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July 5th, 2014, 09:05 AM
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Join Date: Mar 2012
Re: CAT Model questions papers

This is the CAT Model questions paper:

1. Consider the set   2,3, 4........2 1 , S n  
where m is n positive integer than 2007.
Define X as the average of the odd
integers in S and Y as the average of the
even integers in S. What is the value of X
– Y?
a. 0
b. 1
c. 1
2
n
d. 1
2
n
n

e. 2008
2. Ten years ago, the ages of the members of
a joint family of eight people added up to
231 years. Three years later, one member
died at the age of 60 years and a child was
born during the same year. After another
three years, one more member died, again
at 60, and a child was born during the
same year. The current average age of this
eight-member joint family is nearest to:
a. 23 years
b. 22 years
c. 21 years
d. 25 years
e. 24 years
3. A function f(x) satisfies f(1) = 3600, and
f(1) + f(2)+ ……+f(n) = n2f(n), for all
positive integers n > 1. what is the value of
f(9)?
a. 80
b. 240
c. 200
d. 100
e. 120
4. Suppose you have a currency, named
Miso, in three denominations: 1 Miso, 10
Misos and 50 Misos. In how many ways
can you pay a bill of 107 Misos?
a. 17
b. 16
c. 18
d. 15
e. 19
5. A confused bank teller transposed the
rupees and paise when he cashed a cheque
for Shailaja, giving her rupees instead of
paise and paise instead of rupees. After
buying a toffee for 50 paise, Shailaja
noticed that she was left with exactly three
times as much as the amount on the
cheque. Which of the following is a valid
statement about the cheque amount?
a. Over Rupees 7 but less than Rupees 8
b. Over Rupees 22 but less than Rupees
23
c. Over Rupees 18 but less than Rupees
19
d. Over rupees 4 but less than Rupees 5
e. Over Rupees 13 but less than Rupees
14
6. How many pairs of positive integers m, n
satisfy 1 4 1
12 m n
  , where n is an odd
integer less than 60?
a. 6
b. 4
c. 7
d. 5
e. 3
Direction for questions 7 to 10: Each question
is followed by two statements A and B indicate
your responses based on the following
directives:
if the question can be answered using a alone
but not using B alone.
7. The average weight of a class of 100
students is 45 kg. The class consists of two
sections, I and 11, each with 50 students.
The average weight, WI’ of Section I is
smaller than the average weight WII’ of
Section II. If the heaviest student say
Deepak, of Section II is moved to Section
I, and the lightest Student, say Poonam, of
Section I is moved to Section II, then the
average weights of the two sections are
switched, i.e., the average weight of
Section I becomes WII and that of Section
II becomes WI. What is the weight of
Poonam?
A. 1.0 II I W W  
B. Moving Deepak from section II to I
(without any more from I to II) makes
the average weights of the two sections
equal.
a. If the question can be answered using a
alone but not using B alone.
b. If the question can be answered using
B alone but not using A alone.
c. If the question can be answered using
A and B together, but not using either
A or B alone.
d. If the question cannot be answered
even using A and B together.
8. ABC Corporation is required to maintain
at least 400 Kilolitres of water at all times
in its factory, in order to meet safety and
regulatory requirements. ABC is
considering the suitability of a spherical
tank with uniform wall thickness for the
purpose. The outer diameter of the tank is
10 meters. Is the tank’ capacity adequate
to meet ABC’s requirements?
A. The inner diameter of the tank is at
least 8 meters.
B. The tank weighs 30,000 kg when
empty, and is made of a material with
density of 3gm/cc.
a. If the question can be answered using a
alone but not using B alone.
b. If the question can be answered using
B alone but not using A alone.
c. If the question can be answered using
A and B together, but not using either
