In this section we will learn about important CAT question and answers are mostly asked in cat exams. These CAT question and answers are important for all the CAT aspirants preparing for the exam.

## Quantitative Aptitude

### HCF AND LCM

1. 6 different sweet varieties of count 32, 216, 136, 88, 184, 120 were ordered for a particular occasion. They need to be packed in such a way that each box has the same variety of sweet and the number of sweets in each box is also the same. What is the minimum number of boxes required to pack?

(a)129

(b)64

(c)48

(d)97

### FACTORS

If a three digit number ‘abc’ has 3 factors, how many factors does the 6-digit number ‘abcabc’ have?

1. 16 factors
2. 24 factors
3. 16 or 24 factors
4. 20 factors

### REMAINDERS

The integers 573921 and 575713 when divided by a 3 digit number leave the same remainder. What is that 3 digit number?

1. 206
2. 256
3. 274
4. 189

### FACTORIALS

Let K be the largest number with exactly 3 factors that divide 25! How many factors does (k – 1) have?

1. 16
2. 12
3. 9
4. 14

### DIGITS

[x] is the greatest integer less than or equal to x. Find the number of positive integers n such that [n11]=[n13].

1. 31
2. 25
3. 35
4. 40

### RATIOS, MIXTURES; AVERAGES

1 unit of x% alcohol is mixed with 3 units of y% alcohol to give 60% alcohol. If x > y, how many integer values can x take?

1. 19
2. 2
3. 21
4. 13

### PERCENTS, PROFITS, SICI

On a certain sum of money, compound interest earned at the end of three years = Rs. 1456. Compound interest at the end of two years is Rs. 880. Compute the principal invested.

1. Rs. 2,400
2. Rs. 2,800
3. Rs. 2,000
4. Rs. 1,600

### SPEED, TIME, DISTANCE; RACES

In a hurry? Have a go at these problems before you leave!! Maybe we could help you calculate how late you are going to be ….

### LOGARITHMS AND EXPONENTS

log3x3log3x5 < 0. If a, b are integers such that x = a, and x = b satisfy this inequation, find the maximum possible value of a – b.

1. 214
2. 216
3. 200
4. 203

### PIPES, CISTERNS; WORK, TIME

A mining team made a plan to mine up to 300 m in a certain number of days. After working as per plan for 5 days, they added new members to the team and hence could mine 5 m more per day. In this way, 4 days before the planned date, they had mined 295 m. How many meters of mining was initially planned for each day?

1. 30 m
2. 12.5 m
3. 15 m
4. 7.5 m

### SET THEORY

Set Fn gives all factors of n. Set Mn gives all multiples of n less than 1000. Which of the following statements is/are true?

i. F108F84=F12
ii. M12M18=M36
iii. M12M18=M36
iv. M12(M6M4)

1. i, ii and iii only
2. i, iii and iv only
3. i and iii only
4. All statements are true

### GEOMETRY

ABCDE is a regular pentagon. O is a point inside the pentagon such that AOB is an equilateral triangle. What is ∠OEA?

1. 66°
2. 48°
3. 54°
4. 72°

### CO-GEO

Region Q is defined by the equation 2x + y < 40. How many points (r, s) exist such that r is a natural number and s is a multiple of r?

1. 84
2. 92
3. 105
4. 72
1. ### AREA OF TRIANGLE

PQRS is a square of sides 2 cm & ST = 2 cm. Also, PT=RT. What is the area of ∆PST?

1. 2 cm2
2. √3 cm2
3. √2 cm2
4. 1/√2

### TRIGONOMETRY

A man standing on top of a tower sees a car coming towards the tower. If it takes 20 minutes for the angle of depression to change from 30° to 60°, what is the time remaining for the car to reach the tower?

1. 20√3 minutes
2. 10 minutes
3. 10√3 minutes
4. 5 minutes

Let x3– x2 + bx + c = 0 has 3 real roots which are in A.P. which of the following could be true

1. b=2,c=2
2. b=1,c=1
3. b= -1,c = 1
4. b= -1,c= -1

### FUNCTIONS

If f(x)=1g(x), then which of the following is correct?

1. f(f(g(g(f(x))))) = g(f(g(g(g(x)))))
2. f(f(f(g(g(g(f(g(x)))))))) = g(g(g(g(f(g(f(f(x))))))))
3. f(f(g(f(x)))) = g(g(f(g(x))))
4. f(g(f(f(g(f(g(g(x)))))))) = g(g(g(g(f(f(f(f(x))))))))

### INEQUALITIES

Solve the inequality: x3 – 5x2 + 8x – 4 > 0.

