## Logical Reasoning Sets for CAT 2018

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DIRECTIONS for the questions 1 to 2:

15 years ago Mrs. G had three daughters S, R, N. Her age was double the combined age of her three daughters. After some years, she had 2 sons A and K. Now the combined age of all her daughters and sons is double the age of Mrs. G. Age of S is equal to the total age of A and K. Age of Mrs G is equal to the total age of S and R. All the ages are in whole number of years.

Q1) The present age of N is 18 years. Find the present age of Mrs. G (in years).
1) 37
2) 39
3) 41
4) None of these

Q2) If two of the children are twins, they are
1) S, R
2) S, A
3) R, N
4) Can't say

Q3) A person can have at the most 10 books. At least 1 book of Mathematics, Quality Control, Physics and Fine Arts. For every Mathematics book, more than 2 Fine Arts books are required. For every Quality Control book, more than 2 Physics books are required. Mathematics, Quality Control, Physics and Fine Arts books carry 4, 3, 2, and 1 points respectively. Find the maximum possible points.

DIRECTIONS for the questions 4 to 5:

6 people A, B, C, D, E, and F are sitting in 2 rows with 3 chairs facing each other. A person is said to be sitting diagonally opposite to another when he sits in the opposite row immidiately to the right or left of the person who is exactly opposite to him.
B sits diagonally opposite to F.
A sits at the end of one row and E sits opposite to him.

Q4) If D sits at one of the remaining 2 ends, who cannot sit opposite to him?
1) B
2) F
3) C
4) All three can sit

Q5) With reference to the above question, if B and C never sit adjacent to each other, who sits diagonally opposite to A?
1) C
2) B
3) F
4) C or B

DIRECTIONS for the questions 6 to 10:

Alora received a large order for stitching school uniforms from Small Flower School and Little Flower School. He has 2 cutters to cut the fabric, 5 tailors for stitching and 2 assistants to stitch buttons. Each of these 9 persons will work for exactly 10 hours a day. Each of the Small Flower uniform require 20 minutes for cutting the fabric, 1 hour for stitching and 15 minutes for stitching buttons, whereas Little Flower uniform require 30 minutes, 1 hour and 30 minutes respectively for these activities. All the activities can be carried on simultaneously.

Q6) What is the maximum number of Little Flower uniforms that can be completed in a day?

1) 50
2) 20
3) 40
4) 30

Q7) On a particular day, Alora decided to complete 20 Little Flower uniforms. How many Small Flower uniforms can be completed on the same day?

1) 30
2) 40
3) 20
4) 10

Q8) If Alora decides to complete 30 Little Flower uniforms only and no other on a particular day, jow many total man-hours will be idle?

1) 20
2) 40
3) 25
4) 30

Q9) If 1 more assistant is hired, what is the maximum number of Small Flower uniforms that can be completed in a day?

1) 40
2) 50
3) 60
4) 30

Q10) Alora has an option to hire 1 more employee of any category. Which category should he hire to get the maximum increase in production capacity, assuming that he needs to stitch only Small Flower uniforms on that day?

1) Tailor
2) Cutter
3) Assistant
4) Can't say

### Solutions and Explanations

1) Option 2.

2) Option 3.

3) 20

4) Option 3.

5) Option 4.

6) In this question limiting factor is the time taken by Assistant/Cutter for making Little Flower uniforms, which is 30 min/uniform. So, maximum of 40 uniforms can be made. Option 3.

7) 20 Little Flower uniforms consume:
Cutter's 10 man hours, Tailor's 20 man hours, Assistant's 10 man hours
Man hours left after completing 20 Little Flower uniforms.
Cutter's 10 man hours, Tailor's Cutter/Tailor which can work on 30 uniforms with available time. Option 1.

8) Total available man hours in a day = 90
Man hours consumed in 30 Little Flower uniforms = 60
Idle man hours = 90 - 60 = 30. Option 4.

9) Here limiting factor is the number of man hours left with tailor, which allow him to work on maximum of 50 uniforms, so there is no use of adding new assistant. Option 2.

10) Tailor is the limiting factor in increasing production of uniforms from 50 to 60. Therefore, one tailor should be added first to increase production. Option 1.

SCOREPERFORMANCE
9-10 Excellent
7-8 Good
5-6 Satisfactory
1-4 Poor