CAT Quantitative Ability Questions | CAT Number System questions

CAT/2023.1(Quantitative Ability)

Question. 1

CAT/2023.1(Quantitative Ability)

Question. 2

The number of all natural numbers up to 1000 with non-repeating digits is

CAT/2021.1(Quantitative Ability)

Question. 3

The natural numbers are divided into groups as (1), (2, 3, 4), (5, 6, 7, 8, 9), ….. and so on. Then, the sum of the numbers in the 15th group is equal to

CAT/2021.1(Quantitative Ability)

Question. 4

How many three-digit numbers are greater than 100 and increase by 198 when the three digits are arranged in the reverse order?

CAT/2021.2(Quantitative Ability)

Question. 5

For a 4-digit number, the sum of its digits in the thousands, hundreds and tens places is 14, the sum of its digits in the hundreds, tens, and units places is 15, and the tens place digit is 4 more than the units place digit. Then the highest possible 4-digit number satisfying the above conditions is

CAT/2021.3(Quantitative Ability)

Question. 6

A four-digit number is formed by using only the digits 1, 2 and 3 such that both 2 and 3 appear at least once. The number of all such four-digit numbers is

CAT/2021.3(Quantitative Ability)

Question. 7

Consider a sequence of real numbers x₁, x₂, x₃, .... such that x_n+1 = x_n + n - 1 for all n ≥ 1. If x₁ = -1 then x₁₀₀

CAT/2021.3(Quantitative Ability)

Question. 8

The number of distinct pairs of integers (m,n) satisfying |1 + mn| < |m + n| < 5 is

CAT/2020.1(Quantitative Ability)

Question. 9

How many 3-digit numbers are there, for which the product of their digits is more than 2 but less than 7?

CAT/2020.1(Quantitative Ability)

Question. 10

If log₄ 5 = (log₄ y) (log₆ √5), then y equals

CAT/2020.1(Quantitative Ability)

Question. 11

The mean of all 4 digit even natural numbers of the form 'aabb', where a>0, is

CAT/2020.1(Quantitative Ability)

Question. 12

Among 100 students, x₁ have birthdays in January, x₂ have birthdays in February, and so on. If x₀ = max(x₁, x₂, ..., x₁₂), then the smallest possible value of x₀ is

CAT/2020.1(Quantitative Ability)

Question. 13

If a, b and c are positive integers such that ab = 432, bc = 96 and c < 9, then the smallest possible value of a + b + c is

CAT/2020.1(Quantitative Ability)

Question. 14

If y is a negative number such that 2^y2log₃5 = 5^log₂3, then y equals

CAT/2020.1(Quantitative Ability)

Question. 15

A gentleman decided to treat a few children in the following manner. He gives half of his total stock of toffees and one extra to the first child, and then the half of the remaining stock along with one extra to the second and continues giving away in this fashion. His total stock exhausts after he takes care of 5 children. How many toffees were there in his stock initially?

CAT/2020.2(Quantitative Ability)

Question. 16

CAT/2020.2(Quantitative Ability)

Question. 17

Let the m-th and n-thterms of a Geometric progression be 34">3/4 and 12, respectively, when m < n. If the common ratio of the progression is an integer r, then the smallest possible value of r + n - m is

CAT/2020.2(Quantitative Ability)

Question. 18

If x and y are positive real numbers satisfying x + y = 102, then the minimum possible value of 2601(1 + 1x">1/x)(1 + 1y">1/y) is

CAT/2020.2(Quantitative Ability)

Question. 19

How many 4-digit numbers, each greater than 1000 and each having all four digits distinct, are there with 7 coming before 3?

CAT/2020.3(Quantitative Ability)

Question. 20

Let N, x and y be positive integers such that N = x + y, 2 < x < 10 and 14 < y < 23. If N > 25, then how many distinct values are possible for N?

CAT/2020.3(Quantitative Ability)

Question. 21

CAT/2020.3(Quantitative Ability)

Question. 22

How many of the integers 1, 2, … , 120, are divisible by none of 2, 5 and 7?

CAT/2020.3(Quantitative Ability)

Question. 23

CAT/2020.3(Quantitative Ability)

Question. 24

CAT/2020.3(Quantitative Ability)

Question. 25

CAT/2020.3(Quantitative Ability)

Question. 26

How many pairs (a,b) of positive integers are there such that a ≤ b and ab = 4²⁰¹⁷?

