CAT Questions
If n is any odd number greater than 1, then n(n2 - 1) is
- divisible by 24 always
- divisible by 96 always
- divisible by 48 always
- None of these
Let N = 553 + 173 - 723. N is divisible by
- both 3 and 17
- both 7 and 13
- both 3 and 13
- both 17 and 7
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?
- 53
- 75
- 41
- 80
When 2256 is divided by 17, the remainder would be
- 1
- 14
- 16
- None of these
What will be remainder when (6767 + 67) is divided by 68?
- 67
- 63
- 66
- 1
Find the minimum integral value of n such that the division 55n/124 leaves no remainder
- 124
- 123
- 31
- 62
Let k be a positive integer such that k+4 is divisible by 7. Then the smallest positive integer n, greater than 2, such that k+2n is divisible by 7 equals
- 7
- 5
- 9
- 3
Let N = 1421 × 1423 × 1425. What is the remainder when N is divided by 12?
- 0
- 9
- 6
- 3
On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5?
- 0
- 1
- 2
- 4
What is the sum of all two-digit numbers that give a remainder of 3 when they are divided by 7?
- 676
- 777
- 683
- 666
The remainder obtained when a prime number greater than 6 is divided by 6 is
- 1 or 3
- 1 or 5
- 3 or 5
- 4 or 5
The remainder when 784 is divided by 342 is
- 0
- 1
- 49
- 341
The smallest number which when divided by 4, 6 or 7 leaves a remainder of 2, is
- 86
- 80
- 62
- 44
What is the remainder when 496 is divided by 6?
- 0
- 2
- 3
- 4
If x = (163 + 173 + 183 + 193), then x divided by 70 leaves a remainder of
- 0
- 1
- 35
- 69
Which is the least number that must be subtracted from 1856, so that the remainder when divided by 7, 12, and 16 is 4.
- 137
- 140
- 172
- 1361
What is the greatest number which exactly divides 110, 154 and 242?
What is the highest 3 digit number which is exactly divisible by 3, 5, 6 and 7?
A man earns x% on the first Rs. 2,000 and y% on the rest of his income. If he earns Rs. 700 from income of Rs. 4,000 and Rs. 900 from if his income is Rs. 5,000, find x%.
- 10%
- 15%
- 20%
- 25%
How much time will it take for an amount of Rs. 450 to yield Rs. 81 as interest at 4.5% per annum of simple interest?
- 4 years
- 4.5 years
- 5 years
- 5.5 years
A certain sum of money invested at some rate of simple interest triple itself in 4 years. In how many years the principal will become 9 times of itself at the same rate?
In a locality, two-thirds of the people have cable TV, one-fifth have VCR, and one-tenth have both. What is the fraction of people having either cable TV or VCR?
- 23/30
- 2/3
- 17/30
- 19/30
In a certain village, 22% of the families own agricultural land, 18% own a mobile phone and 1600 families own both agricultural land and a mobile phone. If 68% of the families neither own agricultural land nor a mobile phone, then the total number of families living in the village is
- 20000
- 10000
- 8000
- 5000
A five digit number is formed using digits 1, 3, 5, 7 and 9 without repeating any one of them. What is the sum of all such possible numbers?
- 6666666
- 6666600
- 6666660
- 6666000
A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees?
- 80
- 160
- 200
- 320
Consider the five points comprising of the vertices of a square and the intersection point of its diagonals. How many triangles can be formed using these points?
- 4
- 6
- 8
- 10
Boxes numbered 1, 2, 3, 4 and 5 are kept in a row, and they which are to be filled with either a red or a blue ball, such that no two adjacent boxes can be filled with blue balls. Then how many different arrangements are possible, given that all balls of a given colour are exactly identical in all respects?
- 8
- 10
- 15
- 22
How many five-digit numbers can be formed using the digits 2, 3, 8, 7, 5 exactly once such that the number is divisible by 125?
- 0
- 1
- 3
- 4
In a six-node network, two nodes are connected to all the other nodes. Of the remaining four, each is connected to four nodes. What is the total number of links in the network?
- 7
- 13
- 15
- 26
In how many ways can eight directors, the vice chairman and chairman of a firm be seated at a round table, if the chairman has to sit between the the vice chairman and a director?
- 9! × 2
- 2 × 7!
- 2 × 8!
- 2 × 6!
