CAT Questions

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

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

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

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

Line Graph

Answer the questions on the basis of the data presented in the figure below.

 

1. During 1996-2002, the number of commodities that exhibited a net overall increase and net overall decrease, respectively, were

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

2. The number of commodities that experienced a price decline for two or more consecutive years is

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

3. For which commodities did a price increase immediately follow a price decline only once in this period?

  1. Rice, edible oil and dal
  2. Egg and onion
  3. Onion only
  4. Egg and dal

Line Graph

The length of an infant is one of the measures of his or her development in the early stages of his or her life. The figure below shows the growth chart of four infants in the first five months of life.

1. After which month did Seeta's rate of growth start to decline?

  1. Never
  2. Second month
  3. Third month
  4. Fourth month

2. Who grew at the fastest rate in the first two months of life?

  1. Shyam
  2. Geeta
  3. Ram
  4. Seeta

3. The rate of growth during the third month was the lowest for

  1. Ram
  2. Shyam
  3. Seeta
  4. Geeta

4. Among the four infants, who grew the least in the first five months of life?

  1. Shyam
  2. Ram
  3. Geeta
  4. Seeta

Bar Charts

Answer the questions on the basis of the following two charts.

Note: Availability is defined as production less export.

 

1. In which year during the period 1996-1999 was Chaidesh’s export of tea, as a proportion of tea produced, the highest?

  1. 1996
  2. 1997
  3. 1998
  4. 1999

2. In which of the following years was the population of Chaidesh the lowest?

  1. 1995
  2. 1996
  3. 1997
  4. 1999

3. The area under tea cultivation continuously decreased in all four years from 1996 to 1999, by 10%, 7%, 4%, and 1%, respectively. In which year was tea productivity (production per unit of area) the highest?

  1. 1996
  2. 1997
  3. 1998
  4. 1999

Bar Charts

Answer the questions on the basis of the data presented in the figure below.

 

1. Which of the following statements is correct?

  1. September rainfall exceeds 50 cm in each location.
  2. November rainfall exceeds 100 cm in each location.
  3. March rainfall is lower than September rainfall in each location.
  4. None of these

2. Locations 6 and 7 differ from all the rest because only in these two locations

  1. November rainfall is lower than March rainfall.
  2. Peak rainfall occurs in April.
  3. April rainfall is less than 200 cm.
  4. April rainfall exceeds March rainfall.

Bar Charts

The bar chart below shows the revenue received in million US Dollars (USD), from subscribers to a particular Internet service. The data covers the period 2008 to 2012 for the United States (US) and Europe. The bar chart also shows the estimated revenues from subscription to this service for the period 2013 to 2015.

 

1. The difference between the estimated subscription in Europe in 2013 and what it would have been if it were computed using the percentage growth rate of 2012 (over 2011), is closest to:

  1. 10
  2. 20
  3. 50
  4. 80

2. In 2008, sixty percent of subscribers in Europe were men. Given that women subscribers increase at the rate of 10 percent annum and men at the rate of 5 percent per annum, what is the approximate percentage growth of subscribers between 2008 and 2015 in Europe? The subscription prices are volatile and may change each year.

  1. 50
  2. 62
  3. 78
  4. 84

3. Consider the annual percent change in the gap between subscription revenues in the US and Europe. What is the year in which the absolute value of this change is the highest?

  1. 13-14
  2. 11-12
  3. 10-11
  4. 14-15

4. While the subscription in Europe has been growing steadily towards that of the US, the growth rate in Europe seems to be declining. Which of the following is closest to the percent change in growth rate of 2012 (over 2011) relative to the growth rate of 2010 (over 2009)?

  1. 60
  2. 20
  3. 17
  4. 35

Bar Charts

The bar graph given below shows the population (in lakhs) of two countries - Amberland and Marryland - in each year from 2004 to 2009.

1. For which two years was the percentage increase in the population of Marryland over the previous year the same?

  1. 2007 and 2009
  2. 2006 and 2008
  3. 2004 and 2007
  4. 2004 and 2005

2. If the percentage increase in the population of Amberland in 2010 over 2009 was the same as that in 2006 over 2005, then what was the population (in lakhs) of Amberland in the year 2010?