CAT/2019.1(Quantitative Ability)

Question. 27

If the population of a town is p in the beginning of any year then it becomes 3+2p in the beginning of the next year. If the population in the beginning of 2019 is 1000, then the population in the beginning of 2034 will be

CAT/2019.1(Quantitative Ability)

Question. 28

The product of two positive numbers is 616. If the ratio of the difference of their cubes to the cube of their difference is 157 : 3, then the sum of the two numbers is

CAT/2019.1(Quantitative Ability)

Question. 29

If a₁ + a₂ + a₃ + ... + a_n = 3(2ⁿ⁺¹ - 2), then a₁₁ equals [TITA]

CAT/2019.1(Quantitative Ability)

Question. 30

CAT/2019.1(Quantitative Ability)

Question. 31

If m and n are integers such that (2">2–√2)¹⁹ 3⁴ 4² 9^m 8ⁿ = 3ⁿ 16^m (∜64) then m is

CAT/2019.1(Quantitative Ability)

Question. 32

Let x and y be positive real numbers such that log₅(x + y) + log₅(x - y) = 3, and log₂y - log₂x = 1 - log₂3. Then xy equals

CAT/2019.2(Quantitative Ability)

Question. 33

The real root of the equation 2^6x + 2^3x+2 - 21 = 0 is

CAT/2019.2(Quantitative Ability)

Question. 34

Let a, b, x, y be real numbers such that a² + b² = 25 , x² + y² = 169 and ax + by = 65. If k = ay - bx, then

CAT/2019.2(Quantitative Ability)

Question. 35

Let a₁ , a₂ be integers such that a₁ - a₂ + a₃ - a₄ + ........ +(-1)^n-1 a_n = n , for n ≥ 1. Then a₅₁ + a₅₂ + ........ + a₁₀₂₃ equals

CAT/2019.2(Quantitative Ability)

Question. 36

How many factors of 2⁴ x 3⁵ x 10⁴ are perfect squares which are greater than 1? 

CAT/2019.2(Quantitative Ability)

Question. 37

How many pairs (m,n) of positive integers satisfy the equation the equation m² + 105 = n² ? 

CAT/2019.2(Quantitative Ability)

Question. 38

In a six-digit number, the sixth, that is, the rightmost, digit is the sum of the first three digits, the fifth digit is the sum of first two digits, the third digit is equal to the first digit, the second digit is twice the first digit and the fourth digit is the sum of fifth and sixth digits. Then, the largest possible value of the fourth digit is

CAT/2019.2(Quantitative Ability)

Question. 39

The number of common terms in the two sequences: 15, 19, 23, 27, ...... , 415 and 14, 19, 24, 29, ...... , 464 is

CAT/2019.2(Quantitative Ability)

Question. 40

If (2n+1) + (2n+3) + (2n+5) + ... + (2n+47) = 5280 , then what is the value of 1+2+3+ ... +n ?

CAT/2018.1(Quantitative Ability)

Question. 41

While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is

CAT/2018.1(Quantitative Ability)

Question. 42

How many numbers with two or more digits can be formed with the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9 so that in every such number, each digit is used at most once and the digits appear in the ascending order?

CAT/2018.1(Quantitative Ability)

Question. 43

Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is

CAT/2018.1(Quantitative Ability)

Question. 44

The number of integers x such that 0.25 < 2^x < 200, and 2^x + 2 is perfectly divisible by either 3 or 4, is

CAT/2018.2(Quantitative Ability)

Question. 45

Let a₁, a₂, ... , a₅₂ be positive integers such that a₁ ＜ a₂ ＜ ... ＜ a₅₂. Suppose, their arithmetic mean is one less than the arithmetic mean of a₂, a₃, ..., a₅₂. If a₅₂ = 100, then the largest possible value of a₁ is

CAT/2018.2(Quantitative Ability)

Question. 46

Let t₁, t₂,… be real numbers such that t₁+ t₂ +... + t_n = 2n² + 9n + 13, for every positive integer n ≥ 2. If t_k=103, then k equals

CAT/2018.2(Quantitative Ability)

