UPSC CSE Prelims CSAT (Paper II) previous year questions on Numbers (Quantitative Ability), asked from 2016–2026, with answers. There are 96 questions in this post. Attempt each question, then click Show Answer to check.
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1] If 10ᵐ × 1000 × n = 75²⁵ × 25³² × 32⁷⁵, where n is not divisible by 10, then the value of m is [2026/19]
(a) 101
(b) 111
(c) 121
(d) 131
Show Answer
Ans: (b) 111
2] For 1/3 < x < y < 2, which of the following statements is/are always correct?
I. x + 1/x < y + 1/y
II. √(1 + y²)/y < √(1 + x²)/x
Select the answer using the code given below. [2026/21]
(a) I only
(b) II only
(c) Both I and II
(d) Neither I nor II
Show Answer
Ans: (b) II only
3] What is the minimum number of times one needs to measure to get 298 litres of water from a tank, if the measuring cylinders have capacities 1 litre, 6 litres, 25 litres and 100 litres? [2026/22]
(a) 4
(b) 5
(c) 9
(d) 13
Show Answer
Ans: (b) 5
4] Three variables x, y and z take values 2, 3, 4 or 5 such that their values are always distinct. If M and N denote the largest possible value and the smallest possible value, respectively, for the expression {(x × y) + z}; then M – N is [2026/29]
(a) 11
(b) 12
(c) 13
(d) 14
Show Answer
Ans: (c) 13
5] The digit in the unit place of the number 6¹²⁹ × 7³⁰⁷ is [2026/42]
(a) 2
(b) 4
(c) 8
(d) 6
Show Answer
Ans: (c) 8
6] How many three-digit numbers can be expressed as an integral power of 2? [2026/45]
(a) 1
(b) 2
(c) 3
(d) 4
Show Answer
Ans: (c) 3
7] How many times does 5 appear in all two-digit positive integers? [2026/49]
(a) 18
(b) 19
(c) 20
(d) 21
Show Answer
Ans: (b) 19
8] If x and y are two digits and the number 4x5y790 is divisible by 11, then what is the remainder, if x + y is divided by 11? [2026/60]
(a) 1
(b) 3
(c) 5
(d) 7
Show Answer
Ans: (d) 7
9] A is a 2-digit number with different digits. B is also a 2-digit number and is obtained by reversing the digits of A. If A – B is a multiple of 27, where A > B, how many such different A’s are possible? [2026/66]
(a) 6
(b) 9
(c) 12
(d) 18
Show Answer
Ans: (b) 9
10] There are three types of rectangular tiles: 3′ × 3′, 3′ × 7′ and 3′ × 11′. An area of rectangular shape of dimensions 3′ × 100′ is to be covered using these tiles without breaking them. If x and y are the maximum and minimum numbers of tiles of various sizes, respectively, that can be used to cover the area exactly, then x – y is [2026/68]
(a) 20
(b) 12
(c) 10
(d) 7
Show Answer
Ans: (a) 20
11] A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property? [2025/5]
(a) 6
(b) 7
(c) 8
(d) 9
Show Answer
Ans: (c) 8
12] Three prime numbers p, q and r, each less than 20, are such that p − q = q − r. How many distinct possible values can we get for (p + q + r)? [2025/6]
(a) 4
(b) 5
(c) 6
(d) More than 6
Show Answer
Ans: (d) More than 6
13] How many possible values of (p + q + r) are there satisfying 1/p + 1/q + 1/r = 1, where p, q and r are natural numbers (not necessarily distinct)? [2025/7]
(a) None
(b) One
(c) Three
(d) More than three
Show Answer
Ans: (c) Three
14] What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × … × 999? [2025/20]
(a) 1
(b) 3
(c) 5
(d) 9
Show Answer
Ans: (c) 5
15] Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9? [2025/25]
(a) 20
(b) 21
(c) 22
(d) 23
Show Answer
Ans: (c) 22
16] Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30. What is the number of possible values of k? [2025/27]
(a) 4
(b) 5
(c) 6
(d) 7
Show Answer
Ans: (b) 5
17] What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35ⁿ? [2025/35]
