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# Quantitative Apptitude Test for CAT
**1.** What is the number of distinct terms in the
expansion ?
A. 231
B. 253
C. 242
D. 210
E. 228
Directions (Qs.2&3): The figure below shows the plan of a town.
The streets are at right angles to each other. A rectangular park(p) is situated
inside the town with a diagonal road running through it.There is also a
prohibited region(D) in the town.
**2.** Neelam rides her bicycle from her house at A to her
office at B, taking the shortest path. Then the number of possible shortest
paths that she can choose is
A. 60
B. 75
C. 45
D. 90
E. 72
**3.** Neelam rides her bicycle from her house at A to her
club at C,via B taking the shortest path. Then the number of possible shortest
paths that she can choose is
A. 1170
B. 630
C. 792
D. 1200
E. 936
**4.** Suppose, the seed of any positive integer n is defined
as follows: seed(n) = n, if n <10 =seed(s(n)), otherwise, where s(n) indicates
the sum of digits of n. For example, seed(7)=7,seed(248)=
seed(2+4+8)=seed(14)=seed(1+4)=seed(5) =5 etc. How many positive integers n,
such that n< 500, will have seed
A. 39
B. 72
C. 81
D. 108
E. 55
**5.** The integers 1, 2, …. , 40 are written on the
blackboard. The following operation is then repeated 39 times: In eachrep
etition, 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 ?
.
A. 820
B. 821
C. 781
D. 819
E. 780
Directions (Qs.6&7): mark-
(A) If question can be answered from A alone but not from B
alone.
(B) If question can be answered from B alone but not from A
alone.
(C) If question can be answered from A alone as well as from B
alone.
(D) If question can be answered from A and B together but not
from any of them alone.
(E) If question can not be answered even from A and B together.
In a single elimination tournament, any player is eliminated with
a single loss. The tournament is played in multiple rounds subject to the
followings rules:
**(a)** If the number of the players, say n, in any round is
even, yhen the players are grouped into n/2 pairs. The players in each each pair
play a match against each other and the winner moves on to the next round.
**(b)** If the number of the players, say n, in any round is
odd, then one of them is given a bye, that is, he automatically moves on to the
next round. The remaining (n-1) players are grouped into (n-1)/2 pairs. The
players in each pair play a match against each other and the winner moves on to
the next round. No players gets more than one bye in the entire tournament
Thus, if n is even, then n/2 players move on to the next round
while if n is odd, then (n+1)/2 players move on to the next round. The process
is continued toll the final round, which obviously is played between two
players. The winner in the final round is the champion of the tournament.
**6.** What is the number of matches played by the champion?
a. The entry list for the tournament consists of 83 players.
b. The champion received one bye.
**7.** If the number of the players, say n, in the first
round was between 65 and 128, then what is the exact value of n ?
A. Exactly one player received a bye in the entire tournament.
B. One player received a bye while moving on to the fourth round
from the third round.
**8.** A shop stores x kg of rice. The first customer buys
half this amount plus half a kg of rice. The second customer buys half the
remaining amount plus half a kg of rice. Then the third customer also buys half
the remaining amount plus half a kg of rice. Thereafter, no rice is left in the
shop. Which of the following best describes the value of x?
A.
B.
C.
D.
E.
**9.** Consider a right circular cone of base radius 4 cm and
height 10cm. A cylinder is to be placed inside the cone with one of the flat
surfaces resisting on the base of the cone. Find the largest possible total
surface area (in sq cm) of the cylinder.
A.
B.
C.
D.
E.
**10.** Consider obtuse-angled triangles with sides 8 cm, 15
cm and x cm. If x is an integer, then how many such triangles exist?
A. 5
B. 21
C. 10
D. 15
E. 14
**11.** Three consecutive positive integers are raised to the
first, second, and third powers respectively and then added. The sum so obtained
is a perfect square whose square root equals the total of the three originals
integers. Which of the following best describes the minimum, say m, of these
three integers?
A.
B.
C.
D.
E.
**12.** How many integers, greater than 999 but not greater
than 4000, can be formed with the digits 0, 1, 2, 3, and 4, if repetition of
digits is allowed?
A. 499
B. 500
C. 375
D. 376
E. 501
**13.** Find the sum
A.
B.
C.
D.
E.
**14.** In a triangle ABC, the lengths of the sides AB and AC
equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC
such that AD perpendicular to BC. If AD= 3 cm, then what is the radius (in cm)
of the circle circumscribing the triangle ABC ?
A. 17.05
B. 27.85
C. 22.45
D. 32.25
E. 26.25
**15.** Let f(x) be a function satisfying f(x)f(y) = f(xy) for
all real x, y. If f(2) = 4, then what is the value of f(1/2)?
A. 0
B. 1/4
C. 1/2
D. 1
E. Cannot be determined
16. What are the last two digits of
A. 21
B. 16
C. 01
D. 41
E. 31
**17.** Consider a square ABCD with mid
points E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line
passing through F and H. Consider points P and Q, on L and inside ABCD, such
that the angles APD and BQC both equal120°. What is the ratio of the area
of ABQCDP to the remaining area inside ABCD?
A.
B.
C.
D.
E.
**18.** If the root of the equation
are three consecutive integers, then what is the smallest possible value of b?
A.
B. -1
C. 0
D.
E. 1
Directions (Qs. 19& 20): Let , where a, b and c are certain
constants and . It is known that
f(5) =-3f(2) and that 3 is a root of f(x) = 0.
**19.** What is the other root of f(x) =0?
A. -7
B. -4
C. 2
D. 6
E. Cannot be determined
**20.** What is the value of a+ b+ c?
A. 9
B. 14
C. 13
D. 37
E. Cannot be determined
**21.** Rahim plans to drive from city A to station C, at the
speed of 70 km per hour, to catch the train arriving there from B. He must reach
C at least 15 minutes before the arrival of the train. The train leaves B
located 500 km south of AA. 6:15 AM
B. 6: 30 AM
C. 6: 45 AM
D. 7: 00 AM
E. 7: 15 AM
**22.** Two circles, both of radii 1 cm, intersect such that
the circumference of each one passes through the centre of the other. What is
the area (in sq cm) of the intersecting region?
A.
B.
C.
D.
E.
Directions (Qs. 23 &24): Five horses, Red, White, Grey, Black and
spotted participated in a race. As per rules of the race, the persons betting on
the winning horse get four times the bet amount. Moreover, the bet amount is
returned to those betting on the horse that came in third, and the rest lose the
bet amount. Raju bets Rs.3000, Rs.2000 and Rs.1000 on Red, White and Black
horses, respectively and ends up with no profit and no loss.
**
****23.** Which of the following cannot be true?
A. At least two horses finished before Spotted
B. Red finished last
C. There were three horses between Black and Spotted
D. There were three horses between White and Red
E. Grey cam ein second
**
****24.** Suppose, in addition, it is known that Grey came
in fourth. Then which of the following cannot be true?
A. Spotted came in first
B. Red finished last
C. White came in second
D. Black came in second
E. There was one horse between Black and White
**
****25.** The number of common terms in the two sequences
17, 21, 25,…417 and 16, 21, 26, …, 466 is
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