Question. 47

If N and x are positive integers such that N^N = 2¹⁶⁰ and N² + 2^N is an integral multiple of 2^x, then the largest possible x is

CAT/2018.2(Quantitative Ability)

Question. 48

If p³ = q⁴ = r⁵ = s⁶, then the value of log_s (pqr) is equal to

CAT/2018.2(Quantitative Ability)

Question. 49

The smallest integer n for which 4ⁿ ＞ 17¹⁹ holds, is closest to

CAT/2018.2(Quantitative Ability)

Question. 50

The smallest integer n such that n³ - 11n² + 32n - 28 ＞ 0 is

CAT/2018.2(Quantitative Ability)

Question. 51

The value of the sum 7 x 11 + 11 x 15 + 15 x 19 + ..... + 95 x 99 is

CAT/2018.2(Quantitative Ability)

Question. 52

If the sum of squares of two numbers is 97 then which one of the following cannot be their product

CAT/2018.2(Quantitative Ability)

Question. 53

How many two-digit numbers, with a non-zero digit in the units place, are there which are more than thrice the number formed by interchanging the positions of its digits?

CAT/2018.2(Quantitative Ability)

Question. 54

The arithmetic mean of x, y and z is 80, and that of x, y, z, u and v is 75, where u = (x+y)/2 ) and v= (y+z)/2. If x ≥ z, then the minimum possible value of x is

CAT/2017.1(Quantitative Ability)

Question. 55

The number of solutions (x, y, z) to the equation x – y – z = 25, where x, y, and z are positive integers such that x ≤ 40, y ≤ 12, and z ≤ 12 is

CAT/2017.1(Quantitative Ability)

Question. 56

If the square of the 7^th term of an arithmetic progression with positive common difference equals the product of the 3^rd and 17^th terms, then the ratio of the first term to the common difference is

CAT/2017.1(Quantitative Ability)

Question. 57

Let a₁, a₂,.......a_3n be an arithmetic progression with a₁ = 3 and a₂ = 7. If a₁ + a₂ + ......+a_3n = 1830, then what is the smallest positive integer m such that m (a₁ + a₂ + ..... + a_n) > 1830?

CAT/2017.2(Quantitative Ability)

Question. 58

The numbers 1, 2,..., 9 are arranged in a 3 X 3 square grid in such a way that each number occurs once and the entries along each column, each row, and each of the two diagonals add up to the same value. If the top left and the top right entries of the grid are 6 and 2, respectively, then the bottom middle entry is

CAT/2017.2(Quantitative Ability)

Question. 59

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

CAT/2017.2(Quantitative Ability)

Question. 60

Let a₁, a₂, a₃, a₄, a₅ be a sequence of five consecutive odd numbers. Consider a new sequence of five consecutive even numbers ending with 2a₃. If the sum of the numbers in the new sequence is 450, then a₅ is

CAT/2017.2(Quantitative Ability)

Question. 61

How many different pairs (a, b) of positive integers are there such that a ≤ b and

CAT/2017.2(Quantitative Ability)

Question. 62

An infinite geometric progression a₁, a₂, a₃,... has the property that a_n = 3(a_n+1 + a_n+2 +....) for every n ≥ 1. If the sum a₁ + a₂ + a₃ +...... = 32, then a₅ is

CAT/2017.2(Quantitative Ability)

Question. 63

If a₁ = 12×5">1/(2×5) , a₂ = 15×8">1/(5×8), a₃ = 18×11">1/(8×11),...., then a₁ + a₂ + a₃ + ...... + a₁₀₀ is

CAT/2008(Quantitative Ability)

Question. 64

The integers 1, 2, ..., 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b – 1 is written. What will be the number left on the board at the end?

CAT/2008(Quantitative Ability)

Question. 65

What are the last two digits of 7²⁰⁰⁸?

CAT/2008(Quantitative Ability)

Question. 66

If the roots of the equation x³ – ax² + bx – c = 0 are three consecutive integers, then what is the smallest possible value of b?

CAT/2008(Quantitative Ability)

Question. 67

A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?

Comprehension

Let f(x) = ax² + bx + c, where a, b and c are certain constants and a 0 ≠ It is known that f(5) = – 3f(2) and that 3 is a root of f(x) = 0.

