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 [CSAT 2016]

(a) 48 minutes

(b) 50 minutes

(d) 53 minutes

Q2. A person is standing on the first step from the bottom of a ladder. If he has to climbs 4 more steps to reach exactly the middle step, how many steps does the ladder have? [CSAT 2016]

(a) 8

(b) 9

(d) 11

Q3. There are some nectar-filled flowers on a tree and some bees are hovering on it. If one bee lands on each flower, one bee will be left out. If two bees land on each flower, one flower will be left out. The number of flowers and bees respectively are [CSAT 2016]

(a) 2 and 4

(b) 3 and 2

(d) 4 and 3

Q4. How many numbers are there between 100 and 300 which either begin with or end with 2? [CSAT 2016]

(a) 110

(b) 111

(d) None of the above

Q5. How many numbers are there between 99 and 1000 such that the digit 8 occupies the units place? [CSAT 2017]

(a) 64

(b) 80

(d) 104

Q6. Six boys A, B, C, D, E and F play a game of cards. Each has a pack of 10 cards. F borrows 2 cards from A and gives away 5 to C who in turn gives 3 to B while B gives 6 to D who passes on 1 to E. Then the number of cards possessed by D and E is equal to the number of cards possessed by [CSAT 2017]

(a) A, B and C

(b) B, C and F

(d) A, C and F

Q7. 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 6 cm 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 them requires 40 chances to reach the top of the pillars, what is the height of the shortest pillar? [CSAT 2017]

(a) 161 cm

(b) 163 cm

(d) 210 cm

Q8. X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number? [CSAT 2018]

(a) XY

(b) X/Y

(d) (X + Y)/XY

Q9. The number of times the digit 5 will appear while writing the integers from 1 to 1000 is [CSAT 2019]

(a) 269

(b) 300

(d) 302

Q10. 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? [CSAT 2019]

(a) x is greater than y

(b) (y-x) is greater than 15

(d) (x + y) is greater than or equal to 65

Q11. If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is [CSAT 2019]

(a) Always less than the original fraction

(b) Always greater than the original fraction

(d) Such that nothing can be claimed definitely

Q12. 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? [CSAT 2020]

(a) p

(b) q

(d) s

Q13. How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?[CSAT 2020]

(a) 5

(b) 11

(d) 13

Q14. 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? [CSAT 2020]

(a) 28

(b) 29

(d) 31

Q15. The recurring decimal representation 1.272727... is equivalent to [CSAT 2020]

(a)

(b)

(c)

(d)

Q16. For what value of n, the sum of digits in the number (10n+1) is 2? [CSAT 2020]

(a) For n=0 only

(b) For any whole number n

(d) For any real number n

Q17. How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?

(a) Zero

(b) One

(d) Ten

Q18. 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 , , and [CSAT 2020]

(a)

(b)

(c)

(d)

Q19. Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10?[CSAT 2021]

(a) 6

(b) 7

(d) 9

Q20. Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct?

[CSAT 2021]

(a) All the villagers who have their own houses are literate.

(b) Some villagers under 25 years of age are literate.

(d) No villager under 25 years of age has his own house.

Q21. 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 of incorrect responses? [CSAT 2021]

(a) 9

(b) 13

(d) 43

Q22. A person P asks one of his three friends X as to how much money he had. X replied, "If Y gives me ₹40, then Y will have half of as much as Z, but if Z gives me ₹40, then three of us will have equal amount." What is the total amount of money that X, Y and Z have? [CSAT 2021]

(a) ₹420

(b) ₹ 360

(d) ₹270

Q23. 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?[CSAT 2021]

(a) A pencil costs more than a pen

(b) The price of a pencil is equal to that of a pen

(d) The price of a pen is three times the price of a pencil

Q24. A biology class at high school predicted 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 the population? [CSAT 2021]

(a) P = 12 + 50n

(b) P = 50+ 12n

(d) P = 50 (2)^n/12

Q 25. 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? [CSAT 2022]

(a) 40 m

(b) 40.4 m

(d) 50.5 m

Q26. The sum of three consecutive integers is equal to their product. How many such possibilities are there? [CSAT 2022]

