CAT Quant Questions

If N = (11^(p+7)) (7^(q-2)) (5^(r+1)) (3^s) is a perfect cube

• Numbers

If N = (11^{p + 7})(7^{q – 2})(5^{r + 1})(3^s) 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

If the product of three consecutive positive integers is 15600

• 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

Let f(x) = x^2 and g(x) = 2x, for all real x

• 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

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

• Quant Quadratic

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

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

A quadratic function f(x) attains a maximum of 3 at x = 1

• 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

If both a and b belong to the set {1, 2, 3, 4}, then the number of equations

• 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

Let p and q be the roots of the quadratic equation x^2 - (α-2)x - α - 1 = 0

• 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

The number of roots common between the two equations x^3 + 3x^2 + 4x + 5 = 0

• 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

One root of x^2 + kx - 8 = 0 is square of the other. Then the value of k is

• 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

What is the value of m which satisfies 3m^2 - 21m + 30

• 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

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

• 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

The minimum possible value of the sum of the squares of the roots

• 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

What is the sum of the following series? - 64, - 66, - 68, ..., - 100

• 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

If three positive real numbers x, y and z satisfy y - x = z - y and xyz = 4

• 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)

If log3 2, log3 (2^x - 5), log3 (2^x - 7/2) are in arithmetic progression

• Progressions
• Logarithms

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

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

Consider a triangle drawn on the X-Y plane with its three vertices of (41, 0), (0, 41) and (0, 0)

• 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

Consider the set S = {1, 2, 3, ..., 1000}. How many arithmetic progressions can be formed

• 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

For a Fibonacci sequence, from the third term onwards, each term in the sequence

• 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

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

• 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

If the harmonic mean between two positive numbers is to their geometric mean as 12:13

• 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

The number of common terms in the two sequences 17, 21, 25, ...,

• 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

The integers 1, 2, ..., 40 are written on a blackboard. The following operation

• 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

If p, q and r are three unequal numbers such that p, q and r are in AP

• 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

Seema has joined a new Company after the completion of her B.Tech

• 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

The sum of series, (–100) + (–95) + (–90) + …

• 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

An infinite geometric progression a1, a2, a3, ... has the property

• Progressions

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

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

The Maximum Retail Price (MRP) of a product is 55% above its manufacturing cost

• 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%

A dealer offers a cash discount of 20% and still makes a profit of 20%

• 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%

A contractor estimates that a job will earn him Rs 8400

• 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%

A dishonest milkman professes to sell his milk at cost price but he mixes it with water

• 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%

A merchant has 1000 kg of sugar, part of which he sells at 8% profit

• 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

A trader makes a profit equal to the selling price of 75 articles when he sold 100 of the articles

• 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%

After allowing a discount of 11.11%, a trader still makes a gain of 14.28%

• 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%

A shop, which sold same marked price shirts, announced an offer

• 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

The manufacturer of a table sells it to a wholesale dealer at a profit of 10%

• Profit Loss

The manufacturer of a table sells it to a wholesale dealer at a profit of 10%. The wholesale dealer sells the table to a retailer at a profit of 30%. Finally, the retailer sells it to a customer at a profit of 50%. If the customer pays Rs 4290 for the table, then its manufacturing cost (in Rs) is

1. 1500
2. 2000
3. 2500
4. 3000

Mayank buys some candies for Rs 15 a dozen

• Profit Loss

Mayank buys some candies for Rs 15 a dozen and an equal number of different candies for Rs 12 a dozen. He sells all for Rs 16.50 a dozen and makes a profit of Rs 150. How many dozens of candies did he buy altogether?

1. 50
2. 30
3. 25
4. 45

If a seller gives a discount of 15% on retail price, she still makes a profit of 2%

• Profit Loss

If a seller gives a discount of 15% on retail price, she still makes a profit of 2%. Which of the following ensures that she makes a profit of 20%?

1. Give a discount of 5% on retail price
2. Give a discount of 2% on retail price
3. Increase the retail price by 2%
4. Sell at retail price