CAT/2008(Quantitative Ability)

Question. 68

What is the other root of f(x) = 0?

Comprehension

Let f(x) = ax² + bx + c, where a, b and c are certain constants and a 0 ≠ It is known that f(5) = – 3f(2) and that 3 is a root of f(x) = 0.

CAT/2008(Quantitative Ability)

Question. 69

 What is the value of a + b + c?

CAT/2008(Quantitative Ability)

Question. 70

The number of common terms in the two sequences 17, 21, 25,…, 417 and 16, 21, 26,…, 466 is ?

Comprehension

Directions for Questions:

Mark (1) if Q can be answered from A alone but not from B alone.

Mark (2) if Q can be answered from B alone but not from A alone.

Mark (3) if Q can be answered from A alone as well as from B alone.

Mark (4) if Q can be answered from A and B together but not from any of them alone.

Mark (5) if Q cannot be answered even from A and B together.

In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules :

(a) If the number of players, say n, in any round is even, then the players are grouped into n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.

(b) If the number of players, say n, in any round is odd, then one of them is given a bye, that is he automatically moves on to the next round. The remaining (n–1) players are grouped into (n–1)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.

Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n+1)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament.

 

CAT/2008(Quantitative Ability)

Question. 71

What is the number of Matches played by the champion?

A. The entry list for the tournament consists of 83 players.

B. The champion received one bye.

Comprehension

Directions for Questions:

Mark (1) if Q can be answered from A alone but not from B alone.

Mark (2) if Q can be answered from B alone but not from A alone.

Mark (3) if Q can be answered from A alone as well as from B alone.

Mark (4) if Q can be answered from A and B together but not from any of them alone.

Mark (5) if Q cannot be answered even from A and B together.

In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules :

(a) If the number of players, say n, in any round is even, then the players are grouped into n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round.

(b) If the number of players, say n, in any round is odd, then one of them is given a bye, that is he automatically moves on to the next round. The remaining (n–1) players are grouped into (n–1)/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. No player gets more than one bye in the entire tournament.

Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n+1)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament.

 

CAT/2008(Quantitative Ability)

Question. 72

If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n?

A. Exactly one player received a bye in the entire tournament.

B. One player received a bye while moving on to the fourth round from the third round.

CAT/2008(Quantitative Ability)

Question. 73

Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the other. What is the area (in sq. cm.) of the intersecting region?

CAT/2008(Quantitative Ability)

Question. 74

Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is perfect square whose square root equals the total of the three original integers. Which of the following best describes the minimum, say m, of these three integers?

CAT/2007(Quantitative Ability)

Question. 75

Consider the set S = {2, 3, 4, ……, 2n + 1}, where ‘n’ is a positive integer larger than 2007. Define X as the average of the odd integers in S and Y as the average of the even integers in S. What is the value of X – Y?

CAT/2007(Quantitative Ability)

Question. 76

A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja. giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque.

Which of the following is a valid statement about the cheque amount?

(1) Over Rupees 13 but less than Rupees 14

(2) Over Rupees 7 but less than Rupees 8

(3) Over Rupees 22 but less than Rupees 23

(4) Over Rupees 18 but less than Rupees 19

(5) Over Rupees 4 but less than Rupees 5

CAT/2007(Quantitative Ability)

Question. 77

^{How many pairs of positive integers m, n satisfy   where ‘n’ is an odd integer less than 60?}

Comprehension

Directions for Questions 7 to 10: Each question is followed by two statements A and B. Indicate your response based on the following directives.

Mark (1) if the questions can be answered using A alone but not using B alone.

Mark (2) if the question can be answered using B alone but not using A alone.

Mark (3) if the question can be answered using A and B together, but not using either A or B alone.

Mark (4) if the question cannot be answered even using A and B together.

CAT/2007(Quantitative Ability)

Question. 78

Consider integers x, y, z. What is the minimum possible value of  x²y²z² + + ?

A: x + y + z = 89.

B: Among x, y, z two are equal.

Comprehension

Directions for Questions 15 and 16:

Answer the following questions based on the information given below:

Let S be the set of all pairs (i, j) where 1≤ i < j ≤ n and n ≥ 4 . Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise. For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3) are also friends, but (1, 4) and (2, 3) are enemies.

