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Solved IIFT PAPER 2019 INDIAN INSITITUE OF FOREIGN TRADE PAPER 2019 . THNAKYOU KK...

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IIFT 2019

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Quantitative Analysis Instructions For the following questions answer them individually Question 1 You travel by Delhi Metro every day from Botanical Garden, Noida to Hauz Khas, Delhi. At Hauz Khas metro station, you use an escalator to get out of the station. The escalator takes 80 seconds to get you down. One day, the escalator was not working and you walk up the escalator in 50 seconds. How many minutes does it approximately take you to walk up the working escalator?

A 1.5 minutes B

2.2 minutes

C

2.8 minutes

D

2.6 minutes Answer: B

Explanation: It is given that by using the escalator, one can get out of the station in 80 sec. Let us consider the number of steps =80 Speed of the escalator = 1 step/sec When the escalator was not working, the time taken by a person = 50 sec The speed of the person = 80/50=8/5 steps/sec 80

Time taken by a person walking down a moving escalator = =

8 5 −1

80 3 5

=2.22 min B is the correct answer.

Free Mock Test for IIFT Question 2 If

x=8−

A

16 2 25 x

B

64 81 y2

C

25 16 y2

D

81 64 x2

1

2

2, then (x + y) is given by:

32 and y = 2 +

Answer: D Explanation:

x=8−

32 and y = 2 +

2, 1

We have to find the value of (x + y )

(8 −

32 +

2

1 2 2+ 2 )

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8( 2+

2)− 32 (2+ 2+ 2

(

2)+ 1

)2

9 2 2+ 2 )

(

81 6+2 2 1

2

1

( y ) = ( 2+ =(

2− 2 2 )

=

6−4 2 4

=

3−2 2 2

2 2) =

2

x 2 = 64 + 32 − 64

2

2

=96 − 64

2) = 32* 2y2

=32( 3 − 2 we get, x2 81 y2

2

6+2

= 64y2

81 64 x2

=

D is the correct answer. Alternative solution,

32) (2 + 2) = 4 2 ( x (As xy = 8 ⟶ y = 8 ) xy = (8 −

1

2

(x + y ) = (

(xy+1 ) 2 y )

=(

(xy+1 )× x 2 8 )

2 − 1) ×

=(

2(

(8+1 )× x 2 8 )

=

2 + 1 ) = 8 (2 − 1) = 8

81 64

× x2

Question 3 If the co-ordinates of orthocentre and the centroid of a triangle ABC are (—5, 7) and (5, 5), then the circumcentre of the triangle ABC is :

A (25,1) B

(10, 4)

C

(-5,2)

D

(0,6) Answer: B

Explanation: Centroid divides orthocenter and circumcenter in the ratio of 2:1 The co-ordinates of orthocentre and the centroid of a triangle ABC are (—5, 7) and (5, 5) Let the co-ordinate of circumcenter be (x,y) 5=

2x−5 3

= 5 and

2y+7 3

= 5

x=10 and y = 4 Hence the circumcenter = (10, 4)

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Question 4 Consider a cuboidal underground tunnel of length 500 m whose cross-section is given in the figure. If rupees, find the amount of money needed to build the Tunnel.

A

8(4 − π)106 rupees

B

64(4 − π)106 rupees

C

16(4 − π)106 rupees

D

32(4 − π)106 rupees Answer: C

Explanation: Area of the tunnel to be filled with concrete = 16*8-π

(32)

Length of the length along which the tunnel has to be filled with concrete = 500m Volume = 16*8-π

(32) *500

= 32(4 − π)*500 Cost of concrete per 1m3 = 1000 Cost of 32(4 − π)*500 = 32(4 − π)*500*1000 =16(4 − π) ∗ 106 C is the correct answer.

Download IIFT Previous Papers PDF Question 5 In △MNL,line NP bisects the angle MNL. If NP : NL=2: 3 and angle MNL= 120∘ . Then NP: NL: MN is:

A 2:3:4 B

2:3:6

C

2:3:5

D

2:3:9 Answer: B

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1m3 of concrete costs 1000

Explanation: Let the value of MN be p Since NP is the angular bisector 2× M N × NL M N +NL

NP=

cos θ

2× p × 3 x 2x= p+3x cos 60

p=6x NP: NL: MN = 2:3:6 B is the correct answer. Derivation for the length of angular bisector: Let CP be the angular bisector of ∠ ACB . And lengths of AB,BC,CA, CP,AP,PB be c,a,b,x,m,n respectively.

