Quantitative Ability Quiz for XAT

Dear readers,

This quiz consists of questions from past
XAT actual papers. Leave your answers/ responses in the comments section below
and soon we’ll let you know the correct answers!

1. A manufacturer produces two types of products- A and B, which are
subjected to two types of operations, viz. grinding and polishing. Each unit of
product A takes 2 hours of grinding and 3 hours of polishing whereas product B
takes 3 hours of grinding and 2 hours of polishing. The manufacturer has 10
grinders and 15 polishers. Each grinder operates for 12 hours/day and each
polisher 10 hours/day. The profit margin per unit of A and B are Rs. 5/- and
Rs. 7/- respectively. If the manufacturer utilises all his resources for
producing these two types of items, what is the maximum profit that the
manufacturer can earn? 

(A) Rs. 280/- 

(B) Rs. 294/- 

(C) Rs.515/-

(D) Rs. 550/- 

(E) None of the above 

2. A tank internally measuring 150cm x 120cm x l00cm has 1281600cm3 water
in it. Porous bricks are placed in the water until the tank is full up to its
brim. Each brick absorbs one tenth of its volume of water. How many bricks, of
20cm x 6cm x 4cm, can be put in the tank without spilling over the water? 

(A) 1100          (B) 1200          (C) 1150          (D) 1250           (E) None of the above 


3. The chance of India winning a cricket match against Australia is 1/6.
What is the minimum number of matches India should play against Australia so
that there is a fair chance of winning at least one match? 

(A) 3                 (B) 4               (C)
5                (D) 6                (E) None of the above 

4. A chocolate dealer has to send chocolates of three brands to a
shopkeeper. All the brands are packed in boxes of same size. The number of
boxes to be sent is 96 of brand A, 240 of brand B and 336 of brand C. These
boxes are to be packed in cartons of same size containing equal number of
boxes. Each carton should contain boxes of same brand of chocolates. What could
be the minimum number of cartons that the dealer has to send? 

(A) 20               (B)
14              (C) 42              (D) 38  
          (E) 16

5. The scheduling officer for a local police department is trying to
schedule additional patrol units in each of two neighbourhoods – southern and
northern. She knows that on any given day, the probabilities of major crimes
and minor crimes being committed in the northern neighbourhood were 0.418 and
0.612, respectively,  and that the
corresponding probabilities in the southern neighbourhood were 0.355 and 0.520.
Assuming that all crime occur independent of each other and likewise that crime
in the two neighbourhoods are independent of each other, what is the
probability that no crime of either type is committed in either neighbourhood
on any given day?

A. 0.069           B. 0.225           C. 0.690           D. 0.775           E.
None of the above

6. A 25 ft long ladder is placed against the wall with its base 7 ft the
wall. The base of the ladder is drawn out so that the top comes down by half
the distance that the base is drawn out. This distance is in the range:

A. (2, 7)           B. (5, 8)           C. (9, 10)         D. (3, 7 )          E.
None of the above

7. In a locality, there are ten houses in a row. On a particular night a
thief planned to steal from three houses of the locality. In how many ways can
he plan such that no two of them are next to each other?

A. 56                B. 73                C. 80                D. 120              E.
None of the above

Answer question nos. 8 to 9 based on the following information

A man standing on a boat south of a light house observes his shadow to be
24 meters long, as measured at the sea level. On sailing 300 meters eastwards,
he finds his shadow as 30 meters long, measured in a similar manner. The height
of the man is 6 meters above sea level.

8. The height of the light house above the sea level is:

A. 90 meters

B. 94 meters

C. 96 meters

D. 100 meters

E. 106 meters

9. What is the horizontal distance of the man from the light house in the
second position?

A. 300 meters

B. 400 meters

C. 500 meters

D. 600 meters

E. None of the above

10. There are four machines in a factory. At exactly 8 pm, when the
mechanic is about to leave the factory, he is informed that two of the four
machines are not working properly. The mechanic is in a hurry, and decides that
he will identify the two faulty machines before going home, and repair them
next morning. It takes him twenty minutes to walk to the bus stop. The last bus
leaves at 8 : 32 pm. If it takes six minutes to identify whether a machine is
defective or not, and if he decides to check the machines at random, what is
the probability that the mechanic will be able to catch the last bus?

A. 0                  B. 1/6              C. 1/4              D. 1/3              E.

11. Little Pika who is five and half years old has just learnt addition.
However, he does not know how to carry. For example, he can add 14 and 5, but
he does not know how to add 14 and 7. How many pairs of consecutive integers
between 1000 and 2000 (both 1000 and 2000 included) can Little Pika add?

A. 150              B. 155              C. 156              D. 258              E.
None of the above

12. What is the maximum possible value of (21 Sin X + 72 Cos X)?

A. 21                B. 57                C. 63                D. 75                E.
None of the above

Answer question nos. 13 to 15 based on the following information.

Five years ago Maxam Glass Co. had estimated its staff requirements in the
five levels in their organization as: Level-1: 55; Level-2: 65; Level-3: 225;
Level-4: 255 & Level-5: 300. Over the years the company had recruited people
based on ad-hoc requirements, in the process also selecting ex-defence service
men and ex-policemen. The following graph shows actual staff strength at
various levels as on date.

13. The level in which the Ex-Defence Servicemen are highest in percentage
terms is:

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

14. If the company decides to abolish all vacant posts at all levels, which
level would incur the highest reduction in percentage terms?

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

15. Among all levels, which level has the lowest representation of

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

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1(b)    2(b)    
3(b)    4(b)     5(a)     6(e)  
7(a)    8(e)     9(c)   
10(d)    11(c)    12(d)    
13(d)    14(d)     15(c)