CAT/2007(Quantitative Ability)

Question. 79

For general ‘n’, how many enemies will each member of S have?

Comprehension

Directions for Questions 15 and 16:

Answer the following questions based on the information given below:

Let S be the set of all pairs (i, j) where 1≤ i < j ≤ n and n ≥ 4 . Any two distinct members of S are called “friends” if they have one constituent of the pairs in common and “enemies” otherwise. For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1, 2) and (1, 3) are friends, (1, 2) and (2, 3) are also friends, but (1, 4) and (2, 3) are enemies.

CAT/2007(Quantitative Ability)

Question. 80

For general ‘n’, consider any two members of S that are friends. How many other members of S will be common friends of both these members?

CAT/2007(Quantitative Ability)

Question. 81

In a tournament, there are n teams T₁ , T₂ ,..., T_n , with n > 5. Each team consists of ‘k’ players, k > 3. The following pairs of teams have one player in common:

T₁& T₂ ,T₂ & T₃ , ......, T_n, and T_n & T₁ 

No other pair of teams has any player in common. How many players are participating in the tournament, considering all the ‘n’ teams together?

CAT/2007(Quantitative Ability)

Question. 82

Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?

Comprehension

Directions for Questions 24 and 25: Answer the following questions based on the information given below:

CAT/2007(Quantitative Ability)

Question. 83

Which of the following best describes a_n + b_n for even ‘n’?

Comprehension

Directions for Questions 24 and 25: Answer the following questions based on the information given below:

CAT/2007(Quantitative Ability)

Question. 84

If p = 1/3 and q = 2/3, then what is the smallest odd ‘n’ such that a_n+b_n<0.01?

CAT/2006(Quantitative Ability)

Question. 85

CAT/2006(Quantitative Ability)

Question. 86

If x = – 0.5, then which of the following has the smallest value?

CAT/2006(Quantitative Ability)

Question. 87

CAT/2006(Quantitative Ability)

Question. 88

CAT/2006(Quantitative Ability)

Question. 89

CAT/2006(Quantitative Ability)

Question. 90

When you reverse the digits of the number 13, the number increases by 18. How many other twodigit numbers increase by 18 when their digits are reversed?

CAT/2006(Quantitative Ability)

Question. 91

What are the values of x and y that satisfy both the equations?

CAT/2006(Quantitative Ability)

Question. 92

The sum of four consecutive two-digit odd numbers, when divided by 10, becomes a perfect square. Which of the following can possibly be one of these four numbers?

CAT/2006(Quantitative Ability)

Question. 93

Consider the set S = {1, 2, 3, . . ., 1000}. How many arithmetic progressions can be formed from the elements of S that start with 1 and end with 1000 and have at least 3 elements?

CAT/2006(Quantitative Ability)

Question. 94

The number of employees in Obelix Menhir Co. is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:

CAT/2005(Quantitative Ability)

Question. 95

If x = (16³ + 17³ + 18³ + 19³ ), then x divided by 70 leaves a remainder of

CAT/2005(Quantitative Ability)

Question. 96

The digits of a three-digit number A are written in the reverse order to form another three-digit number B. If B > A and B–A is perfectly divisible by 7, then which of the following is necessarily true?

CAT/2005(Quantitative Ability)

Question. 97

The rightmost non-zero digit of the number 30²⁷²⁰ is

CAT/2005(Quantitative Ability)

Question. 98

CAT/2005(Quantitative Ability)

Question. 99

For a positive integer n, let p_n denote the product of the digits of n, and s_n denote the sum of the digits of n. The number of integers between 10 and 1000 for which p_n + s_n = n is

CAT/2004(Quantitative Ability)

Question. 100

What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?

CAT/2004(Quantitative Ability)

Question. 101

Let x and y be positive integers such that x is prime and y is composite. Then

CAT/2004(Quantitative Ability)

Question. 102

Let n( > 1) be a composite integer such that √n is not an integer. Consider the following statements

I : n has a perfect integer-valued divisor which is greater than 1 and less than √n .

II : n has a perfect integer-valued divisor which is greater than √n but less than n

Then,

CAT/2004(Quantitative Ability)

Question. 103

Let a, b, c, d and e be integers such that a = 6b = 12c, and 2b = 9d = 12e. Then which of the following pairs contains a number that is not an integer?

