Question

Average weight of four persons is 67 kg. These persons are A, B, C and D. When E is included in the group, average weight decreases by 2 kg. What is the weight of A? A's weight is 4 kg more than B's weight.
(I) When B is displaced by another person F, whose weight is 4 kg more than E, average weight becomes 64 kg.
(II) When D is displaced by another person G, whose weight is 4 kg more than E, average weight becomes 65 kg.

• A. Statement (I) alone is sufficient, but statement (II) alone is not sufficient.
• B. Statement (II) alone is sufficient, but statement (I) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.

Answer 1

The correct option is C Both statements together are sufficient, but neither statement alone is sufficient.

Given, $A+B+C+D=67\times 4=268$
$A+B+C+D+E=65\times 5=325$
and $A-B=4$
$\therefore E=325-268=57$
(I) $\Rightarrow F=57+4=61$
and $A+C+D=64\times 4-61=195$
(II) $\Rightarrow G=57+4=61$
and $A+B+C=65\times 4-61=199$
Solving the above equations, we can get the value of A. Therefore both statements together can solve the question.