SPI-Aptitude Test 6 Ver 1.0 - Solution Keys

7/27/2019 SPI-Aptitude Test 6 Ver 1.0 - Solution Keys

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General Aptitude Test

Directions: All questions are multiple choice type. For each question, please tickonly option (a, b, c or d) in the given response sheet. Do not write on the questionpaper.

1. Average age of students of an adult school is 40 years. 120 new students whoseaverage age is 32 years joined the school. As a result the average age is decreased

by 4 years. Find the number of students in the school after joining of the new

students.(a) 1200 (b) 120 (c) 360 (d) 240

Solution: Let n me the number of students before the new student join

Total sum of ages of students before new students join = 40 * n

Total sum of ages of students after 120 students of avg age 32 join =40*n + 120*32

Given that overall average age dropped by 4 i.e 40-4 = 36 . Hence40*n + 120*32 = (n+120)*36 – solving n= 120. Total student after new students

joined = 120+120 = 240 Option (d)

Category: Quant

Sub-Category: Algebra

Complexity: Medium

2. When Rs. 250 added to 1/4th of a given amount of money makes it smaller than1/3rd of the given amount of money by Rs. 100. What is the given amount of

money?

(a) Rs. 350 (b) Rs. 600 (c) Rs. 4200 (d) Rs. 3600

Solution: Let x be the given amountx/3 = 250 + x/4 + 100

x = 12*350 = 4200 – Option (c)

Category: Quant

Sub-Category: AlgebraComplexity: Medium

3. The ratio of ages of two persons is 4 : 7 and one is 30 years older than the other.Find the sum of their ages.

(a) 210 b) 110 (c) Rs. 90 d) 140

Solution: Let x and y be the ages

7x=4y ,y-x=30 , 4y=4x+120, x=40,y=70 x+y=110 Option (b)

Category: QuantSub-Category: Algebra



Complexity: Medium

4. The ratio of the age of a gentleman and his wife is 4 : 3. After 4 years this ratio

will be 9 : 7. If at the time of their marriage the ratio was 5 : 3, how many years

ago they were married?(a) 10 (b) 8 (c) 12 (d) 15

Solution: Let h and w be the ages of husband and wife respectively

Given h*3 = w*4After 4 years, (h+4)*7 = (w+4)*9 . Solving the above h=32, w=24. Let n be the

years since marriage. Given (32-n)*3=(24-n)*5, n = 12 Option (c) is the rightanswer

Category: Quant


Complexity: Medium

5. A businessman purchased 35 kg dal of Rs 525 and sells it at the rate of Rs 18 perkg. Then the rate of profit or loss is:.

(a) 20% profit (b) 20% loss (c) 25% loss (d) 20% loss

Solution: Cost price per kg = 525/35 = 15, profit = 18-15/15 = 20%, option (a)

Category: Quant

Sub-Category: Arithmetic

Complexity: Simple

6. The difference and the product of two numbers are 32 and 2145 respectively.

Their sum is:(a) 89 (b) 98 (c) 78 (d) 87

Solution: n1-n2=32, n1*n2=2145In algebra (a+b)^2 = (a-b)^2 – 4ab

n1+n2= sqrt( 32*32 - 4*2145) = 98Option (b)

Category: Quant


Complexity: Medium

7. The average of the first four of five numbers is 40 and that of the last four

numbers is 60. The difference of the last and the first number is:(a) 400 (b) 200 (c) 40 (d) 80

Solution: Sum of the first four = 40*4 = 160Sum of the last four = 60*4 = 240



So 160 + last = first + 240 , or last – first = 240-160 = 80 Option d

Category: Quant


Complexity: Medium

8. 20 labourers can do a work in 20 days if everybody works for 6 hours daily. Then

25 labourers can do the same work in 12 days by working daily for:(a) 8 (b) 6 (c) 4 (d) 10

Solution: Total work in person hours = 20*20*6 = 2400

So 25 labourers have to work for = 2400/ (12*25) = 8 hrs per day

Option (a)

Category: Quant


Complexity: Medium

9. A can copy 50 papers in 10 hours while both A & B can copy 70 papers in 10

hours. Then for how many hours are required for B to copy 26 papers?