CAT/2004(Quantitative Ability)

Question. 104

If a, a + 2 and a + 4 are prime numbers, then the number of possible solutions for a is

CAT/2004(Quantitative Ability)

Question. 105

The remainder, when (15²³ + 23²³) is divided by 19, is

CAT/2003(Quantitative Ability)

Question. 106

A positive whole number M less than 100 is represented in base 2 notation, base 3 notation, and base 5 notation. It is found that in all three cases the last digit is 1, while in exactly two out of the three cases the leading digit is 1. Then M equals

CAT/2003(Quantitative Ability)

Question. 107

How many even integers n, where 100 ≤ n ≤ 200, are divisible neither by seven nor by nine?

CAT/2003(Quantitative Ability)

Question. 108

The number of positive integers n in the range 12 ≤ n ≤ 40 such that the product (n-1)(n-2).....3.2.1 is not divisible by n is

CAT/2003(Quantitative Ability)

Question. 109

What is the remainder when 4⁹⁶ is divided by 6?

CAT/2003(Quantitative Ability)

Question. 110

The seven basic symbols in a certain numeral system and their respective values are as follow :

I = 1 , V = 5 , X = 10, L = 50, C = 100, D = 500, and M = 1000

In general, the symbols in the numeral system are read from left to right, starting with the symbol representing the largest value; the same symbol cannot occur continuously more than three times; the value of the numeral is the sum of the values of the symbols. For example , XXVII = 10 + 10 + 5 + 1 + 1= 27. An exception to the left to right reading occurs when a symbol is followed immediately by a symbol of greater value; then, the smaller value is subtracted from the larger. For example, XLVI = (50 – 10) + 5 + 1 = 46.

The value of the numeral MDCCLXXXVII is

CAT/2003(Quantitative Ability)

Question. 111

The seven basic symbols in a certain numeral system and their respective values are as follow :

I = 1 , V = 5 , X = 10, L = 50, C = 100, D = 500, and M = 1000

In general, the symbols in the numeral system are read from left to right, starting with the symbol representing the largest value; the same symbol cannot occur continuously more than three times; the value of the numeral is the sum of the values of the symbols. For example , XXVII = 10 + 10 + 5 + 1 + 1= 27. An exception to the left to right reading occurs when a symbol is followed immediately by a symbol of greater value; then, the smaller value is subtracted from the larger.

For example, XLVI = (50 – 10) + 5 + 1 = 46.

The value of the numeral MCMXCIX is

CAT/2003(Quantitative Ability)

Question. 112

The seven basic symbols in a certain numeral system and their respective values are as follow :

I = 1 , V = 5 , X = 10, L = 50, C = 100, D = 500, and M = 1000

In general, the symbols in the numeral system are read from left to right, starting with the symbol representing the largest value; the same symbol cannot occur continuously more than three times; the value of the numeral is the sum of the values of the symbols. For example , XXVII = 10 + 10 + 5 + 1 + 1= 27. An exception to the left to right reading occurs when a symbol is followed immediately by a symbol of greater value; then, the smaller value is subtracted from the larger.

For example, XLVI = (50 – 10) + 5 + 1 = 46.

 Which of the following can represent the numeral for 1995?

I. MCMLXXV

II. MCMXCV

III. MVD

IV. MVM

CAT/2002(Quantitative Ability)

Question. 113

Number S is obtained by squaring the sum of digits of a two digit number D. If difference between S and D is 27, then the two digit number D is

CAT/2002(Quantitative Ability)

Question. 114

When 2²⁵⁶ is divided by 17 the remainder would be

CAT/2002(Quantitative Ability)

Question. 115

At a book store, “MODERN BOOK STORE” is flashed using neon lights. The words are individually flashed at intervals of 2(1/2), 4(1/4), 5(1/8) seconds respectively, and each word is put off after a second. The least time after which the full name of the bookstore can be read again is

CAT/2002(Quantitative Ability)

Question. 116

After the division of a number successively by 3, 4 and 7, the remainders obtained are 2, 1 and 4 respectively. What will be the remainder if 84 divides the same number?

