CAT Questions

Geometry

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y = 3x + c, then c is

  1. -5
  2. -6
  3. -7
  4. -8

Numbers

If n is a positive integer, then (√3+1)2n - (√3−1)2n is

  1. An even positive integer
  2. A rational number other than positive integers
  3. An odd positive integer
  4. An irrational number

Numbers

The last digit of the number 32015 is

  1. 1
  2. 3
  3. 5
  4. 7

Numbers

When we multiply a certain two-digit number by the sum of its digits, 405 is achieved. If you multiply the number written in reverse order of the same digits, we get 486. Find the number?

  1. 81
  2. 45
  3. 36
  4. 54

Numbers Divisibility

A positive integer is said to be a prime number if it is not divisible by any positive integer other than itself and 1. Let p be a prime number greater than 5. Then (p2 - 1) is

  1. always divisible by 6, and may or may not be divisible by 12
  2. always divisible by 24
  3. never divisible by 6
  4. always divisible by 12, and may or may not be divisible by 24

Numbers

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?

  1. 1
  2. 2
  3. 3
  4. 4

Numbers

The number of integers n satisfying -–n+2 ≥ 0 and 2n ≥ 4 is

  1. 0
  2. 1
  3. 2
  4. 3

Numbers

What is the right most non-zero digit of the number 302720?

  1. 1
  2. 3
  3. 7
  4. 9

Numbers

The product of all integers from 1 to 100 will have the following numbers of zeros at the end?

  1. 19
  2. 20
  3. 22
  4. 24

Numbers

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?

  1. 21
  2. 25
  3. 41
  4. 67

Numbers Linear Equations

The number of positive integer valued pairs (x, y) satisfying 4x - 17y = 1 and x ≤ 1000 is

  1. 55
  2. 57
  3. 58
  4. 59

Numbers

What are the last two digits of 72008?

  1. 01
  2. 21
  3. 41
  4. 61

Numbers

What is the digit in the unit’s place of 251?

  1. 1
  2. 2
  3. 4
  4. 8

Numbers

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

  1. 5
  2. 6
  3. 7
  4. 8

Numbers Numbers L1

How many times will the digit 5 come in counting from 1 to 99 excluding those which are divisible by 3?

  1. 16
  2. 15
  3. 14
  4. 13

Numbers Numbers L1

What is the number of all possible positive integer values of n for which n2 + 96 is a perfect square?

  1. 2
  2. 4
  3. 5
  4. Infinite

Numbers

If N = (11p + 7)(7q – 2)(5r + 1)(3s) is a perfect cube, where p, q, r and s are positive integers, then the smallest value of p + q + r + s is:

  1. 5
  2. 6
  3. 7
  4. 8
  5. 9

Numbers

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

  1. 1777
  2. 1785
  3. 1875
  4. 1877

Numbers

Let f(x) = x2 and g(x) = 2x, for all real x. Then the value of f(f(g(x)) + g(f(x))) at x = 1 is

  1. 16
  2. 18
  3. 36
  4. 40

Quant Quadratic

Largest value of min(2 + x2, 6 - 3x), when x > 0, is

  1. 1
  2. 2
  3. 3
  4. 4

Quant Quadratic

A quadratic function f(x) attains a maximum of 3 at x = 1. The value of the function at x = 0 is 1. What is the value f(x) at x = 10?

  1. -180
  2. -159
  3. -110
  4. -119

Quant Quadratic

If both a and b belong to the set {1, 2, 3, 4}, then the number of equations of the form ax2+ bx + 1 = 0 having real roots is

  1. 6
  2. 7
  3. 10
  4. 12

Quant Quadratic

Let p and q be the roots of the quadratic equation x2 - (α - 2)x - α - 1 = 0. What is the minimum possible value of p2 + q2?

  1. 0
  2. 3
  3. 4
  4. 5

Quant Quadratic

The number of roots common between the two equations x3 + 3x2 + 4x + 5 = 0 and x3 + 2x2 + 7x + 3 = 0 is

  1. 0
  2. 1
  3. 2
  4. 3

Quant Quadratic

One root of x2 + kx - 8 = 0 is square of the other. Then the value of k is

  1. 2
  2. -2
  3. 8
  4. -8

Quant Quadratic

What is the value of m which satisfies 3m2 - 21m + 30 < 0?

  1. m < 2 or m > 5; 2 < m < 5
  2. 2 < m < 5
  3. m < 2 or m > 5
  4. m > 2

Quant Quadratic

Which of the following values of x do not satisfy the inequality x2 - 3x + 2 > 0 at all?

  1. 0 ≥ x ≥ –2
  2. 0 ≤ x ≤ 2
  3. –1 ≥ x ≥ –2
  4. 1 ≤ x ≤ 2

Quant Quadratic

The minimum possible value of the sum of the squares of the roots of the equation x2 + (a + 3)x - (a + 5) = 0 is

  1. 1
  2. 2
  3. 3
  4. 4

Progressions

What is the sum of the following series?

