IIFT SAMPLE PAPER

MANYACAT
PreparIng You For Tomorrow
(EXPLANATION)
ANSWER KEY

SECTION I
1. [2] 2. [1] 3. [1] 4. [2] 5. [3]
6. [2] 7. [3] 8. [4] 9. [2] 10. [3]
11. [4] 12. [4] 13. [2] 14. [1] 15. [4]
16. [1] 17. [1] 18. [1] 19. [1] 20. [3]
21. [4] 22. [1] 23. [1] 24. [1] 25. [3]
26. [3] 27. [2] 28. [2] 29. [4] 30. [3]
31. [4] 32. [3] 33. [1] 34. [2] 35. [3]
36. [4] 37. [1] 38. [2] 39. [2] 40. [1]
41. [2] 42. [2] 43. [3] 44. [3] 45. [2]
46. [2] 47. [1] 48. [2] 49. [4] 50. [4]

SECTION II
51. [4] 52. [1] 53. [1] 54. [1] 55. [3]
56. [4] 57. [3] 58. [4] 59. [1] 60. [4]
61. [1] 62. [2] 63. [1] 64. [3] 65. [3]
66. [2] 67. [2] 68. [4] 69. [1] 70. [4]
71. [3] 72. [4] 73. [3] 74. [4] 75. [3]
76. [3] 77. [2] 78. [4] 79. [1] 80. [4]
81. [4]
86. [3] MANYACAT
MANYA
P r e p82.
a r [3]
Ing
87. [1]
You Fo83.
r [3]
T o m o r r o w 84. [4]
88. [3] 89. [1]
85. [4]
90. [1]
91. [1] 92. [1] 93. [2] 94. [1] 95. [3]
96. [3] 97. [2] 98. [1] 99. [3] 100. [3]

SECTION III
101. [4] 102. [1] 103. [2] 104. [3] 105. [3]
106. [3] 107. [1] 108. [2] 109. [1] 110. [3]
111. [3] 112. [1] 113. [2] 114. [2] 115. [3]
116. [3] 117. [2] 118. [3] 119. [4] 120. [2]
121. [1] 122. [1] 123. [3] 124. [4] 125. [2]
126. [3] 127. [2] 128. [1] 129. [2] 130. [1]
131. [3] 132. [3] 133. [4] 134. [3] 135. [2]
136. [4] 137. [2] 138. [3] 139. [3] 140. [1]
141. [3] 142. [1] 143. [3] 144. [4] 145. [2]
146. [2] 147. [3] 148. [4] 149. [1] 150. [2]

SECTION IV
151. [2] 152. [2] 153. [3] 154. [3] 155. [1]
156. [1] 157. [1] 158. [2] 159. [2] 160. [2]
161. [1] 162. [3] 163. [1] 164. [3] 165. [4]
166. [1] 167. [2] 168. [2] 169. [4] 170. [4]
171. [3] 172. [4] 173. [1] 174. [4] 175. [2]
176. [3] 177. [1] 178. [3] 179. [3] 180. [4]
181. [1] 182. [3] 183. [2] 184. [3] 185. [2]
186. [2] 187. [3] 188. [3] 189. [1] 190. [1]
191. [4] 192. [4] 193. [4] 194. [3] 195. [4]
196. [1] 197. [1] 198. [3] 199. [1] 200. [2]

Logon to www.manyagroup.com 1

MANYACAT
PreparIng You For Tomorrow
 SOULUTIONS

SECTION I

1. We know that the height of the pole = AC + BC. Let BC = x, then in right triangle
x
ABC tan 60° = ⇒ x = 10 √3.
10
10
Now let AC = y, then cos 60° = ⇒ y = 20. The height of the pole = 20 + 10√3.
y
Ans. [2]

2. Let the side of the square = a units. Then the diagonal of the square = √2a units.
2
a
Hence, the ratio of the areas of both the squares = =1:2
2
( 2a )
Ans [1]