(a) Only one

(b) Only two

(d) No such possibility is there

Q27. 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 original number, the resulting number is divisible by 5. After deleting three digits from the right of original number, the resulting number is divisible by 4. After deleting four digits from the right of original number, the resulting number is divisible by 3. After deleting five digits from the right of 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? [CSAT 2022]

(a) 8

(b) 9

(d) 12

Q28. A person X wants to distribute some pens among 6 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?[CSAT 2022]

(a) 147

(b) 150

(d) 300

Q29. 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 D? [CSAT 2023]

(a) 0

(b) 7

(d) 9

Q30. If p, q, r and s are distinct single digit positive numbers, then what is the greatest value of (p+q) (r + s)? [CSAT 2023]

(a) 230

(b) 225

(d) 221

Q31. What is the sum of all 4-digit numbers less than 2000 formed by the digits 1, 2, 3 and 4, where none of the digits is repeated?[CSAT 2023]

(a) 7998

(b) 8028

(d) 9238

Questions based on rule of counting principles ∑N, ∑N², ∑N³

Q32. What is the total number of digits printed, if a book containing 150 pages is to be numbered from 1 to 150? [CSAT 2017]

(a) 262

(b) 342

(d) 450

Q33. While writing all the numbers from 700 to 1000, how many numbers occur in which the digit at hundred's place is greater than the digit at ten's place, and the digit at ten's place is greater than the digit at unit's place? [CSAT 2018]

(a) 61

(b) 64

(d) 91

Q34. A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have? [CSAT 2019]

(a) 1040

(b) 1048

(d) 1050

Q35. One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195. The torn page contains which of the following numbers? [CSAT 2020]

(a) 5, 6

(b) 7, 8

(d) 11, 12

Q36. In the series AABABCABCDABCDE..., which letter appears at the 100th place? [CSAT 2022]

(a) G

(b) H

(d) J

Q37. What is the sum of all digits which appear in all the integers from 10 to 100? [CSAT 2023]

(a) 855

(b) 856

(d) 911

Q38. 40 children are standing in a circle and one of them (say child-1) has a ring. The ring is passed clockwise. Child-1 passes on to child-2, child-2 passes on to child-4, child-4 passes on to child- 7 and so on. After how many such changes (including child-1) will the ring be in the hands of child-1 again? [CSAT 2023]

(a) 14

(b) 15

(d) 17

Q39. What is the middle term of the sequence Z, Z, Y, Y, Y, X, X, X, X, W, W, W, W, W, ..., A? [CSAT 2023]

(a) H

(b) I

(d) M

Questions based on 2 digits and 3 digits numbers

Q40. Certain 3-digit numbers have the following characteristics: [CSAT 2017]

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? [CSAT 2017]

(a) 2

(b) 4

(d) 8

Q41. A 2-digit number is reversed. The larger of the two numbers is divided by the smaller one. What is the largest possible remainder? [CSAT 2017]

(a) 9

(b) 27

(d) 45

Q42. 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 [CSAT 2017]

(a) 3

(b) 4

(d) None of these

Q43. 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 and last digits is greater than the number itself by 198, the difference between the first and last digits is [CSAT 2018]

(a) 1

(b) 2

(d) 4

Q44. The ratio of a 2-digit natural number to a number formed by reversing its digits is 4: 7. The number of such pairs is [CSAT 2019]

(a) 5

(b) 4

(d) 2

Q45. Let p be a 2-digit number and q be the number consisting of same digits written in reverse order. If px q = 2430, then what is the difference between p and q? [CSAT 2022]

(a) 45

(b) 27

(d) 9

Unit Digit of X^y (Rule of Cyclicity)

Q46. If 3²⁰¹⁹ is divided by 10, then what is the remainder? [CSAT 2021]

(a) 1

(b) 3

(d) 9

Q47. What is the unit digit in the expansion of (57242)^{9×7×5×3×1}? [CSAT 2023]

