Download ADDITIONAL PROBLEMS FOR PRACTICE (1) A circle has 41 points

ADDITIONAL PROBLEMS FOR PRACTICE
(1) A circle has 41 points arranged in a clockwise manner numbered from 0 to 40, as shown in the figure
below. A bug moves clockwise around the circle according to the following rule. If it is at a point i on the
circle, it moves clockwise in 1 second by (1 + r) places, where r is the remainder (possibly 0) when i is
divided by 17. Thus, if it is at position 5, it moves clockwise in one second by (1 + 5) places to point 11.
Similarly, if it is at position 40 it moves (1 + 6) or 7 places to point 6 in one second.
If it starts at point 1, at what point will it be after 2012 seconds?
A.
B.
C.
D.
15
5
31
23
(2) The letters in the word RAINED are permuted in all possible ways and arranged in the alphabetical
order. Find the word at position 28 in the permuted alphabetical order
A. AEDNRI
B. AEDRNI
C. AEIDNR
D. AEDRIN
(3)
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 1, 1, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3,
3, 3, 3, 3, 3, 4.......
In the above sequence, what is the number at the position 2852 of the sequence?
A. 4
B. 3
C. 2
D. 1
(4) Traffic on NH4, the Chennai Bangalore highway moves at a constant speed of 60 kms per hour in
both directions. A Bangalore bound driver passes 20 Chennai bound vehicles in a 2 minute interval.
Assume that the vehicles in the Chennai bound lane are equally spaced. Which of the following answers
is closest to the number of Chennai bound vehicles in a 120 kms stretch of the highway?
A. 600
B. 1200
C. 450
D. 300
(5) The Geocity planning office is exploring the use of cones for water towers, and has built a model in
their office. The model is a hollow, open (no top) right circular cone, as shown in the figure below. An
intelligent mathematical bug is sitting at the point A in the figure, and a drop of honey is accidentally
dropped at point B (on the opposite side of the cone, at the top).
The bug crawls to the honey on the surface of the cone by the shortest path.
If R = 270 cm, and r = 90 cm, then what is the distance (in cm) crawled by the bug before reaching the
honey?
Use π=3.14, √2 = 1.41, and √3 = 1.73
A.
B.
C.
D.
135
270
282.6
141.3
(6) The number of solutions in positive integers to the equation 2x+3y = 763 is
A. 128
B. 225
C. 254
D. 127
(7) If f is a function defined on pairs of positive integers such that for all m,n > 1, f(n,1) = 1, f(n,n) = 1,
f(m,n) = f(n,m), f(m,n) = f(m-1, n-1)+f(m-n,n),f(n,2) = int(n/2), where for any real number x, int(x) is the
largest integer less than or equal to x. The value of f(9,3) is
A. 3
B. 7
C. Cannot be determined from the given information
D. 9
(8) Two vertical poles 2 meters and 8 meters high stand apart on a horizontal plane. The height in
meters of the point of intersection of the lines joining the top of each pole to the bottom of the other
pole is
A. Cannot be determined without knowing the distance between the bottom of the poles
B. 1.8
C. 1.6
D. 5.6
(9) In this question, A^B means A raised to the power B.
One of the roots of the equation 3*x^2 - 86*x+ n = 0 is a prime integer and n is a positive integer.
What is the maximum possible value of n?
A. 611
B. 368
C. 158
D. 1849
(10) For a certain integer n, 5n+16 and 8n+29 have a common factor > 1. The common factor is
A. 13
B. Cannot be determined from the given information
C. 17
D. 11
(11) In this question, A^B means A raised to the power B. Given that one of the zeroes of the cubic
equation ax^3 + bx^2 + cx + d = 0 is zero, the product of the other two zeroes is
A. (- b / a )
B. c / a
C. 0
D. (- c / a)
(12) Backgammon is one of the oldest board games for two players. The playing pieces are moved
according to the roll of dice, and players win by removing all of their pieces from the board. Although
luck is involved and factors into the outcome, strategy plays a more important role in the long run. With
each roll of the dice, players must choose from numerous options for moving their checkers and
anticipate possible counter-moves by the opponent. Earliest record of dice game in India dates back to
Mahabharata. It is said that Shakuni used biased dice to get the desired outcome. Let us say Shakuni
threw 2 biased dice together. For the first die P(6) =1/2 , the other scores being equally likely while for
the second die, P(1) = 2/5 and the other scores are equally likely. What is the probability that Shakuni
will throw a total of 7 in one throw of these two dice?
A. 1/6
B. 13/50
C. 7/36
D. 1/3
(13) f(n) is a function defined for all integers n such that
f(f(n) )+f(n)= 2n+3 for all n.
If f(0)= 1 , what is the value of f(2012)?
A.
B.
C.
D.
2012
Cannot be determined from the given information
2013
4027
(14) In this question, X^Y means, X raised to the power Y.
How many integers x satisfy the equation (x^2 - x - 1) ^ (x + 2) = 1 ?