3. Let the number be x. Then,

1 3 1
× × ×x=8
3 5 7
⇒ x = 8× 35 = 280

4. Ans. [2]
MANYACAT
MANYA
PreparIng You For

h( x)
Tomorrow

x
x
5. Given f(x) = . Therefore, f[h(x)] = x ⇒ = x ⇒ h( x ) = .
1− x 1 − h( x ) 1+ x
Ans. [3]

6. x2 + ax + b = 0
For Manju, x2 + ax + b1 = 0
Sum of roots = –a
6 + 2 = –a ⇒ a = –8
For Anju, x2 + a1 x + b = 0
Multiplication of roots = b
(– 7) × (– 1) = b ⇒ b = 7
∴Equation is x2 – 8x + 7 = 0
⇒ x2 – 7x – x + 7 = 0
or (x – 7) (x – 1) = 0
⇒ x = 7 or 1

7. Let the height of the small cone = h units. Then by the condition given in the question :
1 2 1 1 2 30 10
πr h = × πr 30 ⇒ h = = units.
3 27 3 27 9
Ans [3]

8. Given 5 singers are below the age of 25 years and total 20 members are below the age of 25 years. So, the
number of dancers below 25 years = 20 – 5 = 15. Required Percentage = 15 × 100/60 = 25 %. Ans. [4]

9. Let the cost price = Rs. x and marked price = Rs. y. Then by the condition given in question:

Logon to www.manyagroup.com 2

MANYACAT
PreparIng You For Tomorrow
 x 95 5 c7 − 5h × 100
1.33x = 0.95y ⇒ = ⇒ . Hence, the marked price should be = 40% more than the
y 133 7 5
cost price. Ans [2]
10. Let Y get Rs. y and Z get Rs. z. Then by the condition given in the question y – 20 = z + 20 = x...(1)
Again x + y + z = 120...(2) by equation (1) and (2) we get x = 40, y = 60, z = 20. Ans [3]
11. Since it is not given how many students are between Ravi and Reena we cannot determine Reena’s rank
from the front. Ans. [4]

12. While returning, the speed of the traveler = 50 × 120/100 = 60 kmph. Average speed during the whole
journey = 2 × 50 × 60/(50 + 60) = 54.5 kmph. Ans. [4]

60 × 60
13. In an hour, the bells ring = = 4.28 = 4 times. Ans [2]
LCM of 6, 7, 8, 10

14. Let the usual speed of the person = x kmph and the distance = d km. Then time = d/x hours.
Again by the condition given in question 4d/3x = d/x + 1/3 ⇒ d/x = 1 hour. Ans. [1]

15. B C

Ungrazed Area
MANYACAT
MANYA
PreparIng You For Tomorrow

A D
x
Let, the side of the square garden = x units. Then the length of the rope = units. Then, the area ungrazed
2
x 2 x 2 (4 − x)
= x2 - x ⇒ units.
4 4
Ans. [4]

0.6
16. Let the Tony’s salary = Rs. x. Then, Tina’s salary = 0.6x and the salary of Tito = x = 0.5x. Now by the
1.2
condition given in the question : x + 0.6x + 0.5x = 6300 ⇒ 2.1x = 6300 ⇒ x = 3000. Hence Tony’s salary =
Rs. 3000. Ans. [1]

17. Degrees traveled by the minute hand between 4 : 45 to 5 : 45 = 360° and degrees traveled by the minute
hand between 5 : 45 and 6 : 15 = 180°. Hence, total degrees traveled = 540°. Ans. [1]

18. Total amount of bill = 380 + 5% of 125 = 380 + 5.125 = Rs. 385.125. Ans. [1]

19. 1 hr = 3,600 s
LCM of 6, 7, 8, 9 and 12
2 6, 7, 8, 9, 12
2 3, 7, 4, 9, 6

3 3, 7, 2, 9, 3
1, 7, 2, 3,1

Logon to www.manyagroup.com 3

MANYACAT
PreparIng You For Tomorrow
 = 2 × 2 × 3 × 7 × 2 × 3 = 504
3600
∴Number of times = =7
504