(a) 2

(b) 4

(d) 8

Exponents and Number of Zero

Q48. How many zeroes are there at the end of the following product? 1 X 5 X 10 X 15 X 20 X 25 X 30 X 35 X 40 X 45 X 50 X 55 X 60 [CSAT 2020]

(a) 10

(b) 12

(d) 15

Q49. If 15 X 14 X 13 X … X 3 X 2 X 1 = 3^M X n , where m and n are positive integers, then what is the maximum value of m? [CSAT 2022]

(a) 7

(b) 6

(d) 4

Divisibility

Q50. If ABC × DEED = ABCABC; where A, B, C, D and E are different digits, what are the values of D and E? [CSAT 2015]

(a) D=2 , E=0

(b) D=0 E=1

(d) D = 1, E=2

Q51. If R and S are different integers both divisible by 5, then which of the following is not necessarily true? [CSAT 2016]

(a) R-S is divisible by 5

(b) R+S is divisible by 10

(d) R2 x S² is divisible by 5

Q52. An 8-digit number 4252746B leaves remainder 'O' when divided by 3. How many values of B are possible? [CSAT 2019]

(a) 2

(b) 3

(d) 6

Q53. Two Statements are given followed by two Conclusions: [CSAT 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

(d) Both Conclusion-I and Conclusion-II

Q54. A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4? [CSAT 2020]

(a) 2n

(b) 3n

(d) 3n+1

Q55. Let XYZ be a 3-digit number, where (X+Y+ Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by [CSAT 2020]

(a) 3

(b) 9

(d) (X + Y + Z)

Q56. When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such number?

[CSAT 2021]

(a) 15713

(b) 15723

(d) 15873

Q57. The number 3798125P369 is divisible by 7. What is the value of the digit P? [CSAT 2021]

(a) 1

(b) 6

(d) 9

Q58. For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by [CSAT 2023]

(a) 7 and 11 only

(b) 11 and 13 only

(d) 7, 11 and 13

Q59. A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13? [CSAT 2023]

(a) 11

(b) 9

(d) 1

Q60. 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? [CSAT 2023]

(a) 64

(b) 80

(d) 100

Remainder Theorem

Q61. What is the remainder when 51 x 27 x 35 x 62 x 75 is divided by 100? [CSAT 2020]

(a) 50

(b) 25

(d) 1

Q62. If 3²⁰¹⁹ is divided by 10, then what is the remainder? [CSAT 2021]

(a) 1

(b) 3

(d) 9

Q63. What is the remainder when 91 x 92 x 94 x 95 x 96 x 97 x 98 x 99 is divided by 1261? [CSAT 2022]

(a) 3

(b) 2

(d) 0

Q64. What is the remainder when 85 x 87 x 89 x 91 x 95 x 96 is divided by 100? [CSAT 2023]

(a) 0

(b) 1

(d) 4

Q65. If today is Sunday, then which day is it exactly on 10¹⁰ th day? [CSAT 2023]

(a) Wednesday

(b) Thursday

(d) Saturday

Q66. What is the remainder if 2¹⁹²is divided by 6? [CSAT 2023]

(a) 0

(b) 1

(d) 4

HCF and LCM

Q67. Three persons start walking together and their steps measure 40 cm, 42 cm and 45 cm respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps? [CSAT 2011]

(a) 25 m 20 cm

(b) 50 m 40 cm

(d) 100 m 80 cm

Q68. There are five hobby clubs in a college viz, photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days? [CSAT 2013]

(a) 3

(b) 5

(d) 18

Q69. 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? [CSAT 2014]

(a) 12:40 hrs

(b) 12:48 hrs

(d) 13:04 hrs

Q70. 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 [CSAT 2014]

(a) 6

(b) 7

(d) 9

Q71. There are five hobby clubs in a college photography, yachting, chess, electronics and gardening. The gardening group meets every second day, the electronics group meets every third day, the chess group meets every fourth day, the yachting group meets every fifth day and the photography group meets every sixth day. How many times do all the five groups meet on the same day within 180 days? [CSAT 2016]