CAT/2002(Quantitative Ability)

Question. 117

If u, v, w and m are natural numbers such that u^m + v^m = w^m, then one of the following is true

CAT/2002(Quantitative Ability)

Question. 118

7⁶ⁿ – 6⁶ⁿ, where n is an integer > 0, is divisible by

CAT/2001(Quantitative Ability)

Question. 119

Out of 128 boxes of oranges, each box contains at least 120 and at most 144 oranges. The number of boxes containing the same number of oranges is at least

CAT/2001(Quantitative Ability)

Question. 120

In a 4 - digit number, the sum of the first two digits is equal to that of the last two digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?

CAT/2001(Quantitative Ability)

Question. 121

Anita had to do a multiplication. Instead of taking 35 as one of the multipliers, she took 53. As a result, the product went up by 540. What is the new product?

CAT/2001(Quantitative Ability)

Question. 122

In a number system the product of 44 and 11 is 3414. The number 3111 of this system, when converted to the decimal number system, becomes

CAT/2001(Quantitative Ability)

Question. 123

Every ten years the Indian government counts all the people living in the country. Suppose that the director of the census has reported the following data on two neighbouring villages Chota Hazri and Mota Hazri

Chota Hazri has 4,522 fewer males than Mota hazri.

Mota Hazri has 4,020 more females than males.

Chota Hazri has twice as many females as males.

Chota Hazri has 2,910 fewer females than Mota Hazri.

What is the total number of males in Chota Hazri?

CAT/2001(Quantitative Ability)

Question. 124

Let x, y and z be distinct integers. x and y are odd positive, and z is even positive. Which one of the following statements can not be true?

CAT/2000(Quantitative Ability)

Question. 125

Convert 1982 in base 10 to base 12

CAT/2000(Quantitative Ability)

Question. 126

Let D be a recurring decimal of the form D = 0.a1 a2 a1 a 2 a 1 a 2 .............where a1 and a2 lie between 0 and 9. Further at most one of them is zero. Which of the following numbers necessarily produces an integer when multiplied by D?

CAT/2000(Quantitative Ability)

Question. 127

P is the product of all the prime numbers between 1 to 100. Then the number of zeroes at the end of P are

CAT/2000(Quantitative Ability)

Question. 128

N = 1421 × 1423 × 1425 what is the remainder when N is divided by 12?

CAT/2000(Quantitative Ability)

Question. 129

CAT/2000(Quantitative Ability)

Question. 130

There are two integers 34041 and 32506, when divided by a three-digit integer n, leave the same remainder. What is the value of n?

CAT/2000(Quantitative Ability)

Question. 131

If x, y and z are odd integers then which of the following is necessarily false?

CAT/2000(Quantitative Ability)

Question. 132

55³ +17³ - 72³ is divisible by

CAT/1999(Quantitative Ability)

Question. 133

If n = 1 + x, where ‘x’ is the product of four consecutive positive integers, then which of the following statements is/are true?

I. ‘n’ is odd

II. ‘n’ is prime

III. ‘n’ is perfect square

CAT/1999(Quantitative Ability)

Question. 134

n² =  12345678987654321, then, n = ?

CAT/1999(Quantitative Ability)

Question. 135

When 7⁸⁴ is divided by 342, what is the remainder?

CAT/1999(Quantitative Ability)

Question. 136

A, B, C are three distinct digits. AB is a two digit number and CCB is a three digit number such that (AB)² = CCB where CCB > 320. What is the possible value of the digit B?

CAT/1999(Quantitative Ability)

Question. 137

For the given pair (x, y) of positive integers, such that 4x – 17y = 1 and x ≤ 1000, how many integer values of y satisfy the given conditions

CAT/1998(Quantitative Ability)

Question. 138

Five digit numbers are formed using only 0,1,2,3,4 exactly once. What is the difference between the maximum and minimum number that can be formed?

CAT/1998(Quantitative Ability)

Question. 139

n³ is odd. Which of the following statements is/are true?

I. n is odd

II. n² is odd

III. n² is even

CAT/1998(Quantitative Ability)

Question. 140

(BE)² = MPB, where B, E, M and P are distinct integers, then M = ?