(a) 10 (b) 11 (c) 12 (d)13

Solution: Given that A along can copy 50 papers in 10 hours and A&Bcombined copy 70 papers in 10 hours , B is copying only 70-50 =20 papers in

10 hours. So time required for B to copy 26 papers = 10 * 26/20 = 13 hours

Option (d)

Category: Quant


Complexity: Medium

10. What is the max possible 3 digit prime number?

(a) 983 (b) 993 (c) 997 (d) 999

Solution: Only 997 and 983 in the list are prime numbers 997 is the greatestOption (c)

Category: Quant


Complexity: Simple

11. Complete the series 2, 7, 24, 77, ----



(a) 135 (b) 237 (c) 238 (d) 266

Solution:

2 x 3 + 1 = 7

7 x 2 + 3 = 2424 x 3 + 5 = 7777 x 3 + 7 = 238 Option (c)

Category: Quant

Sub-Category: Numeric Logic

Complexity: Medium

12. In a church all the villagers used to come on Sundays for the weekly prayers. Mr.X who used to sit in the left row decided to sit one day in the right row there were

equal no of villagers sitting on both the sides. But when Mr. Y who used sit in the

right row decided to sit in the left row then the persons in the left row is twice theno of persons in the right row. Find the total no of villagers?

(a) 7 (b) 6 (c) 5 (d) 4

Solution: Let L and R be the initial number of the left and right respectively

When Mr X moved to right row, # of people of the left = L -1 right = R + 1Given that L – 1 = R + 1 or L = R + 2

When Mr Y move to left – number of people on the left = L-1+1 = LPeople of the right – R+1-1= R. Given that L = 2R , as L = R+2 solving

R =2 and L =4 L+R =6 Option (b)

Category: Quant


Complexity: Medium

13. If VXUPLVH is written as SURMISE, what is SHDVD

(a) PEASA (b) PFBSB (c) PECSC (d) PFASA

Solution:

V X U P L V H

S U R M I S EThe code for the nth alphabet is n-2 position in the eng language alphabet series

Hence SHDVD would be PEASA – Option (a)

Category: Analytical

Sub-Category: Logical Reasoning

Complexity: Simple

14. Find the missing number in the series: 2, 5, __ , 19 ,37, 75.



(a) 7 (b) 8 (c) 9 (d) 10

Solution: The series is an alternating series

2 x 2 + 1 = 5

5 x 2 – 1 = 9 (Option c)

9 x 2 + 1 = 1919 x 2 – 1 = 3737 x 2 + 1 = 75

Category: Quant


Complexity: Medium

15. In a meeting, every person shakes hands with the other only once. If there are 15

handshakes, how many persons attended the meeting?.(a) 3 (b) 4 (c) 5 (d) 6

Solution: Let us assume that there are n people in the meeting

The first person shakes hands with n-1 people

The second person shakes hands uniquely with n-2 peopleThe similarly third person shakes hands uniquely with n-3 people

(n-1) th person shakes hands uniquely n-(n-1) people = 1 personTotal handtakes (n-1) + (n-2) + ( n-3) + (n – n+1)

Total handshakes = n*n – ( 1+2+3...n) = 15n*n - n (n+1)/2 = 15

Solving: n^2 – n = 30 The two roots of the quadratic equation are n = 6 or n=-5since n is positive n = 6 . There are 6 people in the room Option (d)

Alternative solution: Using permutation and combinations. Number of ways inwhich n people have unique handshakes = nC2 and given that nC2 = 15

nC2 = n! / (n-2)! 2! =15 this will also result in the equation n^2 – n = 30 as above

Category: Quant


Complexity: Medium

Directions for questions 16-17: Choose the word which has the same meaning asthe word marked in italics.

