Saturday, March 14, 2015

Free Test Number 002 for CAT, XAT and other MBA Exams

Five Free questions to help you prepare for CAT, XAT and other MBA Exams. Answers are avail below. Ask a doubt in the comment section in case you have doubts.

Today we focus on Verbal Ability questions. These questions have appeared in the most recent XAT Paper (XAT 2015).

Q1: The first and the last sentences of the paragraph are numbered 1 & 6. The others, labeled as A,B,C and D, are given below:

1. The world of cinema is indeed a strange one and baffles many a critic.


A. But there are incorrigible optimists who see a bright future.
B. The pundits still predict doom and they insist that it is the end of the road for cinema.
C. At the temples of the box office, fortunes are made and unmade.
D. The world of cinema has, they say, its own attraction.


6. Perhaps a positive outlook is not unwarranted. A doomsday approach is far too fatal at this stage.

Which of the following combinations given below is the most logically ordered?


a. 1DBAC6
b. 1CDAB6
c. 1CBAD6
d. 1BDAC6
e. 1BADC6

Q2. Which of the following is not a term of "disapproval"?

a. childlike
b. awful
c. imbecile
d. charlatan
e. infantile

Q3. It is a curious historical fact that modern quantum mechanics began with two quite different mathematical formulations: the different equation of Schrodinger, and the matrix algebra of Heisenberg. The two, apparently dissimilar, approaches were proved to be mathematically equivalent. Which of the following sentences would most meaningfully follow the above paragraph?

a. The two approaches did not start with the same mathematical formulations.
b. These two points of view were destined to complement one another and were ultimately synthesized in Dirac's transformation theory.
c. A third mathematical formulation given by Feynman combines the matrix algebra of Heisenberg and Integral calculus of Leibniz.
d. Quantum mechanics evolved in the twentieth century and came very close to particle physics, especially after the CERN experiments in Switzerland.
e. Earlier, the two formulations were mathematically similar.

Q4: Ranu is an ordinary sportsperson. In the last two university sprint events, her performances in the heats were pathetic. Which of the following, if true, weakens the above argument the most?

a. She had participated in the college swimming competition and finished last.
b. She is a national shot-put champion.
c. The last two times, Ranu had to compete with national level runners. Had she been in other heats, she would have reached quarterfinals.
d. Ranu was the only player who represented her college in the sprint events.
e. In the college sprint events, Ranu always won.

Q5. In the traditions of many religions throughout the world (including Judaeo – Christian beliefs), there has long been a sustained belief that the Universe as we know it today did not exist forever in the past, and that there was a spontaneous act which gave birth to all that has been, and all that will be. In other words, the Universe itself has not been eternal as our senses might indicates at first glance, ...

Which of the following options can meaningfully complete the above sentence?

a. but has a limited lifespan after its creation.
b. but our senses give us the right knowledge.
c. however, on second glance, our religious beliefs are right.
d. however, it is a ball of intense energy
e. however, it could not have been created.


Answer Key:

Q1: c
Q2: a
Q3: b
Q4: b
Q5: a

Friday, March 13, 2015

Solutions to Free Test 001

Today we look at the detailed solutions for Free test 001 for CAT, XAT and other MBA Exams.

1. 5 Students take a math test, and score different marks. The sum of the scores taken 2 at a time are: 38, 51, 55, 60, 64, 68, 72, 77, 85, 94. What is the difference between student with highest and lowest score?

Let a,b,c,d,e be the 5 scores, with a < b < c < d < e.
So, a + b = 38, d + e = 94 -- (1)
Also, adding all scores 4(a+b+c+d+e) = 664
Or, a + b + c + d + e = 166 -- (2)

From (1) and (2),
c  = 166 - 38 - 94 = 34

The second largest number, 51, has to be the sum of a,c and second largest number, 85, has to be the sum of c,e
So, a = 51 - 34 = 17 and e = 85 - 34 = 51

Required difference = 51  - 17 = 34.

2.  What is the remainder when 7100 is divided by 121?

 73 = 243 = 1(mod 121)
100 = 3x33 + 1
So, 7100= 133x7 (mod 121) = 7(mod 121)


3. Which among the following is the smallest?
21/2, 31/3, 41/4, 61/6 and 121/12

We will start by converting all numbers to the 12th power:
21/2 = 26/12 = 641/12
31/3 = 34/12 = 811/12
41/4 = 43/12 = 641/12
61/6 = 62/12 = 361/12
121/12 = 121/12

So, we have the smallest number as 121/12

4. 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?

The last digits of 4 consecutive odd numbers can be
(1,3,5,7) = last digit will be 6
(3,5,7,9) = last digit will be 4
(5,7,9,1) = last digit will be 2
(7,9,1,3) = last digit will be 0
(9,1,3,5) = last digit will be 8

Of this, (7,9,1,3) is the only possibility.
Let the numbers be 10a+7, 10a+9, 10a+11, 10a+13, where a is a single digit number.
Sum = 40a + 40 = 10 (4a+4)
Dividing by 10, we have 4(a+1)
This means that a+1 is a perfect square, and a > 0

So, a = 3 or 8
We have: 37,39,41,43 and 87,89,91,93.
Of these only 41 is present in the options.

5. A number of children are standing in a circle. They are evenly spaced and the 14th child is diametrically opposite the 37th child. How many children are in the circle?

Since the 14th is diametrically opposite the 37th, there are 37 - 14 = 23 children in the semicircle
So total children = 23x2 = 46

Free Test Number 001 for CAT, XAT and other MBA Exams

Five Free questions to help you prepare for CAT, XAT and other MBA Exams. Answers are avail below. Ask a doubt in the comment section in case you have doubts.

1. 5 Students take a math test, and score different marks. The sum of the scores taken 2 at a time are: 38, 51, 55, 60, 64, 68, 72, 77, 85, 94. What is the difference between student with highest and lowest score?

a. 27
b. 34
c. 43
d. Cannot be determined.

2.  What is the remainder when 7100 is divided by 121?

a. 7
b. 21
c. 49
d. None of the Above

3. Which among the following is the smallest?
21/2, 31/3, 41/4, 61/6 and 121/12

a. 21/2
b.41/4
c.61/6 
d.121/12

4. 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?

a. 21
b. 25
c. 41
d. 67

5. A number of children are standing in a circle. They are evenly spaced and the 14th child is diametrically opposite the 37th child. How many children are in the circle?

a. 46
b. 40
c. 42
d. Cannot be determined


Answer Keys:

1. (b) - 34
2. (a) - 7
3. (d) - 121/12
4. (c) - 41
5. (a) - 46

Solutions can be found here.