From triangles CPB and CPA using cosine rule we get:

n 2 = a2 + x2 − 2axCos (C ) and m2 = b2 + x2 − 2bxCos (C ) b

According to angle biscetor rule: m a2

=

.'. b2 a2 b2

=

=

a n

2 2 n2 a +x −2axCos(C) 2 2 m2 = (b +x −2bxCos(C) .

a2 +x2 −2axCos(C) b2 +x2 −2bxCos( C)

Upon equating we get, (a2 −b2)x−2ab(a −b)Cos(C)

= since x

=0

0,

2ab(a−b)Cos(C) a2 −b 2 x=

.'.x=

2abCos(C) a+b .

Question 6 A group of women in a society decided to execute interior and exterior decoration of the society in a week’s time. Since 11 women dropped out every day from the second day, the entire decoration was completed on beginning ? (Answer to the nearest integer)

A 137 B

141

C

145

D

148 Answer: C

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12th day. How many women participated at the

Explanation: Let x be the number of women who decided to execute the interior and exterior decoration of the society in a week’s time Let the efficiency of each of them be 1 Total work = 7x Number of women who worked on first day = x Number of women who worked on second day = x-11 Number of women who worked on third day = x-22 .... On similar lines, the number of women who worked on nth day = x-(n-1)11 Number of women who worked on day 12=x-121 x+x-11+x-22+........x-(n-1)11 = 7x 12x-(11+22+....121)=7x 12

5x= 2

(2 × 0 + 11 × 11 )

x=145 C is the correct answer. Question 7 Joseph is in a dilemma. He has been offered a job which would pay him ₹ 80,000 per month for first three years and ₹ 1,20,000 per month for the next three years, and ₹ 1,50,000 per month for the remaining four years. He has also been offered an MBA at a prestigious place and he is considering whether to accept the job or go for the MBA. The first year tuition fee for the MBA program is ₹ 16,00,000 and the second year tuition fee for the MBA program is ₹ 20,00,000. After MBA, he'll get a salary of ₹ 2,00,000 per month for the first four years and then ₹ 2,50,000 per month for the remaining four years. What will be the approximate percentage gain for Joseph in opting for the MBA instead of the job in the 10 years horizon considering no discounting of money ?

A 23% B

25%

C

27%

D

29% Answer: B

Explanation: The sum accrued by Joseph if he had taken the job = (80000*3+120000*3+150000*4)*12 =144*105 If Joseph has taken the MBA program, tuition fee for the program = 1600000+2000000 Sum accrued post MBA = 200000*12*4+250000*12*4=21600000 Net amount = 21600000-3600000 = 180* 105 Net gain if Joseph had taken MBA over job 10 years down the lane= 36*10^5 36× 10 5

Percentage of gain = 144× 10 5 =25% B is the correct answer.

Download IIFT GK PDFs

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Question 8 AB is the tangent on the circle at point A. The line BC meets the circle at points C and E. Line AD bisects the angle EAC. If angle EAC =

60∘ and angle BAC : angle ACB = 2: 5. Find angle ABC :

A

40∘

B

60∘

C

30∘

D

None of the options Answer: A

Explanation: Let us consider angle CAB=2x and angle ACB=5x From Alternate segment theorem, angle AEC = 2x

In triangle AEC, 60+180-5x+2x=180 3x=60 x=20 In triangle ABC, angle ABC = 180-7*20=40 A is the correct answer. Question 9 KBC restaurant chain regularly conducts survey of its customers. The customers are asked to rate the food quality, service and price as Excellent, Good and Fair. Customers are also asked whether they would comeback. It was foundthat 76% of customers say that they will come back. Amongst those whosay that they will come back, 57% rate the restaurant as Excellent, 36% rate it as Good and remainderrate it as Fair. Of those whosay that they will not return, the respective values are 14%, 32% and 54%. What percentage of customers rated the restaurant as good ?

A 27.4% B

35%

C

51%

D

30.7%

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Answer: B Explanation: Let the total customers be 100. Number of customers who said that they will return = 76x Number of customers who said that will not return = 24x Number of customers among those who said that they will return rated the restaurant as good = 76x*0.36 Number of customers among those who said that they will not return rated the restaurant as good = 24x*0.32 Number of customers who rated the restaurant as good = 76x*0.36+24x*0.32 = 35.04x Percentage of customers who rated the restaurant as good = approx 35% B is the correct answer. Question 10 Four couples are to be seated in a circular table such that each couple sits together. In how many ways they can sit such that two males sit to the right of their female partners and the other two malessit to the left of their female partners ?