A or B alone.
d. If the question cannot be answered
even using A and B together.
9. Consider integers x, y and z. What is the
minimum possible value of 2 2 2 x y z   ?
A. 89 x y z   
B. Among x, y, z two are equal
a. If the question can be answered using a
alone but not using B alone.
b. If the question can be answered using
B alone but not using A alone.
c. If the question can be answered using
A and B together, but not using either
A or B alone.
d. If the question cannot be answered
even using A and B together.
10. Rahim plans to draw a square JKLM with
a point O on the side JK but is not
successful. Why is Rahim unable to draw
the square?
A. The length of OM is twice that of OL.
B. The length of OM is 4 cm.
a. If the question can be answered using a
alone but not using B alone.
b. If the question can be answered using
B alone but not using A alone.
c. If the question can be answered using
A and B together, but not using either
A or B alone.
d. If the question cannot be answered
even using A and B together.
DIRECTIONS for questions 11 to 12: Cities A
and B are in different time zones. A is located
3000 km east of B. The table below describes the
schedule of an airline operating non-stop flights
between A and B. All the times indicated are local
and on the same day.
Departure Arrival
City Time City Time
B 8:00 am A 3.00 pm
A 4:00 pm B 8:00 pm
Assume that planes cruise at the same speed in
both directions. However, the effective speed is
influenced by a steady wind blowing from east to
west at 50 km per hour.
11. What is the time difference between A and
B?
a. 1. hour and 30 minutes
b. 2 hours
c. 2 hours and 30 minutes
d. 1 hour
e. Cannot be determined
12. What is the plane’s cruising speed in km
per hour?
a. 700
b. 500
c. 600
d. 500
e. Cannot be determined
DIRECTIONS for questions 13 to 14: Shabnam
is considering three alternatives to invest her
surplus cash for a week. She wishes to guarantee
maximum returns on her investment. She has
three options, each of which can be utilized fully
or partially in conjunction with others.
Option A: Invest in a public sector bank. It
promises a return of +0.10%.
Option B: Invest in mutual funds of ABC Ltd. A
rise in the stock market will result in a return of
+5%, while a fall will entail a return of-3%.
Option C: Invest in mutual funds of CBA Ltd. A
rise in the stock market will result in a return of -
2.5%, while a fall will entail a return of +2%.
13. The maximum guaranteed return to
Shabnam is
a. 0.25%
b. 0.10%
c. 0.20%
d. 0.15%
e. 0.30%
14. What strategy will maximize the
guaranteed return to Shabnam?
a. 100% in option A
b. 36% in option B and 64% in option C
c. 64% in option B and 36% in option C
d. 1/3 in each of the three options
e. 30% in option A, 32% in option B and
38% in option C
DIRECTIONS for questions 15 and 16: Let S
be the set of all pairs (i,j) where 1£I < £n and n3 4.
Any two distinct members of S are called
“friends” if they have one constituent of the pairs
in common and “enemies” otherwise. For
example, if n = 4, then S = {(1,2), (1,3), (1,4),
(2,3), (2,4), (3,4)}. Here, (1,2) and (1,3) are
friends, (1,2) and (2,3) are also friends, but (1,4)
and (2,3) are enemies.
15. For general n, how many enemies will
each member of S have?
a. 3 n 
b.   2 1 3 2
2
n n  
c. 2 7 n 
d.   2 1 5 6
2
n n  
e.   2 1 7 14
2
n n  
16. For general n, consider any two members
of S that are friends. How many other
members of S will be common friends of
both these members?
a.   2 1 5 8
2
n n  
b. 2 6 n 
c.   1 3
2
n n
d. 2 n 
e.   2 1 7 16
2
n n  
17. In a tournament, there are n terms
1' 2 ' .... n T T T with 5 n  . Each term consists
of k players 3 k  , The following pairs of
teams have one player in common:
1 T & 2' 2 T T & 3 1 ....... n T T & ' n T and n T &
1 T . No other pair of teams has any player
in common. How many players are
participating in the tournament considering
all the n terms together?