Let S be the set of five-digit numbers formed by digits 1, 2, 3, 4 and 5, using each digit exactly once such that exactly two odd position are occupied by odd digits. What is the sum of the digits in the rightmost position of the numbers in S?
- 192
- 216
- 228
- 294
Ten points are marked on a straight-line and 11 points are marked on another straight-line. How many triangles can be constructed with vertices from among the above points?
- 495
- 550
- 1045
- 2475
There are 6 tasks and 6 persons. Task 1 cannot be assigned either to person 1 or to person 2; task 2 must be assigned to either person 3 or person 4. Every person is to be assigned one task. In how many ways can the assignment be done?
- 144
- 180
- 192
- 360
What is the number of distinct terms in the expansion of (a + b + c)20?
- 210
- 231
- 242
- 253
During the essay writing stage of MBA admission process in a reputed B-School, each group consists of 10 students. In one such group, two students are batch mates from the same IIT department. Assuming that the students are sitting in a row, the number of ways in which the students can sit so that the two batch mates are not sitting next to each other, is
- 3540340
- 2874590
- 2903040
- None of the above
In the board meeting of a FMCG Company, everybody present in the meeting shakes hand with everybody else. If the total number of handshakes is 78, the number of members who attended the board meeting is
- 7
- 9
- 11
- 13
Ramesh plans to order a birthday gift for his friend from an online retailer. However, the birthday coincides with the festival season during which there is a huge demand for buying online goods and hence deliveries are often delayed. He estimates that the probability of receiving the gift, in time, from the retailers A, B, C and D would be 0.6, 0.8, 0.9 and 0.5 respectively.
Playing safe, he orders from all four retailers simultaneously. What would be the probability that his friend would receive the gift in time?
- 0.004
- 0.006
- 0.216
- 0.994
- 0.996
If a 4 digit number is formed with digits 1, 2, 3 and 5. What is the probability that the number is divisible by 25, if repetition of digits is not allowed?
- 1/12
- 1/6
- 1/8
- 1/4
An unbiased dice is thrown. What is the probability of getting
- (i) an even number
- (ii) a multiple of 3
- (iii) an even number or a multiple of 3
- (iv) an even number and a multiple of 3
One card is drawn from a pack of 52 cards, each of the 52 cards being equally likely to be drawn. Find the probability that the card drawn is:
- (i) an ace
- (ii) red
- (iii) either red or king
- (iv) red and a king
There are 4 red & 5 green balls in bag A and 5 red & 6 green balls in bag B. If a bag is selected at random and a ball is selected from that, what is the probability that it is red?
The internal evaluation for Economics course in an Engineering programme is based on the score of four quizzes. Rahul has secured 70, 90 and 80 in the first three quizzes. The fourth quiz has ten True-False type questions, each carrying 10 marks. What is the probability that Rahul’s average internal marks for the Economics course is more than 80, given that he decides to guess randomly on the final quiz?
- 12/1024
- 11/1024
- 11/256
- 12/256
A dice is rolled twice. What is the probability that the number in the second roll will be higher than that in the first?
- 5/36
- 8/36
- 15/36
- 21/36
- None of the above
Consider the system of linear equation
x1 + 2x2 + x3 = 3
2x1 + 3x2 + x3 = 3
3x1 + 5x2 + 2x3 = 1
The system has
- Infinite no. of solutions
- No solution
- Unique solution
- Exactly 3 solutions
The number of solutions of the equation 2x + y = 40 where both x and y are positive integers and x ≤ y is:
- 7
- 13
- 14
- 18
Three times the first of three consecutive odd integers is 3 more than twice the third. What is the third integer?
- 5
- 9
- 11
- 15
Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r ≠ 0?
- x + 2y - 3z = p
- 2x + 6y - 11z = q
- x - 2y + 7z = r
- 5p - 2q - r = 0
- 5p + 2q + r = 0
- 5p + 2q - r = 0
- 5p - 2q + r = 0
If x and y are integers, then the equation 5x + 19y = 64 has
- A solution for -59 < y < -56
- No solution for x > 250 and y > -100
- A solution for 250 < x < 300
- No solution for x < 300 and y < 0
Using only 2, 5, 10, 25, and 50 paisa coins, what will be the minimum number of coins required to pay exactly 78 paise, 69 paise and Rs. 1.01 to three different persons?
- 17
- 18
- 19
- 20