20. Let the radius of the circle be R1 = r.

∴Area of circle A1 = πr2
Radius is increased by 100%
∴R2 = 2r
A2 = π×(2r)2
A 2 − A1
Area of the circle increased = × 100
A1
2 2
4ππ − πr
= 2
× 100
πr
= 300%

21. For P = 1, the value of equation 4 – 7 + 5 = 2, i.e., the positive value. Ans. [4]

22. Since the average of the three numbers is 410, hence the total of the three numbers = 410 × 3 = 1230. Let
the other two number are x and x + 25. Then, by the condition given in the question :
2x + 25 = 1230 – 185 ⇒ x = 510. Hence the smallest number = 185. Ans. [1]

23.
[1] MANYACAT
MANYA
Let the numbers be x and y. Then by the condition given in the question x + y/ 2y = 3/5 ⇒ x/y = 1/5. Ans.
PreparIng You For Tomorrow

24. 104. Ratio of shares = A : B : C

A : B = 100 : 50
B : C = 100 : 40
⇒ A : B : C = 200 : 100 : 40
= 10 : 5 : 2
5
∴B’s share = × 1683 = Rs. 495
17
25. Length of the smaller cube = 1 mm
Length of the bigger cube = 1 m = 1,000 mm
Volume of the bigger cube
So number of cubes =
Volume of the smaller cube
1000 × 1000 × 1000
= = 1,00,00,00,000
1×1×1
Since each smaller cube is having a side of 1 mm, while joining these small cubes end-to-end, total length
of this cube-rope will be 1 × 1,00,00,00,000 mm = 1,000 km.
ab
26. Use a + b +
100
10 × 10
⇒ 10 − 10 − = −1%
100

27. Total number of valid votes

Logon to www.manyagroup.com 4

MANYACAT
PreparIng You For Tomorrow
 Difference
= × 100
Percentage difference
440
= × 100
72 − 28
440
= × 100
44
= 1,000
∴Total number of voters = 1000 + 350 = 1,350

28. A rectangular solid has 12 sides in which 4 sides represent length, 4 represent breadth and 4 represent
height.
Sum of all sides = 4l + 4b + 4h = 4 x (l + b + h) a multiple of 4.

29. 10% of Rs. 500 = Rs. 50 and 5% of Rs. 50 = Rs. 2.5

1
30. 1 hour work of the leak =
6
1
1 hour work of the tap =
10
1 6 × 10
=

MANYACAT
MANYA
The tap can fill the tank in 1 1 10 − 6 = 15 hr
Pr−
eparIng You For Tomorrow
6 10
1
∴Capacity of the tank = 15 × 60 × 3 = 3,150 L
2

31. The smallest such number is 1.

32. Work with choices

33. Simple interest on Rs. 645 for 1 year = 690 – 645

= Rs. 45
Simple interest for 4 years = 45 × 4 = Rs. 180
∴Principal = 645 – 180 = Rs. 465

34. 2x + 3y + 4z = 27 … (i)
and 3x + 2y + z = 33 … (ii)
Adding (i) and (ii), we get 5(x + y + z) = 60
⇒ (x + y + z) = 12

∴Average =
( x + y + z ) = 12 = 4
3 3

35. Time Relative speed Distance between A and B

1 p.m. 0 km/hr 8 km
2 p.m. –3 km/hr 11 km
3 p.m. –2 km/hr 13 km
4 p.m. –1 km/hr 14 km
5 p.m. 0 km/hr 14 km
6 p.m. +1 km/hr 13 km
7 p.m. +2 km/hr 11 km
Logon to www.manyagroup.com 5

MANYACAT
PreparIng You For Tomorrow
 8 p.m. +3 km/hr 8 km
9 p.m. +4 km/hr 4 km
Hence, between 9 p.m. and 10 p.m. the relative speed is 5 km/hr. As distance between them is 4 km, the
4
time required is × 60 = 48 min.
5

2
πr
36. Area grazed by one horse =
4

D C

A B
| a a |
| 2 a 2 |

Area grazed by four horses = πr2

63
Here, r =
2
.
PreparIng

When a is side of square ABCD.