a.   1 n k
b.   1 k n
c.   2 n k
d.   2 k n
e.    1 1 n k  
18. Consider four digit numbers for which the
first two digits are equal and the last two
digits are also equal. How many such
numbers are perfect squares?
a. 3
b. 2
c. 4
d. 0
e. 1
Directions for questions 19 to 20: Mr. David
manufactures and sells a single product at a fixed
price in a niche market. The selling price of each
unit is Rs. 30. On the other hand, the cost, in
rupees, of producing x units is 2 240 bx cx   ,
where b and c are some constants. Mr. David
noticed that doubling the daily production from 20
to 40 units increases the daily production cost by
2 66 %
3
.
However, an increase in daily production from 40
to 60 units results in an increase of only 50% in
the daily production cost. Assume that demand is
unlimited and that Mr. David can sell as much as
he can produce. His objective is to maximize the
profit.
19. How many units should Mr. David
produce daily?
a. 130
b. 100
c. 70
d. 150
e. Cannot be determined
20. What is the maximum daily profit, in
rupees, that Mr. David can realize from his
business?
a. 620
b. 920
c. 840
d. 760
e. Cannot be determined
21. The price of Darjeeling tea (in rupees per
kilogram) is 100+0. 10n, on the nth day of
2007 (n = 1,2,3,….100) and then remains
constant. On the other hand, the price of
Ooty tea (in rupees per kilogram) is
89+0.15n, on the nth day of 2007 (n =
1,2….365). on which date in 2007 will be
prices of these two varieties of tea be
equal?
a. May 21
b. April 11
c. May 20
d. April 10
e. June 30
22. Two circles with centers P and Q cut each
other at two distinct points A and B. The
circles have the same radii and neither P
nor Q falls within the intersection of the
circles. What is the smallest range that
includes all possible values of the angle
AQP in degrees?
a. Between 0 and 90
b. Between 0 and 30
c. Between 0 and 60
d. Between 0 and 75
e. Between 0 and 45
23. 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 of
f(x) at x = 10?
a. –119
b. –159
c. –110
d. –180
e. –105
SECTION-II
Directions for questions 26 to 29: Answer the
following questions based on the information
given below:
A health-drink company’s R&D department is
trying to make various diet formulations, which
can be used for certain specific purposes. It is
considering a choice of 5 alternative ingredients
(O, P. Q, R, and S), which can be used in different
proportions in the formulations. The table below
gives the composition of these ingredients. The
cost per unit of each of these ingredients k O: 150,
P: 50, Q: 200, R: 500. S: 100.
Ingredient Composition
Carbo
Hydrate
%
Protein
%
Fat % Minerals
%
O 50 30 10 10
P 80 20 0 0
Q 10 30 50 10
S 45 50 0 5
26. For a recuperating patient, the doctor
recommended a diet containing. 10%
minerals and at least 30% protein. In how
many different ways can we prepare this
diet by mixing at least two ingredients?
a. One
b. Two
c. Three four
d. None
27. Which among the following is the
formulation having the lowest cost per unit
for a dieth av-ing 10% fat and at least 30%
protein? The diet has to be formed by
mixing two ingredients.
a. P and Q
b. P and S
c. P and R
d. Q and S
e. R and S
28. In what proportion P, Q and S should be
mixed to make a diet having at least 60%
carbohydrate at the lowest per unit cost?
a. 2:1:3
b. 4:1:2
c. 2:1:4
d. 3:1:2
e. 4:1:1
29. The company is planning to launch a
balanced diet required for growth needs of
adolescent children. This diet must contain
at least 30% each of carbohydrate and
protein, no more than 25% fat and at least
5% minerals. Which one of the following
combinations of equally mixed ingredients
is feasible?
a. O and P
b. R and S
c. P and S
d. Q and R
e. O and S


Remaining questions are in the attachment, download it freely from here…………
Attached Files
File Type: pdf CAT Model questions paper.pdf (372.6 KB, 62 views)


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