A 144 B

288

C

1440

D

720 Answer: B

IIFT Free Topic-Wise Important Questions (Study Material) Question 11 Nawab has two sons Saif and Amir who have export businesses. Nawab’s satisfaction/ utility level is given by adding twice of the satisfaction level of Saif with the satisfaction level of Amir. If Saif makes a profit of ₹ 100, his satisfaction level goes up by 10% and if he suffers a loss of ₹100, his satisfaction level goes down by 10%. If Amir makes profit of ₹ 100, his satisfaction level goes up by 5% and if he suffers a loss of ₹ 100, his satisfaction level goes down by 15%. Currently, Nawab’s satisfaction level is 24 and the satisfaction level of Saif is the same as the satisfaction level of Amir. If Saif makes a profit of 100 and Amir suffers a loss of ₹ 100, what is the approximate percentage change in Nawab’s satisfaction level?

A 1.25% B

1.33%

C

1.5%

D

1.66% Answer: D

Explanation: Nawab’s satisfaction/ utility level is given by adding twice of the satisfaction level of Saif with the satisfaction level of Amir. Saif makes a profit of ₹ 100, his satisfaction level goes up by 10% and if he suffers a loss of ₹100, his satisfaction level goes down by 10%. Amir makes profit of ₹ 100, his satisfaction level goes up by 5% and if he suffers a loss of ₹ 100, his satisfaction level goes down by 15%. Nawab’s satisfaction level is 24 and the satisfaction level of Saif is the same as the satisfaction level of Amir Let x be the satisfaction level of Saif

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24=3x x=8 If Saif makes a profit of 100 and Amir suffers a loss of ₹ 100, the satisfaction level of Saif and Amir goes up by 10% and goes down by 15% respectively. The satisfaction of Saif and Amir = 8.8 and 6.8 Nawab's new satisfaction/ utility level = 2*8.8+6.8 =24.4 24.4−24 24

Percentage change = =1.67%

D is the correct answer. Question 12 A man standing on the line joining the two poles finds that the top of the poles make an angle of elevation of 60∘ and 45∘ respectively. After walking for sometime towards the other pole, the angles change to 30∘ and 60∘ respectively. The ratio of the height of the poles is :

A

3−1 2

B

3+1 3

C

3−1 4

D

3+1 4

Answer: A Explanation: Let 'a' and 'b' be the heights of the two poles X be the initial position of the man and the angles of elevation be 600 and450 a 3 and distance between pole 2 and X = b

Distance between pole 1 and X =

Let Y be the position of the man after walking sometime towards the other pole = Distance between Y and pole 1 =

a

3 and distance between the pole 2 and Y =

b 3

Since the distance between the poles will remain the same a 3+b= a b

=

a

3+

b 3

3−1 2

A is the correct answer. Question 13 An E-rickshaw owner makes 24 trips a month with 4 passengers per trip. If his interest cost for purchase of E-rickshaw is ₹ 120/month, he earns 15 percent profit a month (Profit is the difference between revenue and cost). What will be the approximate percentage profit for the same month if the owner undertakes 20 trips a month with 5 passengers and his interest cost is reduced by 10 percent for the month ? Assume: (a) Total cost to be proportional to the interest cost. (b) Revenue per passenger is the same in both cases.

A 33.33 B

66.67

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C

72

D

100 Answer: A

Explanation: Consider the revenue per passenger = P => Total revenue = 24*4P = 96P Since the total cost is proportional to interest, it can be assumed as 120*K Total cost*(1+Profit/100)=Revenue => 120K(1+15/100) = 96P ..........(1) New Revenue = 20*5P = 120*(0.9)K*(1+Profit/100) ..........(2) Dividing (2) by (1), 25/24 = (0.9/1.15)(1+Profit/100) Profit/100 = (25*23)/(18*24) - 1 = 1.33-1 => Profit = 33%, Option A is the answer.

Top 500+ Free Questions for IIFT Question 14 400 students were admitted to the 2018-19 MBA batch. 200 of them did not choose “Business Statistics”. 100 of them did not choose “International Management’. There were 80 students who did not choose any of the two subjects. Find the number of students who chose both Business Statistics and International Management.