A. 2
B. None of the other 3 choices
C. 4
D. 3
(15) After a ship wreck, the sole survivor lands in The Island of Moreau inhabited by 3 types of people Knights, Knaves and Spies. Knights always tell the truth. Knaves always lie and Spies can either lie or tell
the truth. The survivor is greeted by a set of 3 inhabitants (A,B,C) comprising of 1 Knight, 1 Knave and 1
spy. The sailor cannot make out their identity but they all know each other's identities. The sailor wants
to find out the Knight among them, so that he can get reliable information on how to leave the island.
So he asks them to reveal their identities and they answer as below:
A: I am not a Spy
B: I am a Knave
C: If you ask me, I would say that A is the spy
Identify the person A.
A. Knave
B. Knight
C. Cannot be determined
D. Spy
(16) There are only seven houses on a street. Each house is occupied by one of the seven girls:
Eesha, Usha, Nisha, Aasha, Varsha, Anusha, Natasha.
The following are to be noted:
-All the houses are on the same side of the street, which runs from west to east.
-Natasha does not live in the first or the last house on the street.
-Eesha lives in the fourth house from the west end of the street.
-Nisha lives next to the Eesha.
-Anusha lives east of both Eesha and Nisha but west of Usha.
If Aasha lives immediately west of Eesha, which one of the following statements must be false?
A. Varsha lives next to Aasha.
B. Anusha lives next to Nisha.
C. Anusha lives next to Usha.
D. Varsha lives next to Natasha.
(17) How many words can be formed with the letters of word UNPREDICTABLY if the order of vowels do
not change and NO two vowels can occupy consecutive places ?
A. 76204800
B. 15120
C. 17160
D. 259459200
(18) The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest
of the three. If the median of the three numbers is 5, then the sum of the three is:
A. 30
B. 5
C. 20
D. 25
(19) A and B start from their house at 10am. They travel from their house on MG road at 20Kmph and
40kmph.There is a T junction on their path. A turn left at the T junction at 12:00 noon. B reaches the T
junction earlier and turns right. Both of them continue travelling till 2:00pm. What is the distance
between A and B at 2:00pm?
A. 120 km
B. 150 km
C. 140 km
D. 160 km
(20) Jake is faster than Paul. Jake and Paul each walk 24 km. The sum of their speeds is 7 km/h and the
sum of times taken by them is 14 hours. Then, Jake's speed is equal to:
A. 7kmph
B. 5kmph
C. 4kmph
D. 3kmph
(21) A man goes upstream for a distance of 10 km in 5 hrs. Another man goes downstream the same
distance of 10kms in 3 hrs. What is the difference in speeds of the two men if the river speed is 0.5
kmph?(round the answer to two decimals)
A. 2.45
B. 2.3
C. 1.56
D. 1.33
(22) Two vehicles A and B leaves from city Y to city X. A overtakes B at 10:30am and reaches city X at
12:00pm. It waits for 2hrs and returns to city Y. On its way it meets B at 3:00pm and reaches city Y at
5:00pm.B reaches city X waits for 1hr and returns to city Y. After how many hours will B reach city Y
from the time A overtook him for the first time?
A. 37.5 hrs
B. 50 hrs
C. 49.5 hrs
D. 41.5 hrs
(23) In this question, A^B means A raised to the power B.
The HCF of 2472, 1284 and a third number n is 12. If their LCM is 2^3 * 3^2 * 5^1 * 103 * 107, then the
number n can be:
A. 22*33*103
B. 22*32*51
C. None of these
D. 22*32*71
(24) Find the number of divisors of 1728 (including 1 and 1728).
A. 18
B. 20
C. 30
D. 28
(25) Two forest officials in their respective divisions were involved in the harvesting of tendu leaves. One
division had an average output of 21 tons from a hectare and the other division, which had 12 hectares
of land less, dedicated to tendu leaves, got 25 tons of tendu from a hectare. As a result, the second
division harvested 300 tons of tendu leaves more than the first. How many tons of tendu leaves did the
first division harvest?
A. 3600
B. 3150
C. 3450
D. 3500
(26) In how many ways can 7 different objects be divided among 3 persons so that either one or two of
them do not get any object?
A. 84
B. 180
C. 381
D. 36
(27) What is the distance in cm between two parallel chords of lengths 32 cm and 24 cm in a circle of
radius 20 cm?
A. 3 or 21
B. 2 or 14
C. 4 or 28
D. 1 or 7
(28) The price of a commodity (in rupees per kilogram) is 100 + 0.1n, on the nth day of 2007 (n = 1, 2, ...,
100), and then remains constant. On the other hand, the price of another commodity (in rupees per
kilogram) is 89 + 0.15n, on the nth day of 2007 (n = 1, 2, ..., 365). On which date in 2007, will the prices
of these two commodities be equal?
A. April 10
B. May 21
C. April 11
D. May 20
(29) Two sides of a plot measure 64 meters and 120 meters and the angle between them is a right angle.
The other two sides measure 85 meters each and the other three angles are not right angles. If plot is
convex (none of the internal angles are greater than 180 degrees), what is the area of the plot (in sq
metres)?
A. 7452.5
B. 7308
C. 13460
D. 8940
(30) Three distinct single-digit numbers A, B and C are in Geometric Progression. If abs(x) for real x is the
absolute value of x (x if x is positive or zero, and -x if x is negative), then the number of different possible
values of abs(A + B - C) is
A. 6
B. 4
C. 5
D. 3