(a) 5

(b) 18

(d) 3

Q72. A lift has the capacity of 18 adults or 30 children. How many children can board the lift with 12 adults? [CSAT 2018]

(a) 6

(b) 10

(d) 15

Q73. 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? [CSAT 2019]

(a) 4

(b) 8

(d) 12

Q74. Seeta and Geeta go for a swim after a gap of every 2 days and every 3 days respectively. If on 1st January both of them went for a swim together, when will they go together next? [CSAT 2019]

(a) 7th January

(b) 8th January

(d) 13th January

Q75. If you have two straight sticks of length 7.5 feet and 3.25 feet, what is the minimum length can you measure? [CSAT 2020]

(a) 0.05 foot

(b) 0.25 foot

(d) 3.25 feet

Q76. What is the least 4-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case? [CSAT 2020]

(a) 1012

(b) 1022

(d) 1222

Q77. What is the greatest length x such that 3 and 8 are integral multiples of x? [CSAT 2020]

(a) 1

(b) 1

(d) 1

Q78. Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again? [CSAT 2021]

(a) Monday

(b) Wednesday

(d) Sunday

Q79. What is the smallest number greater than 1000 that when divided by any one of the numbers 6, 9, 12, 15, 18 leaves a remainder of 3? [CSAT 2022]

(a) 1063

(b) 1073

(d) 1183

Q80. 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 second 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 pm, they together turn green. At what time will they change to green next, simultaneously? [CSAT 2023]

(a) 4:00 pm

(b) 4:10 pm

(d) 4:30 pm

Number of Factors

Q81. Let x be a positive integer such that 7x + 96 is divisible by x. How many values of x are possible? [CSAT 2023]

(a) 10

(b) 11

(d) Infinitely many

Q82. How many natural numbers are there which give a remainder of 31 when 1186 is divided by these natural numbers? [CSAT 2023]

(a) 6

(b) 7

(d) 9

Surds, Indices and exponents

Q83. What is the largest number among the following? [CSAT 2020]

(a)
(b)
(c)
(d)

Q84. Which number amongst 2⁴⁰, 3²¹, 4¹⁸ and 8¹² is the smallest? [CSAT 2022]

(a) 2⁴⁰

(b) 3²¹

(d) 8¹²

Square, Cube and Square root

Q85. A gardener has 1000 plants. He wants to plant them in such a way that the number of rows and the number of columns remains the same. What is the minimum number of plants that he needs more for this purpose? [CSAT 2013]

(a) 14

(b) 24

(d) 34

Q86. 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? [CSAT 2016]

(a) 12

(b) 21

(d) 45

Q87. 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? [CSAT 2017]

(a) 42

(b) 38

(d) 16

Q88. If X is between -3 and -1, and Y is between -1 and 1, then X² - Y² is in between which of the following? [CSAT 2018]

(a) -9 and 1

(b) -9 and -1

(d) 0 and 9

Q89. How many pairs of natural numbers are there such that the difference of whose squares is 63? [CSAT 2020]

(a) 3

(b) 4

(d) 2

Number System (Statement Based Questions)

Q90. If x-y = 8, then which of the following must be true? [CSAT 2018]

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.

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2 nor 3

Q91. Consider two statements S1 and S2 followed by a question: [CSAT 2019]

S1: p and q both are prime numbers.

S2: p + q is an odd integer.

Question: Is pq an odd integer?

Which one of the following is correct?

(a) S1 alone is sufficient to answer the question

(b) S2 alone is sufficient to answer the question

(d) Both S1 and S2 are necessary to answer the question

Q92. Two Statements S1 and S2 are given below with regard to four numbers P, Q, R and S followed by a Question:

S1: R is greater than P as well as Q.

S2: S is not the largest one.

Question:

Among four numbers P, Q, R and S, which one is the largest?

Which one of the following is correct in respect of the above Statements and the Question? [CSAT 2020]

(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.

Q93. Two Statements S1 and S2 are given below followed by a Question: [CSAT 2020]

S1: There are not more than two figures on any page of a 51-page book.