16. The company’s 24 hrs helpline was inundated with calls from customers.

(a) overwhelmed (b) submerged (c) rendered dysfunctional (d) attacked

Solution: inundated in this context means overwhelmed with work – Option (a)

Category: Verbal

Sub-Category: VocabularyComplexity: Medium



17. The company mitigated supplier’s non-performance risks through appropriatepenalty clauses in the contract.

(a) decreased (b) alleviated (c) reduced (d) intensified

Solution: mitigated in this context means alleviated – Option (b) . Mitigationdoes not reduce or decrease the probability of risk and is meant to only alleviatethe impact and hence option (b) is the most appropriate answer

Category: Verbal

Sub-Category: Vocabulary

Complexity: Medium

Directions for questions 18-19: Select the most appropriate word to fill in theblanks.

18. There is now a greater ______ of their rights among consumers in the developingcountries.

(a) awareness (b) appreciation (c) knowledge (d) concern

Solution: awareness Option a is the most appropriate word

Category: Verbal


Complexity: Simple

19. Enid Blyton had written many books. Indeed she was such a ______ writer!(a) profuse (b) prolific (c) great (d)

profound

Solution: awareness Option b prolific signifies the number of books in the context and

hence the appropriate optionSolution: awareness Option a is the most appropriate word

Category: Verbal


Complexity: Simple

Directions for question 20: Read the given sentence and select the lettercorresponding to the part which has a grammatical error. One and only one partis in error.

20. The bureau / is announced that the rain /will continue for/another 36 hours..(a) (b) (c) (d)

Solution: Option (b) – incorrect verb ‘is’ – should be ‘has’

Solution: awareness Option a is the most appropriate word

Category: Verbal

Sub-Category: Errors in useComplexity: Simple



21. Four friends R, G, N, K were sharing apizza. They decided that the oldest friend would get the extrapiece. R is two months older than G, who is three months

younger than N. K is one month older than G. Who should get theextra piece of pizza?(a) R (b) G c) N (d) K

Solution: R = G + 2, N = 3 + G K = G + 1 N IS THE ELDEST Option (c)



Complexity: Simple

Directions for questions 22-25: Answer the questions based on the following

information.

A popular 24x7 New Channel has called a few eminent people for a live television

debate. In addition to the moderator, there will be a pilot, a writer, an attorney, and anexplorer in the debate. The people in the debate are G, H, J, K, and L, which includes

the moderator. The channel has made seating arrangements for the debate, which mustfollow the following guidelines

The moderator must sit in the middle, in seat #3.The attorney cannot sit next to the explorer.

L is the pilot.The writer and the attorney sit on either side of the moderator.

H, who is not the moderator, sits between K and J.

The moderator does not sit next to J or L.G, who is the attorney, sits in seat #4.

22. Who is the moderator?(a) H (b) J (c) K (d) L

23. What is J’s position in the sitting arrangement?(a) 1 (b) 2 (c) 3 (d) 5

24. What is J’s occupation?(a) writer (b) pilot (c) moderator (d) explorer

25. Who is the writer?

(a) K (b) J (c) H (d) L

All questions from 22 to 25 are



Complexity: Medium

Solution for 22 to 25



1 2 3 4 5

Explorer Writer Moderator Attorney Pilot

J H K G L

Logic• Moderator occupies seat number 5

• The moderator does not seat next to either J and L – this means , J and L occupy

the ending seats ( 1 or 5)

• G is the attorney and is given to occupy seat #4 and writer cannot take seat #5

• Since attorney cannot sit next to the explorer, explorer cannot take seat #5

• Only L the pilot can take seat #5 and hence Seat #1 is occupied by J.

• Since H is not the moderator , he will occupy Seat #2

• Since attorney and writer are there on the either side of the moderator, H is the

writer and J is the explorer



Response Sheet

Directions: For each question, please tick or mark only option (a, b, c or d). Donot mark more than one column for a question.

Example:

Responses:

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Date: ________________________



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SPI-Aptitude Test 6 Ver 1.0 - Solution Keys

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