(a) 3
(b) 4
(c) 5
(d) 7
Show Answer
Ans: (b) 4
18] If P = +, Q = −, R = ×, S = ÷, then insert the proper notations between the successive numbers in the equation 60 _ 15 _ 3 _ 20 _ 4 = 20: [2025/38]
(a) SPRQ
(b) QRPS
(c) QRSP
(d) SPQR
Show Answer
Ans: (b) QRPS
19] If N² = 12345678987654321, then how many digits does the number N have? [2025/40]
(a) 8
(b) 9
(c) 10
(d) 11
Show Answer
Ans: (b) 9
20] If n is a natural number, then what is the number of distinct remainders of (1ⁿ + 2ⁿ) when divided by 4? [2025/46]
(a) 0
(b) 1
(c) 2
(d) 3
Show Answer
Ans: (c) 2
21] What is the 489th digit in the number 123456789101112…? [2025/48]
(a) 0
(b) 3
(c) 6
(d) 9
Show Answer
Ans: (d) 9
22] Consider the following statements:
I. There exists a natural number which, when increased by 50%, can have its number of factors unchanged.
II. There exists a natural number which, when increased by 150%, can have its number of factors unchanged.
Which of the statements given above is/are correct? [2025/64]
(a) I only
(b) II only
(c) Both I and II
(d) Neither I nor II
Show Answer
Ans: (c) Both I and II
23] What is the remainder when 9³ + 9⁴ + 9⁵ + 9⁶ + … + 9¹⁰⁰ is divided by 6? [2025/67]
(a) 0
(b) 1
(c) 2
(d) 3
Show Answer
Ans: (a) 0
24] Let x be a real number between 0 and 1. Which of the following statements is/are correct?
I. x² > x³
II. x > √x
Select the correct answer using the code given below: [2025/79]
(a) I only
(b) II only
(c) Both I and II
(d) Neither I nor II
Show Answer
Ans: (a) I only
25] The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers? [2025/80]
(a) There is only one such number
(b) There are only two such numbers
(c) There can be more than one such number
(d) No such number exists
Show Answer
Ans: (c) There can be more than one such number
26] In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, -, x each at the most two times. What is the smallest non-negative value of the expression? [2024/6]
(a) 3
(b) 2
(c) 1
(d) 0
Show Answer
Ans: (d) 0
27] How many consecutive zeros are there at the end of the integer obtained in the product x x x x ………. ?? [2024/9]
(a) 50
(b) 55
(c) 100
(d) 200
Show Answer
Ans: (d) 200
28] On January 1st, 2023, a person saved rupee 1 . On January 2nd, 2023, he saved rupee 2 more than that on the previous day. On January 3rd , 2023 he saved 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? [2024/10]
(a) 7th January, 2023
(b) 8th January, 2023
(c) 9th January, 2023
(d) Not possible
Show Answer
Ans: (b) 8th January, 2023
29] + is divisible by which of the following numbers? [2024/15]
(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
Show Answer
Ans: (b) 3 and 37 but not 2
30] What is the rightmost digit preceding the zeros in the value of ? [2024/17]
(a) 1
(b) 3
(c) 7
(d) 9
Show Answer
Ans: (d) 9
31] 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? [2024/18]
(a) 1
(b) 2
(c) 3
(d) 4
Show Answer
Ans: (c) 3
32] 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. 1. The unit digit of S can be 0.
2. 2. The unit digit of S can be 9.
3. 3. The unit digit of S can be 5.
Which of the statements given above are correct? [2024/20]
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
Show Answer
Ans: (c) 1 and 3 only
33] Consider the following:
l. 1000 litres = 1
2. 2. 1 metric ton = 1000 kg
3. 3. 1 hectare = 10000
Which of the above are correct? [2024/30]
(a) 1, and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1,2 and 3
Show Answer
Ans: (d) 1,2 and 3
34] Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even.