A 180 B

220

C

280

D

300 Answer: A

Explanation: The number of students in 2018-19 MBA batch = 400 Number of students who did not choose 'Business Statistics' = 200 Number of students who did not choose 'International Management' = 100 Number of students who did not choose any of the two subjects = 80 Number of students who choose at least one of the two subjects = 400-80=320

140+x=320

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x=320-140=180 A is the correct answer. Question 15 At what time between 2.00 pm and 3.00 pm,the two arms of a watch are completely opposite to each other ?

A 2.40 pm B

2.44 pm

C

2.45 pm

D

247 pm Answer: B

Explanation: Time when the tho hands of the clock are completely opposite to each other between 2.00 pm and 3.00 pm let x be the minutes covered in between 2.00 pm and 3.00 pm 180=

11x−60∗2 2

x=43.6 B is the correct answer. Question 16 The number

37371 − 26371 is divisible by:

A 10 B

11

C

12

D

15 Answer: B

Explanation: Option A:

37371 − 26371 mod 10 =7371

− 6371

Since 7 and 10 are co-prime to each other 1

1

E(10) = 10*( (1 − 2 ) (1 − 5 ) =4

74 mod 10 = 1 74∗92 ∗ 73 mod 10 = 1 ∗ 73 mod 10 =3 6371 mod 10 = 0 Hence 37 371 −

26371 is not divisible by 10

Option B:

37371 − 26371 mod 11 4371 − 4371 mod 11 Hence 37 371 −

26371 is divisible by 11 Downloaded from cracku.in

Option C:

37371 − 26371 mod 12 1371 − 2371 mod 12 Hence 37 371 −

26371 is not divisible by 12

Option D:

37371 − 26371 mod 15 7371 − 11371 mod 15 37371 − 26371 is not divisible by 15 B is the correct answer.

Download IIFT Syllabus PDF Question 17 A motorboat takes the passengers from Rishikesh to Haridwar and back. Both the cities, Rishikesh and Haridwar are located on the banks of River Ganga. During Kumbh Mela,to earn more money, the owner of the motorboat decided to have more trips from Rishikesh to Haridwar and back, so he increased the speed of the motorboat in still water, by 50%. By increasing the speed, he was able to cut down the travel time from Rishikesh to Haridwarand back, by 60%. Whatis the ratio of the speed of motorboating still water to that of the speed of river Ganga? 11 6

A

B

11 6

C

3 2

D

3 2

Answer: A Explanation: Let the speed of the boat in the still water = 100x and the travel time = 100t and the distance between Rishikesh and Haridwar be 'd' Let the speed of the river be 100r Since the owner of the motorboat decides to increase the number of trips, he increased the speed. Increased speed in still water = 150x Final travel time = 40t d 100x+100r

+

d 100x−100r

= 100t ---(1)

After the ease in speed d 150x+100r

+

d 150x−100r

= 40t ---(2)

Dividing 1 by 2, we get x/r =

11 6

A is the correct answer. Question 18 A cricket team has 11 players and each of them has played 20 matchestill date. Virat, Rohit, Mahendra, Rahul and Shikhar have scored runs at an average of 60, 55, 50, 45 and 40 respectively. Rest of the players have scored at an average of 25 each. In the next 10 matches, Virat and Rohit each scored 900 runs whereas Mahendra scored twice that of Rahul. After 30 matches, if Virat’s new average score is twice that of Rahul, what is the approximate average score of Mahendra ?

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A 49 B

41

C

43

D

45 Answer: C

Explanation: The average scores of Virat, Rohit, Mahendra, Rahul and Shikhar in the first 20 matches are 60, 55, 50, 45,40 respectively. In the next 10 matches, Virat and Rohit each scored 900 runs whereas Mahendra scored twice that of Rahul. Virat's score in 30 matches = 60*20+900=2100 Let us consider Rahul scored x runs in last 10 matches, then Mahendra scores 2x runs. Rahul's score in 30 matches = 45*20+x=900+x Mahendra's score in 30 matches = 50*20+2x = 1000+2x It is given that After 30 matches, Virat’s new average score is twice that of Rahul. 2100=2(900+x) x=150 Mahendra's score in 30 matches =1300 Average score of Mahendra = 43 C is the correct answer. Question 19 A square of length 1 m is inside a square of length 2 m and four quarter circles are joined as shown in the figure. The value of y —x is given by,

A

8−π 10

B

4−π 5

C

2π−1 8

D

π−3 4

Answer: D Explanation:

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From the above figure area of the region bounded by ABCDEFGH = Are of the sq...