  1. 2040
  2. 1800
  3. 1760
  4. 1980

Mixed Graphs

Each point in the graph below shows the profit and turnover data for a company. Each company belongs to one of the three industries: textile, cement and steel.

 

1. For how many companies does the profit exceed 10% of turnover?

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

2. For how many steel companies with a turnover of more than 2000 is the profit than 300?

  1. 0
  2. 1
  3. 2
  4. 7

3. An investor wants to buy stock of only steel or cement companies with a turnover more than 1000 and profit exceeding 10% of turnover. How many choices are available to the investor?

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

Mixed Graphs

The data points in the figure below represent monthly income and expenditure data of individual members of four families - A, B, C and D. Savings is defined as

Savings = Income - Expenditure

 

1. Which family has the lowest average income?

  1. A
  2. B
  3. C

2. Which family has the highest average expenditure?

  1. A
  2. B
  3. C
  4. D

3. Which family has the lowest average savings?

  1. A
  2. B
  3. C
  4. D

4. The highest amount of savings accrues to a member of which family?

  1. A
  2. B
  3. C
  4. D

Mixed Graphs

The following sketch shows the pipelines carrying material from one location to another. Each location has a demand for material.

The demand at Vaishali is 400, at Jyotishmati is 400, at Panchal is 700, and at Vidisha is 200. Each arrow indicates the direction of material flow through the pipeline. The flow from Vaishali to Jyotishmati is 300. The quantity of material flow is such that the demands at all these locations are exactly met. The capacity of each pipeline is 1,000.

 

1. The quantity moved from Avanti to Vidisha is

  1. 1000
  2. 800
  3. 700 
  4. 200

2. The free capacity available at the Avanti-Vaishali pipeline is

  1. 0
  2. 100
  3. 200
  4. 300 

Mixed Graphs

The graph given below shows the statistics of 12 Cricket players. Each point on the graph indicates the average score per match of a player and the number of matches played by that player. Each of the players plays for one of the four teams - Team 1, Team 2, Team 3 and Team 4.

 

1. If only the runs scored by the above mentioned 12 players are considered, then which team has got the maximum aggregate score?

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

2. How many players are there who have played more than 200 matches and have scored less than 9,000 runs?

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

3. What is the overall average score of those players of Team 4, whose averages are better than the average of that player who has played the second highest number of matches for Team 3?

  1. 42.50
  2. 41.16
  3. 42.07
  4. 43.40 

Pie Charts

Chart 1 shows the distribution by value of top 6 suppliers of MFA Textiles. Chart 2 shows the distribution by quantity of top 6 suppliers of MFA Textiles. The total value is 5760 million Euro (European currency). The total quantity is 1.055 million tonnes.

1. The country which has the highest average price is

  1. India
  2. Switzerland
  3. Turkey
  4. USA

2. The average price in Euro per kilogram for Turkey is roughly

  1. 4.80
  2. 5.60
  3. 4.20
  4. 6.20

Pie Charts

A traveler spent some money in six different nations. The pie charts given below show the money spent in each of the nations as a percentage of the total money spent in that year. The money spent in China in the year 2007 was 75% less than the money spent in China in the year 2006. The money spent in India was same for the two years.

 

1. In the year 2007, what percentage of the total money spent by the traveler was spent in China?

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

2. If the money spent by the traveler in Britain, America and Africa together was 32 dollars more in 2006 than in 2007, then how much money (in dollars) was spent by the traveler in Australia in the year 2007?

  1. 120
  2. 96
  3. 80
  4. 64

Pie Charts

Study the following pie charts regarding to sales of 5 models of cars for the years 2010 and 2011, and answer the question

 

1. If the 2010 sales for all car models is 80,000 and these have grown by 25% in 2011, then what is the approximate increase in the number of Figo cars sold in 2011 over 2010?

  1. 2,200
  2. 4,500
  3. 4,860
  4. 12,200 

2. If the 2010 sales for all car models is 80,00 and these have grown by 25% in 2011, then how many models have grown more than the average growth rate for all the models taken together?

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