- 64, - 66, - 68, …… , - 100

  1. - 1458
  2. - 1558
  3. - 1568
  4. - 1664
  5. None of the above

Progressions

If three positive real numbers x, y and z satisfy y - x = z - y  and xyz = 4, then what is the minimum possible value of y?

  1. 2(1/4)
  2. 2(2/3)
  3. 2(1/3)
  4. 2(3/4)

Progressions Logarithms

If log3 2, log3 (2x - 5), log3 (2x - 7/2) are in arithmetic progression, then the value of x is equal to

  1. 2
  2. 3
  3. 4
  4. 5

Progressions Linear Equations

Consider a triangle drawn on the X-Y plane with its three vertices of (41, 0), (0, 41) and (0, 0), each vertex being represented by its (X, Y) coordinates. The number of points with integer coordinates inside the triangle (excluding all the points on the boundary) is

  1. 741
  2. 780
  3. 800
  4. 820

Progressions

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?

  1. 3
  2. 4
  3. 6
  4. 7

Progressions

For a Fibonacci sequence, from the third term onwards, each term in the sequence is the sum of the previous two terms in that sequence. If the difference in squares of 7th and 6th terms of this sequence is 517, what is the 10th term of this sequence?

  1. 76
  2. 108
  3. 123
  4. 147

Progressions

Fourth term of an arithmetic progression is 8. What is the sum of the first 7 terms of the arithmetic progression?

  1. 7
  2. 35
  3. 56
  4. 64

Progressions

If the harmonic mean between two positive numbers is to their geometric mean as 12 : 13; then the numbers could be in the ratio

  1. 12 : 13
  2. 4 : 9
  3. 2 : 3
  4. 1/12 : 1/13

Progressions

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

  1. 19
  2. 20
  3. 77
  4. 78

Progressions

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?

  1. 821
  2. 820
  3. 819
  4. 781

Progressions

If p, q and r are three unequal numbers such that p, q and r are in A.P., and p, r-q and q-p are in G.P., then p : q : r is equal to

  1. 1 : 2 : 3
  2. 2 : 3 : 4
  3. 3 : 2 : 1
  4. 1 : 3 : 4

Progressions

Seema has joined a new Company after the completion of her B.Tech from a reputed engineering college in Chennai. She saves 10% of her income in each of the first three months of her service and for every subsequent month, her savings are Rs. 50 more than the savings of the immediate previous month. If her joining income was Rs. 3000, her total savings from the start of the service will be Rs. 11400 in

  1. 6 months
  2. 12 months
  3. 18 months
  4. 24 months

Progressions

The sum of series, (–100) + (–95) + (–90) + …………+ 110 + 115 + 120, is:

  1. 0
  2. 220
  3. 340
  4. 450
  5. None of the above

Progressions

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

  1. 1/32
  2. 2/32
  3. 3/32
  4. 4/32

Profit Loss

The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost. The product is sold through a retailer, who earns 23% profit on his purchase price. What is the profit percentage (expressed in nearest integer) for the manufacturer who sells his product to the retailer? The retailer gives 10% discount on MRP.

  1. 31%
  2. 22%
  3. 15%
  4. 13%
  5. 11%

Profit Loss

A dealer offers a cash discount of 20% and still makes a profit of 20%, when he further allows 16 articles to a dozen to a particularly sticky bargainer. How much percent above the cost price were his wares listed?

  1. 75%
  2. 66 2/3%
  3. 100%
  4. 80%

Profit Loss

A contractor estimates that a job will earn him Rs 8400. His estimate covers material, labour and 5% profit. The cost of material and labour is in the ratio of 3 : 7. When the contractor begins his job, however, he discovers that the cost of material has increased by 10% and the labour cost has risen by 15%. Calculate his loss percent

  1. 7.36%
  2. 7.59%
  3. 7.49%
  4. 7.39%

Profit Loss

A dishonest milkman professes to sell his milk at cost price but he mixes it with water and thereby gains 25%. The percentage of water in the mixture is

  1. 4%
  2. 6.25%
  3. 20%
  4. 25%

Profit Loss

A merchant has 1000 kg of sugar, part of which he sells at 8% profit and the rest at 18% profit. He gains 14% on the whole. The quantity sold at 18% profit is

  1. 640 kg
  2. 400 kg
  3. 600 kg
  4. 560 kg

Profit Loss

A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles. What % profit did he make in the transaction?

  1. 100%
  2. 200%
  3. 250%
  4. 300%

Profit Loss

After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percentage above the cost price does he mark on his goods?

  1. 16%
  2. 22.22%
  3. 28.56%
  4. 35%

Profit Loss Linear Equations

A shop, which sold same marked price shirts, announced an offer - if one buys three shirts then the fourth shirt is sold at a discounted price of ₹100 only. Patel took the offer. He left the shop with 20 shirts after paying ₹20,000. What is the marked price of a shirt?

  1. ₹1260
  2. ₹1300
  3. ₹1350
  4. ₹1400
  5. ₹1500