CSAT DAILY MISSION #69

Read the following information carefully and answer the questions that follow:

Only six people M,N,P,Q,S and T work for a company in Delhi. The Delhi offices have three departments (Accounts, Administration, Personnel) and are spread over the first three floors of a building.
There are three men and three women in the group. The women work in different departments on different floors while the men all work in the same department yet on different floors.
– N and S work in the same department, but not in Personnel
– Q is a woman who works in Administration but not on the Second Floor
– P is a man who works on the First Floor
– S and M work on the First and Third floors respectively although they are in the same department

Question 1

Which of the following groups comprises the women?

(A) SQT

(B) QMT

(D) Data Inadequate

Question 2

Which department does T work in?

(A) Accounts

(B) Personnel

(D) Either (A) or (B)

Question 3

Which pair works on the Second Floor?

(A) PT

(B) SM

(D) None of these

Question 4

If T is transferred out of Delhi, will any department fall vacant?

(A) No

(B) Yes, Accounts

(D) Yes, Personnel

Question 5

If a woman has to be promoted as Head to oversee all the departments, who can be promoted without affecting the work adversely in any of the departments?

(A) N

(B) Q

(D) S

SOLUTIONS TO DAILY CSAT MISSION # 70

1. (A) 2. (A) 3. (A) 4. (C) 5. (B)

Explanations
1. The objective of giving this question is to acquaint you guys with how a typical kind of fraction can be factorised. The rule is : If a fraction is expressed as 1/(p x q) where ‘p’ and ‘q’ are consecutive natural numbers, then 1/(p x q) = (1/p) – (1/q) when p is smaller than q.
This means that 1/(8 x 9) = 1/8 – 1/9. Or 1/30 = 1/5 – 1/6. Or 1/380 = 1/19 – 1/20. You can use this rule to solve many problems, like this one. Here, 1/2 = 1/1 – 1/2 ; 1/6 = 1/2 – 1/3 ; 1/12 = 1/3 – 1/4 and so on until 1/156 = 1/12 – 1/13. So, N comes out to be 1/1 – 1/2 + 1/2 – 1/3 + 1/3 – 1/4 + 1/4 – 1/5 + ……. + 1/12 – 1/13. Apart from the first and last term, all other terms will get cancelled out. So, N = 1/1 – 1/13 = 12/13.

2. Let the total number of coins initially in the collection be ‘x’.
So, number of gold coins initially = x/3.
After 10 more gold coins are added, the total number of coins now in the collection becomes = x + 10.
And, the number of gold coins now in the collection becomes = x/3 + 10.
Given, (x/3 + 10) = 1/4(x + 10).
Solving this, ‘x’ come out to be 80. So, total coins now in the collection = 80 + 10 = 90.

3. If the bottles are to be completely filled with the respective liquids, it means the capacity of each bottle must be a factor of each fluid’s volume. So, we can take bottles of capacity 1 L, 2 L, 5 L and even 10 L, because in all these cases, the bottles will get completely filled by each of the three fluids.
But it has been asked to find the least number of bottles. To fulfill that criterion, each bottle’s capacity must be the highest common factor of the three total volumes.
HCF of 200, 260 and 300 = 20. So, the bottles have to be of 20 L capacity.
The number of bottles required = 200/20 + 260/20 + 300/20 = 38.
(Note: Even bottles with capacity of 10 L could have been used, but in that case the number of bottles required would have been 200/10 + 260/10 + 300/10 = 76, which is not the least number)

4. The average contribution to the fund by the initial five men = Rs.30000/5 = Rs.6000.
So, when a sixth member joins, he will first contribute this prevailing average share of Rs.6000, and then give another Rs.6000 to grow the fund. The total money in the fund now rises to Rs.42000 and each person’s average share becomes Rs.42000/6 = Rs.7000.
Then, when a seventh member joins, he will first contribute the prevailing average share of Rs.7000, and then another Rs.7000 to grow the fund. The total money in the fund now becomes Rs.56000 and each person’s share becomes Rs.56000/7 = Rs.8000.

5. Let the initial length be l and the initial width be w. So, initial area = lw.
The new length = 1.4l. The new width = 0.8w. So, new area = 1.4l x 0.8w = 1.12lw.
So, percentage change in area = (1.12lw – lw)/lw x 100 = 12%.