Consider the following statements.
1. 1. (p − r)²(qs) is even.
2. 2. (q − s)q²s is even.
3. 3. (q + r)²(p + s) is odd.
Which of the statements given above are correct? [2024/39]
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
Show Answer
Ans: (d) 1, 2 and 3
35] What is the number of fives used in numbering a 260-page book? [2024/45]
(a) 55
(b) 56
(c) 57
(d) 60
Show Answer
Ans: (b) 56
36] + is divisible by [2024/54]
(a) 3
(b) 7
(c) 10
(d) 11
Show Answer
Ans: (c) 10
37] 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? [2024/55]
(a) 3
(b) 4
(c) 5
(d) 6
Show Answer
Ans: (c) 5
38] 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? [2024/75] (Operations are to be replaced simultaneously)
(a) 15
(b) 0
(c) -15
(d) -25
Show Answer
Ans: (d) -25
39] In some code, letters P, Q, R, S, T represent numbers 4, 5, 1O, 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? [2024/80]
(a) 1
(b) 2
(c) 3
(d) Cannot be determined due to insufficient data
Show Answer
Ans: (b) 2
40] What is the remainder when 85 X 87 X 89 X 91 X 95 X 96 is divided by 100? [2023/7]
(a) 0
(b) 1
(c) 2
(d) 4
Show Answer
Ans: (a) 0
41] What is the unit digit in the expansion of ? [2023/8]
(a) 2
(b) 4
(c) 6
(d) 8
Show Answer
Ans: (a) 2
42] 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
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? [2023/14]
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Show Answer
Ans: (a) 1 only
43] Consider the following in respect of prime number p and composite number c.
1. (p+c)/(p-c) can be even
2. 2P+C can be odd.
3. pc can be odd.
Which of the statements given above are correct? [2023/15]
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
Show Answer
Ans: (d) 1, 2 and 3
44] For any choices of values of X, Y and Z, the 6-digit number of the form XYZXYZ is divisible by? [2023/17]
(a) 7 and 11 only
(b) 11 and 13 only
(c) 7 and 13 only
(d) 7, 11 and 13
Show Answer
Ans: (d) 7, 11 and 13
45] How many distinct 8-digit numbers can be formed by rearranging the digits of the number 11223344 such that odd digits occupy odd positions and even digits occupy even positions? [2023/19]
(a) 12
(b) 18
(c) 36
(d) 72
Show Answer
Ans: (c) 36
46] If 7@9@10=8, 9@11@30=5, 11@17@21=13 what is the value of 23@4@15? [2023/24]
(a) 6
(b) 8
(c) 13
(d) 15
Show Answer
Ans: (a) 6
47] A number N is formed by writing 9 for 99 times. What is the remainder if N is divided by 13? [2023/27]
(a) 11
(b) 9
(c) 7
(d) 1
Show Answer
Ans: (a) 11
48] 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? [2023/28]
(a) 64
(b) 80
(c) 81
(d) 100
Show Answer
Ans: (c) 81
49] How many natural numbers are there which give a remainder of 31 when 1186 is divided by these natural numbers? [2023/45]
(a) 6
(b) 7
(c) 8
(d) 9
Show Answer
Ans: (d) 9
50] Let pp, qq and rr be 2-digit numbers where p < q < r. If pp + qq + rr = tto, where tto is a 3-digit number ending with zero, consider the following statements:
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? [2023/46]
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Show Answer
Ans: (c) Both 1 and 2
51] If today is Sunday, then which day is it exactly on th day? [2023/49]
(a) Wednesday
(b) Thursday
(c) Friday
(d) Saturday
Show Answer
Ans: (a) Wednesday
52] What is the remainder if is divided by 6? [2023/74]
(a) 0
(b) 1
(c) 2
(d) 4
Show Answer
Ans: (d) 4
53] 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? [2022/5]
(a) 8
(b) 9
(c) 11
(d) 12
Show Answer
Ans: (a) 8
54] Which number amongst and is the smallest? [2022/9]
(a)
(b)
(c)
(d)
Show Answer
Ans: (b)
55] 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 to D. The number of coins D has now, is the smallest two- digit number. How many coins does A have in the beginning? [2022/28]
(a) 76
(b) 68
(c) 60
(d) 52
Show Answer
Ans: (d) 52
56] How many seconds in total are there in x weeks, x days, x hours, x minutes, and x seconds? [2022/35]
(a) 11580x
(b) 11581x
(c) 694860x
(d) 694861x
Show Answer
Ans: (d) 694861x
57] What is the remainder when 91x92x93x94x95x96x97x98x99 is divided by 1261? [2022/58]
(a) 3
(b) 2
(c) 1
(d) 0
Show Answer
Ans: (d) 0
58] 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? [2022/65]
(a) 1063
(b) 1073
(c) 1083
(d) 1183
Show Answer
Ans: (c) 1083
59] 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.