MANYACAT
MANYA You For Tomorrow

∴Area left ungrazed = a2 – πr2

2
= 632 – π×
 63 
 
2
 22 1 
× 1 −
× 
= 632  7 4

 28 − 22  2 6
×  = 63 ×
= 632  28  28
3
= 632 ×
14
63 × 9 × 3
= = 850.5 m2
2

37. A | | B
Speed of A
=
Speed of B
Time taken by B to complete the remaining dis. after meeting
Time taken by A to complete the remaining dis. after meeting
4
= =2
1
Speed of A = 2 × Speed of B.
Logon to www.manyagroup.com 6

MANYACAT
PreparIng You For Tomorrow
 So, the first train is twice as fast as the second train.

x 169 13
38. 1+ = =
12144 12
x13
⇒ = −1
12 12
x 1
⇒ =
12 12
⇒ x =1

39. -25 (x2 – 2 2 x + 2) ≥ 0

⇒ x - 2 2 x + 2≤ 0
2

⇒ (x - 2 )2 = 0
As the square of a real number cannot be negative.
∴(x - 2 ) = 0 ⇒ x = 2

40. g(x) = x3 + 2 ⇒ g(2) = 23 + 2 = 10

f(x, y) = xy ⇒ f(3, 10) = 3 × 10 = 30

41. To calculate the number of games, it will be (n –1), i.e. 150 – 1 = 149.

Alternative method: MANYACAT

MANYA
PreparIng You For Tomorrow

As there are 150 members, so in order to decide the champion there has to be one less than the total number
of members, i.e., 149 games.

42. 328 = (34)7 = (81)7 = (80 + 1)7

When divided by 80, remainder is 1.

 7+ 5 7 − 5
 7+ 5 2 + 7− 5 2 ( ) ( )
43.  + = 
 7− 5 7 + 5  7−5 
 
7+5+2 7 5 +7+5−2 7 5
=
7−5
24
= = 12
2

44. In ∆ABC, BC is the circumference of a cylindrical pole.

When the insect climbs the pole in spirals, it will be covering AC = 2 2
3 + 4 = 5ft.
A

B C
For every 5 ft of spiral distance, effective height covered by the insect = 4 ft
Logon to www.manyagroup.com 7

MANYACAT
PreparIng You For Tomorrow
 5
Hence, if the height of this pole is 16 ft, the insect will travel = 16 × = 20 ft
4
45. Circumference of wheel = πd
Distance traveled by wheel in n revolutions = nπd
22
= 100 × × 63
7
= 19,800 cm = 198 m

x
2 x
46. + 2 − 2 = 1280
2
x 5
⇒2  2  = 1280
x 1280 × 2
⇒2 = = 512
5
x x 9
⇒2 = 512 ⇒ 2 =2
⇒x =9

47. [1] No of batches = 12 symbol 180 \f "Symbol" \s 8× 1.5 = 18; no. of sugar cups = 18 symbol 180 \f "Symbol"
\s 8× 6 = 108.

MANYACAT
MANYA
PreparIng You For
48. [2] No. of people who do not prefer chicken or fish = 50 + 60 - 90 = 20.
Tomorrow

49. [4] We get x/4 - x/5 = ¼; solving we get x = 5. [x is the distance].

50. [4] Squaring, (x - 1/x)² = x² + 1/x² - 2 = 4. Squaring once again, (x² + 1/x²) = x4 + 1/x4 + 2 = 36 Hence x4 + 1/x
= 34.

SECTION II

51. [4] Ram says that only 2 alternatives are possible but Sita gives a third one.

52. [1] The survey could have underestimated dishonest students if they admitted that they were honest.

53. [1] If you believe Anu Malik, then J or L are insane. But from statement I, both must be insane together.

54. [1] It is assumed that a married person loses his identity. Statements II & III are not in the statement.

55. [3] If some other benefit is obtained, then the disadvantage of marriage can be overcome, hence [3].

