CAT 2025 Lesson : Arrangements - Case 7

Read the following and answer the questions that follow

A group of students A, B, C, D, E, F, G, H and I visit Sheesh Mahal in Jaipur and play a game of standing in a horizontal line in front of a mirror as per the directions seen in the reflection. The group consists of four girls and five boys and none of the boys are at the extreme end positions. All the boys stand together with no girl in between. A takes the lead and stands in the centre to give directions as per those seen in the reflection. Some other directions which A gives are:

(a) G is on the extreme left while A is to the immediate left of D.
(b) C stands to the right of A and is not a girl.
(c) H is second to the left of B and to the immediate right of G.
(d) E is not on the extreme ends and is not a girl.
(e) B always stands between two boys.
[IIFT 2019]

16) Which of the following statements is always true?

(1) F and I are girls
(2) E is a boy but A is a girl
(3) A and E stand together
(4) C and I stand together

17) If there are two students between F and D, then I as per reflection is:

(1) On the extreme right
(2) Immediate left of D
(3) Immediate right of C
(4) Four places to the right of A

18) Who is three places to the right of A considering A's direction sense and not that of the reflection?

(1) F
(2) I
(3) H
(4) E

Solution
Case solution:

The key point in this case is there are two arrangements, actual and mirror.

When arranging a person in the actual side, the exact opposite must be done in the mirror. eg., If a person is to be placed on the left in the actual side, in the mirror side, the person will be placed on the right.

To proceed with the case let's start arranging the mirror side first.

A stands in the centre, is common in both the arrangements.

G is extreme left to A, hence, in the mirror side G is to the extreme right.

A is to the immediate left of D, hence, in the mirror side A is to the immediate right of D.

H is to the immediate right of G and 2nd to the left of B. Thus in the mirror side, H is to the immediate left of G and two places to the right of B. This means, B is two places to the left of H.



B stand between two boys, which makes A and the person to the right of B in the mirror side a boy.
C is a boy and is to the right of A, and hence, to the left of A in the mirror side.

All 5 boys have to come together, hence, C has to be placed to the immediate left of D in the mirror side which in turn makes B and D boys too.
E is not a girl and hence E fills the empty boy spot.



Thus, G, H, I and F are girls and the remaining two spots are filled by either I or F as their position cannot be uniquely determined with the available clues.



16)
F and I are girls as the gender of all the students can be uniquely determined.

Answer: (1) F and I.

17)
If there are two students between F and D, that means, F is standing at the first followed by I. Thus, I is to the immediate left of C in the actual side and in the reflection side I is to the immediate right of C.

Answer: (3) Immediate right of C

18) Three places to the right of A in the actual side will be H.

Answer: (3) H

Answer:
16) (1) F and I are girls
17) (3) Immediate right to C
18) (3) H