1. (2, ∞)
2. ((1, 2) ∪ (2, ∞)
3. (-∞, 1) ∪ (2, ∞)
4. (-∞, 1)

### POLYNOMIALS

Polynomials is a simple topic which involves a lot of basic ideas. Make sure you know the basics.

How many pairs of integer (a, b) are possible such that a2 – b2 = 288?

1. 6
2. 12
3. 24
4. 48

### PROGRESSIONS

Consider a, b, c in a G.P. such that |a + b + c| = 15. The median of these three terms is a, and b = 10. If a > c, what is the product of the first 4 terms of this G.P.?

1. 40000
2. 32000
3. 8000
4. 48000

### COMBINATORICS

Sum of three Natural numbers a, b and c is 10. How many ordered triplets (a, b, c) exist?

1. 45
2. 36
3. 54
4. 28

### DATA SUFFICIENCY

What is n? Statement 1: n > 10
Statement 2: n < 12

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

## Verbal Ability

### PARA JUMBLE

A. But that would require a tough look at the economy, at the dearth of productivity, and at how it might be possible to restore conditions of growth. It would require serious investment, risk-taking, and nerve.

B. If those currently carping about the tax affairs of the rich really did care about raising tax revenues, they would concentrate on raising the volume of wealth that can be taxed.

C. The problem with the eagerness to recast economic problems, from a failure to cut the deficit to the continued inability to restore conditions of growth, as a moral issue and an erring on the part of selfish individuals who just aren’t giving enough back, leaves the real problems untouched.

D. These are not qualities today’s political class have in abundance. So, instead, they continue to project blame, singling out individuals for moral censure in the hope that they will increase their payments to the state.

3. BACD
4. CABD

### SENTENCE CORRECTION

One of the problems that occur as a result of coal mining is the increasing incidences of lung cancer.

1. that occurs as a result of coal mining are the increasing incidences
2. that occurs as a result of coal mining is the increasing incidence
3. that occur as a result of coal mining are the increasing incidences
4. that occur as a result of coal mining is the increasing incidence

### PARAGRAPH COMPLETION

Where you get to choose how the movie ends; or how it should end!

### CRITICAL REASONING

It’s time to read between the sentences… think between them rather!

### WORD USAGE

Word Usage questions often appear in the CAT. Questions from the topic for Practice.

### PARA SUMMARY

Questions from Para Summary.

### TEXT COMPLETION

Text Completion questions often feature in the CAT. Take a look at these for practice.

## DI and LR

### BAR GRAPHS

In 2002, the growth rate of the overall sector was 39%, what was the growth rate seen by SCT?

1. 50%
2. 75%
3. 30%
4. 40%

In 2004, the entire industry added $4bn, of which an increase of$1bn was contributed by COGN, what was the growth rate seen by the entire sector in 2004?

1. 20%
2. 34%
3. 52%
4. Cannot be determined

### PIE CHARTS

What was the profit margin for company B?

1. 12.33%
2. 8.33%
3. 11.11%
4. 12.5%

How much profit did company E make?

1. Rs. 40 Crores
2. Rs. 35 Crores
3. Rs. 50 Crores
4. Rs. 60 Crores

What was the profit margin for company B?

1. 12.33%
2. 8.33%
3. 11.11%
4. 12.5%

### MULTIPLE GRAPHS

Multiple Graphs questions often feature in the CAT.Questions from this topic for practice.

### WORD PROBLEMS

Five students, P, Q, R, S and T stand in a line in some order and receive cookies and biscuits to eat. No student gets the same number of cookies or biscuits. The person first in the queue gets the least number of cookies. Number of cookies or biscuits received by each student is a natural number from 1 to 9 with each number appearing at least once.

1. Who was 4th in the queue?

2. How many cookies did Q get?

### LINE GRAPHS

Line Graphs questions often feature in the CAT.Questions from this topic for practice.

### SEQUENCING

Sequencing questions often feature in the CAT.Questions from this topic for practice.

### GRID PUZZLES

If you remove the two squares on opposite ends of a diagonal on a chess board, is it impossible to fill the remaining 62 squares with dominoes?

### MATH PUZZLES

There is only one natural number whose successor is a perfect cube and predecessor is a perfect square. Find it.

### VISUALIZATION

350 million Rubiks cubes have been sold thus far. That’s staggering. Buy one and have a good look at it.

### OTHER PATTERNS

Did you know that number of spirals in the heads of Sunflowers is either 21 and 34, or 34 and 55.Do you know what is special about these numbers?

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