S2: There is at least one figure on every page. Question: Are there more than 100 figures in that book?

Which one of the following is correct in respect of the above Statements and the Question?

(a)Both S1 and S2 are sufficient to answer the Question, but neither S1 alone nor S2 alone is sufficient to answer the Question.

(b) S1 alone is sufficient to answer the Question.

(d) S2 alone is sufficient to answer the Question.

Q94. Two Statements S1 and S2 are given below followed by a Question: [CSAT 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.

Q95. Two Statements S1 and S2 are given below with regard to two numbers followed by a Question: [CSAT 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.

Q96. Consider all 3-digit number (without repetition of digits) obtained using three non-zero digits, which are multiples of 3. Let S be their sum. Which of the following is/are correct? [CSAT 2021]

1. S is always divisible by 74.

2. S is always divisible by 9.

Select the correct answer using the code given below:

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Q97. The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54. [CSAT 2021]

Consider the following statements:

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

(d) Neither 1 nor 2

Q98. A bill for₹ 1,840 is paid in the denominations of ₹50, ₹20 and₹ 10 notes. 50 notes in all are used. Consider the following statements:

1. 25 notes of₹ 50 are used and the remaining are in the denominations of₹ 20 and ₹10.

2. 35 notes of ₹20 are used and the remaining are in the denominations of₹ 50 and₹ 10.

3. 20 notes of ₹10 are used and the remaining are in the denominations of₹ 50 and ₹20.

Which of the above statements are not correct? [CSAT 2022]

(a) 1 and 2 only

(b) 2 and 3 only

(d) 1, 2 and 3

Q99. Five friends P, Q, X, Y and Z purchased some notebooks. The information is given below: relevant

1. Z purchased 8 notebooks more than X did.

2. P and Q together purchased 21 notebooks.

3. Q purchased 5 notebooks less than P did.

4. X and Y together purchased 28 notebooks.

5. P purchased 5 notebooks more than X did.

If each notebook is priced ₹40, then what is the total cost of all the notebooks? [CSAT 2022]

(a) ₹2,600

(b) ₹2,400

(d) ₹2,320

Q100. Consider the Question and two Statements given below: [CSAT 2022]

Question: Is x an integer?

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 the Statements?

(a) Statement-1 alone is sufficient to answer the Question.

(b) Statement-2 alone is sufficient to answer the Question.

(d) Both Statement-1 and Statement-2 are not sufficient to answer the Question.

Q101. 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. [CSAT 2022]

Consider the following statements:

1. The 4-digit least value of x is 1332.

2. The 3-digit greatest value of x is 888.

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Q102. Consider the following statements in respect of two natural number p and q such that p is a prime number and q is a composite number: [CSAT 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?

(a) 1 and 2 only

(b) 2 and 3 only

(d) 1, 2 and 3

Q103. 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:[CSAT 2023]

1. p+q+r-s-t is definitely even.

2. 2p+q+2r-2s+t is definitely odd.

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Q104. Consider the following in respect of prime number p and composite number c. [CSAT 2023]

1. can be even.

2. 2p + c can be odd.

3. pc can be odd.

Which of the statements given above are correct?

(a) 1 and 2 only

(b) 2 and 3 only

(d) 1, 2 and 3

Q105. Question: Is p greater than q? [CSAT 2023]

Statement-1: pxq 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?

(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.

Q106. Question: Is (p + q - r) greater than (p – q + r), where p, q and r are integers? [CSAT 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?

(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.

Q107. Consider a 3-digit number. [CSAT 2023]

Question: What is the number?

Statement-1: The sum of the digits of the number is 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?

(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.