CAT/1998(Quantitative Ability)

Question. 141

Three wheels can complete respectively 60,36,24 revolutions per minute. There is a red spot on each wheel that touches the ground at time zero. After how much time, all these spots will simultaneously touch the ground again?

CAT/1998(Quantitative Ability)

Question. 142

A certain number when divided by 899 leaves the remainder 63. Find the remainder when the same number is divided by 29.

CAT/1998(Quantitative Ability)

Question. 143

A is the set of positive integers such that when divided by 2,3,4,5 and 6 leaves the remainders 1,2,3,4 and 5 respectively. How many integer(s) between 0 and 100 belongs to set A?

CAT/1998(Quantitative Ability)

Question. 144

Number of students who have opted the subjects A, B, C are 60, 84, 108 respectively. The examination is to be conducted for these students such that only the students of the same subject are allowed in one room. Also the number of students in each room must be same. What is the minimum number of rooms that should be arranged to meet all these conditions?

CAT/1998(Quantitative Ability)

Question. 145

What is the digit in the unit place of 2⁵¹ ?

CAT/1998(Quantitative Ability)

Question. 146

A hundred digit number is formed by writing first 54 natural numbers in front of each other as 12345678910111213.................5354. Find the remainder when this number is divided by 8

CAT/1997(Quantitative Ability)

Question. 147

If n is an integer, how many values of n will give an integral value of (16n² + 7n + 6) / n?

CAT/1997(Quantitative Ability)

Question. 148

A student, instead of finding the value of 7/8th of a number, found the value of 7/18th of the number. If his answer differed from the actual one by 770, find the number.

CAT/1997(Quantitative Ability)

Question. 149

If m and n are integers divisible by 5, which of the following is not necessarily true?

CAT/1997(Quantitative Ability)

Question. 150

Which of the following is true?

CAT/1997(Quantitative Ability)

Question. 151

P, Q and R are three consecutive odd numbers in ascending order. If the value of three times P is three less than two times R, find the value of R.

CAT/1997(Quantitative Ability)

Question. 152

CAT/1997(Quantitative Ability)

Question. 153

P and Q are two integers such that (PQ) = 64. Which of the following cannot be the value of P + Q?

CAT/1996(Quantitative Ability)

Question. 154

If a number 774958A96B is to be divisible by 8 and 9, the values of A and B, respectively, will be

CAT/1996(Quantitative Ability)

Question. 155

If n is any odd number greater than 1, then n(n² – 1) is

CAT/1996(Quantitative Ability)

Question. 156

CAT/1996(Quantitative Ability)

Question. 157

A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs 1148, but the inventory reduced by 54.

What is the actual price per piece ?

CAT/1996(Quantitative Ability)

Question. 158

A salesman enters the quantity sold and the price into the computer. Both the numbers are two-digit numbers. Once, by mistake, both the numbers were entered with their digits interchanged. The total sales value remained the same, i.e. Rs 1148, but the inventory reduced by 54.

 What is the actual quantity sold ?

CAT/1995(Quantitative Ability)

Question. 159

Two positive integers differ by 4 and sum of their reciprocals is 10/21. Then one of the number is

CAT/1995(Quantitative Ability)

Question. 160

Three bells chime at an interval of 18, 24 and 32 minutes respectively. At a certain time they begin to chime together. What length of time will elapse before they chime together again?

CAT/1995(Quantitative Ability)

Question. 161

For the product n(n+1)(2n+1), n ∈ N, which one of the following is not necessarily true?

CAT/1995(Quantitative Ability)

Question. 162

The remainder obtained when a prime number greater than 6 is divided by 6 is

CAT/1995(Quantitative Ability)

Question. 163

Cost of 72 hens is Rs .....96.7..... Then, what will be the cost of hen, where two digits in place of “ ....... ” are not visible or are written in illegible hand-writing?

CAT/1995(Quantitative Ability)

Question. 164

Three consecutive positive even numbers are such that thrice the first number exceeds double the third number by 2 then the third number is

CAT/1995(Quantitative Ability)

Question. 165

5⁶ – 1 is divisible by

CAT/1994(Quantitative Ability)

Question. 166

What is the smallest number which when increased by 5 is completely divisible by 8, 11 and 24?

CAT/1994(Quantitative Ability)

Question. 167

 Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12 and 16 will leave the same remainder 4