College of Admission Tests Multan

Placement Arrangements

Solve the question of and select the option from the choices A through D/E. Check your Answer and view the explanation.

Four couples—J, K, L, M—are standing in a line. Their positions are numbered consecutively from 1 to 8, and each person is holding hands with the persons on either side of him or her.

J and J are holding hands.

K and K are not holding hands.

L and L are holding hands.

One of the Ls is at one end of the line, and one of the Ms is at the other end.

Question: 2

If J is in position 2, it must be true that
  • M is in position 3.
  • J is in position 4.
  • K is in position 7.
  • L is in position 5.
  • M is in position 5.

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Correct Answer: E

The conditions “J and J are holding hands” and “L and L are holding hands” are naturally symbolized as JJ and LL, respectively. The condition “K and K are not holding hands” can be symbolized as K...K. [The symbol ~(KK) would also work well, but the symbol K...K is more descriptive because it shows the space between the Ks.] The condition “One of the Ls is at one end of the line, and one of the Ms is at the other end” can be symbolized as L=1st/last and M=1st/last. The diagram will consist of eight dashed lines numbered 1 through 8, from left to right:

JJ

LL

K ... K

L = First / Last

M = First / Last

1to8line -27320368

No significant conditions can be derived from the given information, and no conditions can be placed on the diagram. So we attack the questions.

Place a J in position 2:

21arrangementq -30218860

Then, from the condition JJ, the other J must be in position 3, since only L or M can be first.

22arrangementq -99763672

Next, since the Ls must be together and one of them must be either first or last, they must be in positions 7 and 8. This in turn forces M to be first:

23arrangementq -31371746

Next, from the condition K...K, we see that the Ks must be in positions 4 and 6, which in turn forces the other M into position 5. Thus our uniquely determined diagram is

24arrangementq -15497181

The answer is (E).