Discussion

Question:

Each of these questions is followed by two statements. As the answer,
Mark (a), If the question can be answered with the help of statement I alone,
Mark (b), If the question can be answered with the help of statement II, alone,
Mark (c), If both, statement I and statement II are needed to answer the question, and
Mark (d), If the question cannot be answered even with the help of both the statements.

Is the average of the largest and the smallest of four given numbers greater than the average of the four numbers?
I. The difference between the largest and the second largest numbers is greater than the difference
between the second smallest and the smallest numbers.
II. The difference between the largest and the second largest numbers is less than the difference
between the second largest and the second smallest numbers.

Explanation:

If the numbers are a, b, c and d such that a < b < c < d, then from statement I, we get (d – c) > (b – a).
So we can say, (d + a) > (b + c) or (d + a) + (d + a) > (b + c) + (d + a). Dividing both the sides by 4, we get

$\frac{(d + a)}{2} > \frac{(a + b + c + d)}{4}$ .

This shows that the average of the largest and the smallest of four numbers is indeed greater than the average of all the 4 numbers. Hence, we can answer the question using first statement only.

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