Q108. Consider the following statements: [CSAT 2021]

1. The sum of 5 consecutive integers can be 100.

2. 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

(d) Neither 1 nor 2

Q109. There are large numbers of silver coins weighing 2 gm, 5 gm, 10 gm, 25 gm, 50 gm each. Consider the following statements:

1. To buy 78 gm of coins one must buy at least 7 coins.

2. To weigh 78 gm using these coins one can use less than 7 coins.

Which of the statements given above is/are correct? ? [CSAT 2023]

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

Q110. Consider the following:

I. A + B means A is neither smaller nor equal to B.

II. A - B means A is not greater than B.

III. A×B means A is not smaller than B.

IV. A ÷ B means A is neither greater nor equal to B.

V. A ± B means A is neither smaller nor greater than B.

Statement: P×Q, P – T, T ÷ R, R± S

Conclusion-1: Q T

Conclusion-2: S + Q

Which one of the following is correct in respect of the above Statement and the Conclusions? [CSAT 2023]

(a) Only Conclusion-1 follows from the Statement.

(b) Only Conclusion-2 follows from the Statement.

(d) Neither Conclusion-1 nor Conclusion-2 follows from the Statement.

BASIC NUMERACY

Q111. Consider the following sum: *+1 *+2 *+*3+*1=21* [CSAT 2018]

In the above sum, stands for

(a) 4

(b) 5

(d) 8

Q112. 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 [CSAT 2019]

(a) 2

(b) 5

(d) 8

Q113. In the sum ®+1®+5®+®®+®1] = 1®®, for which digit does the symbol ® stand? [CSAT 2020]

(a) 2

(b) 3

(d) 5

Q114. 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? [CSAT 2020]

(a) 1

(b) 2

(d) 4

Q115. Consider the following addition problem: 3P+4P+PP + PP = RQ2; where P, Q and R are different digits.

What is the arithmetic mean of all such possible sums? [CSAT 2021]

(a) 102

(b) 120

(d) 220

Q116. Consider the following multiplication problem: (PQ) × 3 = RQQ, where P, Q and R are different digits and R ≠ 0. [CSAT 2021]

What is the value of (P+R) ÷ Q?

(a) 1

(b) 2

(d) Cannot be determined due to insufficient data.

Q117. If ABC and DEF are both 3-digit numbers such that A, B, C, D, E and F are distinct non-zero digits that ABC + DEF = 1111, then what is the value of A+B+C+D+E+F[CSAT 2023]

(a) 28

(b) 29

(d) 31

Q118. 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?[CSAT 2023]

(a) 18

(b) 16

(d) Cannot be determined due to insufficient data

Q119. 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, I are distinct digits. If E = 0, F = 8, then what is A + B + C equal to? [CSAT 2023]

(a) 6

(b) 7

(d) 9

Q120. Let pp, qq and rr be 2-digit numbers, where p

1. The number of possible values of p is 5.

2. The number of possible values of q is 6.

Which of the above statements is/are correct?

(a) 1 only

(b) 2 only

(d) Neither 1 nor 2

BODMAS

Q121. If $ means 'divided by'; @ means 'multiplied by'; # means 'minus', then the value of 10#5@1$5 is [CSAT 2019]

(a) 0

(b) 1

(d) 9

CSAT 2024

Q122. How many consecutive zeros are there at the end of the integer obtained in the product 1² x 2⁴ x 3⁶ x 4⁸ x... x25⁵⁰? [CSAT 2024]

(a) 50

(b) 55

(d) 200

Q123. 222³³³ +333²²² is divisible by which of the following numbers? [CSAT 2024]

(a) 2 and 3 but not 37

(b) 3 and 37 but not 2

(d) 2, 3 and 37

Q124. What is the rightmost digit preceding the zeros in the value of 30³⁰? [CSAT 2024]

(a) 1

(b) 3

(d) 9

Q125. 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? [CSAT 2024]

(a) 1

(b) 2

(d) 4

Q126. 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? [CSAT 2024]

(a) 3

(b) 4

(d) 6

Q127. 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: [CSAT 2024]

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?

(a) 1 and 2 only

(b) 2 and 3 only

(d) 1, 2 and 3

Q128. Consider the following: [CSAT 2024]

1. 1000 litres = 1 m³

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

(d) 1, 2 and 3

Q129. 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? [CSAT 2024]

(a) 2

(b) 4

(d) 8

Q130. Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements: [CSAT 2024]

1. (p-r)²(qs) is even.

2. (q-s)q²s is even.