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? [2022/67]
(a) 1 and 2 only
(b) 2 and 3 only
(c) 1 and 3 only
(d) 1, 2 and 3
Show Answer
Ans: (d) 1, 2 and 3
60] If 15×14×13×…×3×2×1= × n where m and n are positive integers, then what is the maximum value of m? [2022/74]
(a) 7
(b) 6
(c) 5
(d) 4
Show Answer
Ans: (b) 6
61] If is divided by 10, then what is the remainder? [2021/5]
(a) 1
(b) 3
(c) 7
(d) 9
Show Answer
Ans: (c) 7
62] The number 3798125P369 is divisible by 7. What is the value of the digit P? [2021/6]
(a) 1
(b) 6
(c) 7
(d) 9
Show Answer
Ans: (b) 6
63] 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? [2021/8]
(a) P = 12 + 50n
(b) P = 50 + 12n
(c) P = 50 (
(d) P = 50
Show Answer
Ans: (d) P = 50
64] Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10? [2021/19]
(a) 6
(b) 7
(c) 8
(d) 9
Show Answer
Ans: (d) 9
65] Consider all 3-digit numbers (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?
1. S is always divisible by 74.
2. S is always divisible by 9.
Select the correct answer using the code given below: [2021/36]
(a) 1 only
(b) 2 only
(c) Both 1 and 2
(d) Neither 1 nor 2
Show Answer
Ans: (c) Both 1 and 2
66] What is the value of ‘X’ in the sequence 2, 7, 22, 67, 202, X, 1822? [2021/50]
(a) 603
(b) 605
(c) 607
(d) 608
Show Answer
Ans: (c) 607
67] When a certain number is multiplied by 7, the product entirely comprises ones only (1111…). What is the smallest such number? [2021/79]
(a) 15713
(b) 15723
(c) 15783
(d) 15873
Show Answer
Ans: (d) 15873
68] How many zeroes are there at the end of the following product? [2020/7]
lx5x10x15x20x25x30x35x40x45x50x55x60
(a) 10
(b) 12
(c) 14
(d) 15
Show Answer
Ans: (a) 10
69] 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? [2020/9]
(a) p
(b) q
(c) q
(d) s
Show Answer
Ans: (c) q
70] How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits? [2020/10]
(a) Zero
(b) One
(c) Nine
(d) Ten
Show Answer
Ans: (a) Zero
71] How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4? [2020/37]
(a) 5
(b) 11
(c) 12
(d) 13
Show Answer
Ans: (c) 12
72] What is the largest number among the following? [2020/50]
(a)
(b)
(c)
(d)
Show Answer
Ans: (c)
73] What the greatest length x such that 3 m and 8 m are integral multiples of x? [2020/51]
(a) m
(b) m
(c) m
(d) m
Show Answer
Ans: (d) m
74] The recurring decimal representation 1.272727… is equivalent to? [2020/53]
(a) 13/11
(b) 14/11
(c) 127/99
(d) 137/99
Show Answer
Ans: (b) 14/11
75] What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case? [2020/54]
(a) 1012
(b) 1022
(c) 1122
(d) 1222
Show Answer
Ans: (b) 1022
76] What is the remainder when 51 x 27 x 35 x 62 x 75 is divided by 100? [2020/56]
(a) 50
(b) 25
(c) 5
(d) 1
Show Answer
Ans: (a) 50
77] For what value of n, the sum of digits in the number ( + 1) is 2? [2020/58]
(a) For n = 0 only
(b) For any whole number n
(c) For any positive integer n only
(d) For any real number n
Show Answer
Ans: (b) For any whole number n
78] How many pairs of natural numbers are there such that the difference of whose squares is 63? [2020/75]
(a) 3
(b) 4
(c) 5
(d) 2
Show Answer
Ans: (a) 3
79] 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? [2020/76]
(a) 2/3
(b) 3/4