56. [4] If a majority of people complained about losing their identity, then the statement would be strengthened.

57. [3] If the painter works on Thursday, then the carpenter and the plumber have come before him and D must
also be before E. This leaves E for Friday.

58. [4] If the painter works on Friday, all others are before him. but E can work on Wednesday or Tuesday, hence
e) is wrong.

59. [1] We get : I, E, PL, C, P, hence a).

Logon to www.manyagroup.com 8

MANYACAT
PreparIng You For Tomorrow
60. [4] T and A do not live in any of the end houses, hence B and D live there. They own grey and mauve cars,
hence e) is wrong.

61. [1] If A owns the violet car, only one color (orange) is left for T.
62. [2] B is at the extreme, so T can be adjacent to him, hence b) is not necessarily true.

63. [1] Since A is at 5, places 4 and 6 must not have smokers. Hence TVM can occupy 1, 2 or 3 places only and S
and K can occupy 4 or 6. As K is not an answer choice, we can say that A must be next to S.

64. [3] From Q. 135.

65. [3] V and K must be together, hence V must be at 3 and K at 4.

66. [2] If T takes over the duties of S, then he must talk on the phone and therefore he cannot be next to M, who
requires silence. Thus T or M must ask for a change in seating plan.

67. [2] We get OQPNLM. Hence Q is before P.

68. [4] NLPOWM. Then Q is immediately before M.

69. [1] From Q. 127

70. [4] B must precede C, hence must be at 4.

MANYACAT
71. [3] B cannot be at 3 because it would mean then C must come after lunch, which is not allowed.
MANYA
PreparIng You For Tomorrow
72. [4] D must be at 1, F at 2; then B and C must come after lunch, which means that C must be at 5.

73. [3] We get DBCAFE from this condition.

74. [4] Zeenat is between Akbar and Anthony while Parveen is unwilling to stay next to any occupied cottage,
hence statement V can be derived.

75. [3] We get - Amar Akbar Zeenat Anthony - Parveen - Hema. There are 4 people next to vacant cottages.

76. [3] From Q. 149.

77. [2] It is given that S and T must be together and K is at 3. Only b) satisfies all the conditions.

78. [4] In this choice, K is not at 3, which is a required condition.

79. [1] If V is at 5 and K is at 3 then the only positions for S and T are 1 and 2 since they have to be together.

80. [4] KTS are at positions 3, 4 and 5. Hence V cannot be at 5.

81. From statement I, we get 1, 3, 5, 7, 9.

From statement II, all numbers which are multiples of 3.
Combining both, we get the numbers 3 and 9.
Hence, we cannot decide.

82. Both the statements are needed.

a b
Apply =
sinA sinB

Logon to www.manyagroup.com 9

MANYACAT
PreparIng You For Tomorrow
83. Both the statements are needed.
1 1
First statement says x > or x < ;
2 2
Second statement indicates x > 0.
84. Cannot be determined. The second statement indicates that Raju can be a liar or can be truthful.

85. Cannot be determined. The length of the race has to be known.

For questions 86 to 88: The possible combinations that meet all the conditions

Mon Tue Wed Thurs Fri Sat Sun

a) N M R O/P S Q P/O
b) M N R O/P S P/O Q
On the basis of these possibilities, we can solve the questions easily.

86. [3]

87. [1]

88. [3]

For questions 89 to 92: For solving these questions, we use the diagram given below:

A
MANYACAT
MANYA
PreparIng

x B
You For Tomorrow

b
a
y d z

C
c

A = 40, B = 50 and C = 30

A + B + C = 120
n(A∪B∪C) = 100 – 20 = 80
Number that play exactly two games
(x + y + z = 20)
Thus, we get the following equations
(a + b + c) + d = 80 – 20 = 60
(a + b + c) + 3d = 120 – 2 (20) = 80
∴ d = 10 = n (A∩C)

89. Number of students playing at least 2 games = 20 + 10 = 30.

90. Number of students playing exactly one game = 80 – 30 = 50.

91. Number of students playing exactly one game = 100 – 20 = 80

Logon to www.manyagroup.com 10

MANYACAT
PreparIng You For Tomorrow
92. Number of students playing all 3 games =d = 10

93. In alternative [1], V and Z are not supposed to sit together.

Alternative [2], is correct.
In alternative [3], Y sits at the head of table.
In alternative [4], X sits at the head of table.