3. (q+r)²(p+s) is odd.

Which of the statements given above are correct?

(a) 1 and 2 only

(b) 2 and 3 only

(d) 1, 2 and 3

Q131. What is the number of fives used in numbering a 260-page book? [CSAT 2024]

(a) 55

(b) 56

(d) 60

Q132. 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? [CSAT 2024]

(α) 9

(b) 8

(d) Cannot be determined due to insufficient data

Q133. 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? [CSAT 2024]

(a) One triplet

(b) Two triplets

(d) Four triplets

Q134. 32⁵ +2²⁷ is divisible by [CSAT 2024]

(α) 3

(b) 7

(d) 11

Q135. Let p and q be positive integers satisfying p

(a) 3

(b) 4

(d) 6

Q136. A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question: What are the values of m and n, where m and n are natural numbers? [CSAT 2024]

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

Q137. A Question is given followed by two Statements I and II. Consider the Question and the Statements.

Question: What are the unique values of x and y, where x, y are distinct natural numbers? [CSAT 2024]

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

Q138. A Question is given followed by two Statements I and II. Consider the Question and the Statements. There are three distinct prime numbers whose sum is a prime number. [CSAT 2024]

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

Q139. A Question is given followed by two Statements I and II. Consider the Question and the Statements. [CSAT 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

Q140. In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q – S = 2S and

T = R + S + 3, then what is the value of P+R-T? [CSAT 2024]

(a) 1

(b) 2

(d) Cannot be determined due to insufficient data

Q141. In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, -, x each at most two times. Which is the smallest non-negative value of the expression? [CSAT 2024]

(a) 3

(b) 2

(d) 0

Q142. On January 1^st, 2023, a person saved Rs. 1.

On January 2^nd, 2023, he saved Rs. 2 more than that on the previous day. On January 3^rd, 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? [CSAT 2024]

(a) 7^th January 2023

(b) 8^th January, 2023

(d) Not possible

Q143. A Question is given followed by two Statements I and II. Consider the Question and the Statements. [CSAT 2024]

A person buys three articles p, q and r for 50. The price of the article q is 16 which is the least.

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

Q144.If a + b means a - b; a - b means a x b; a x b means a ÷ b; a ÷ b means a + b, then what is the value of 10 + 30 - 100 x 50 ÷ 25 (Operations are to be replaced simultaneously) [CSAT 2024]

(a) 15

(b) 0

(d) -25

Q. No.	Answer	Q. No.	Answer	Q. No.	Answer	Q. No.	Answer
1	a	41	d	81	c	121	d
2	b	42	d	82	d	122	d
3	c	43	b	83	c	123	b
4	a	44	b	84	b	124	d
5	c	45	d	85	b	125	c
6	b	46	c	86	b	126	b
7	b	47	a	87	b	127	c
8	a	48	a	88	d	128	d
9	b	49	b	89	a	129	d
10	c	50	c	90	d	130	d
11	b	51	b	91	b	131	b
12	c	52	c	92	c	132	a
13	c	53	a	93	c	133	d
14	b	54	d	94	d	134	c
15	b	55	b	95	c	135	c
16	b	56	d	96	c	136	c
17	a	57	b	97	b	137	c
18	d	58	d	98	d	138	a
19	d	59	a	99	a	139	d
20	b	60	c	100	d	140	b
21	a	61	a	101	a	141	d
22	b	62	c	102	d	142	b
23	c	63	d	103	a	143	c
24	d	64	a	104	d	144	d
25	b	65	a	105	d
26	c	66	d	106	c
27	a	67	a	107	d
28	c	68	a	108	c
29	c	69	b	109	c
30	b	70	b	110	b
31	a	71	d	111	d
32	b	72	b	112	d
33	c	73	b	113	b
34	c	74	d	114	c
35	b	75	b	115	c
36	c	76	b	116	b
37	b	77	d	117	d
38	b	78	b	118	a
39	b	79	c	119	a
40	b	80	b	120	c

NUMBER SYSTEM PYQ's

TOPIC:- NUMBER SYSTEM

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