(c) 4/5
(d) 5/6
Show Answer
Ans: (d) 5/6
80] A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4? [2020/77]
(a) 2n
(b) 3n
(c) 2n+4
(d) 3n+1
Show Answer
Ans: (d) 3n+1
81] The number of times the digit 5 will appear while writing the integers from 1 to 1000 is? [2019/9]
(a) 269
(b) 271
(c) 300
(d) 302
Show Answer
Ans: (c) 300
82] 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? [2019/15]
(a) 4
(b) 8
(c) 10
(d) 12
Show Answer
Ans: (b) 8
83] 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 [2019/50]
(a) always less than the original fraction
(b) always greater than the original fraction
(c) always equal to the original fraction
(d) such that nothing can be claimed definitely
Show Answer
Ans: (b) always greater than the original fraction
84] A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have? [2019/53]
(a) 1040
(b) 1048
(c) 1049
(d) 1050
Show Answer
Ans: (c) 1049
85] 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? [2019/60]
(a) 2
(b) 5
(c) 7
(d) 8
Show Answer
Ans: (d) 8
86] 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 [2019/69]
(a) 13 units
(b) 15 units
(c) 16 units
(d) 30 units
Show Answer
Ans: (d) 30 units
87] An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible? [2019/75]
(a) 2
(b) 3
(c) 4
(d) 6
Show Answer
Ans: (c) 4
88] Consider the following sum:
•+1•+2•+•3+•1=21•
In the above sum, • stands for [2018/2]
(a) 4
(b) 5
(c) 6
(d) 8
Show Answer
Ans: (d) 8
89] If X is between -3 and -1, and Y is between -1 and 1, then – is in between which of the following? [2018/23]
(a) -9 and 1
(b) -9 and -1
(c) 0 and 8
(d) 0 and 9
Show Answer
Ans: (d) 0 and 9
90] X and Y are natural numbers other than 1, and Y is greater than X. Which of the following represents the largest number? [2018/24]
(a) XY
(b) X/Y
(c) Y/X
(d) (X+Y)/XY
Show Answer
Ans: (a) XY
91] 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 tens place is greater than the digit at unit’s place? [2018/36]
(a) 61
(b) 64
(c) 85
(d) 91
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Ans: (c) 85
92] Certain 3-digit numbers have 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? [2017/49]
(a) 2
(b) 4
(c) 6
(d) 8
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Ans: (b) 4
93] How many numbers are there between 99 and 1000 such that the digit 8 occupies the units place? [2017/51]
(a) 64
(b) 80
(c) 90
(d) 104
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Ans: (c) 90
94] What is the total number of digits printed, if a book containing 150 pages is to be numbered from 1 to 150? [2017/80]
(a) 262
(b) 342
(c) 360
(d) 450
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Ans: (b) 342
95] If R and S are different integers both divisible by 5, then which of the following is not necessarily true? [2016/62]
(a) R – S is divisible by 5
(b) R + S is divisible by 10
(c) R x S is divisible by 25
(d) is divisible by 5
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Ans: (b) R + S is divisible by 10
96] How many numbers are there between 100 and 300 which either begin with or end with 2? [2016/63]
(a) 110
(b) 111
(c) 112
(d) None of the above
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Ans: (a) 110