94. Since V and Y sit together, W and T sit near Z leaving X next to T.

95. U X Z

Y V T

96. U V Y

W T X

97. U 1 2

Y V
MANYACAT
MANYA
P rX
eparIng You For Tomorrow

For questions 98 to 100: Use diagrams to arrive at the correct answers.

98. [1]

99. [3]

100. [3]

Logon to www.manyagroup.com 11

MANYACAT
PreparIng You For Tomorrow
 SECTION IV

151. [2] The passage is about the Victorians’ idea of invention, which resulted in a number of useless inventions.

152. [2] It is stated that inventions should facilitate life, i.e., utility should over-ride the mere act of inventing.

153. [3] It is the author’s view of inventions that triumphs.

154. [3] “numerous plans and inventions.”

155. [1] The discussion about the mousetrap shows that Alice regards utility as more important.

156. [1] The knight wants to do things in a particular way even if they are useless and serve no purpose. Hence the
best choice to describe the Victorian era is a).

157. [1] a see brackets in the passage.

158. [2] From the Victorian era, when some inventions did not serve any purpose, it moved to the Industrial
Revolution, during which all inventions were put to commercial use.

159. [2] It was the Industrial era that produced wealth.

160. [2] The passage talks about the art and utility of inventions, hence the best choice is b).

MANYACAT
161. [1] “is to make sure that their site name is top-of-mind”, i.e., awareness.
MANYA
PreparIng You For Tomorrow
162. [3] Third paragraph: “providing a tangible cue about the service always helps.”

163. [1] Fourth paragraph: “single most important benefit that is sought by a consumer.”

164. [3] Fifth paragraph: unexpected positive service

165. [4] Spends on billboards are going down because advertisers are looking at other options, according to the
passage.

166. [1] In a bid to fill up empty coffers, municipal corporations are giving permissions to put up hoardings without
any limit.

167. [2] The companies are holding out and are making average profits, as stated.

168. [2] Only television is mentioned in the passage.

169. [4] The article does not make any future predictions.

170. [4] The article is about dotcom advertising but later talks of hoardings and outdoor advertising. Only e) reflects
both these themes.

171. [3] Antipode: an exact opposite.

172. [4] Moribund: dying, stagnant, obsolescent

173. [1] Pristine: immaculate, unspoiled, original state.

174. [4]Insidious: gradual and harmful

Logon to www.manyagroup.com 12

MANYACAT
PreparIng You For Tomorrow
175. [2] Ingenuity: inventiveness

176. [3]

177. [1]

178. [3]

179. [3] Lurk and wait are synonyms, so are abscond and depart.

180. [4] Exhort is to urge; goad is to prod.

181. [1] Look for units of measurement

182. [3] We use needle to knit, loom to weave.

183. [2] Zoology is the study of animals, botany is the study of plants.

184. ‘Equilibrium’ means a state of composure.

185. Synopsis is a brief review of a subject.

186. Partisan is to take parts or sides.

MANYACAT
187. Metamorphosis is to change form completely.

188. MANYA
PreparIng You
Controversy is a dispute, argument or debate.
For Tomorrow

189. [1]

190. [1]

191. [4]

192. [4]

193. [4] success….. accomplishment

194. [3] frugal: economical in manner

195. [4] truculent - fierce or cruel. A ferocious manner will alienate her colleagues

196. [1] A person should not be categorized, or labeled as……

197. [1] acerbic - bitter

198. [3] to take exception to - were in opposition to

199. [1] unprecedented - without precedence

200. [2] cursory- careless or without details

Logon to www.manyagroup.com 13

MANYACAT
PreparIng You For Tomorrow