Question

Given that p and q belong to a set of natural numbers

If set S = {7, q , 12, 8, p , 9}, is p + q greater than 18?
(1) The range of set S is less than 9.
(2) The average of p and q is less than the average of set S.

• A. (A)
• B. (B)
• C. (C)
• D. (D)

Answer 1

The correct option is B

(B)

(1) INSUFFICIENT: Statement (1) tells us that the range of S is less than 9. The range of a set is the positive difference between the smallest term and the largest term of the set. We cannot get a definite answer from this data
Let p = 7 and q = 7. The range ofSis less than 9 and p + q $<$ 18, so we conclude YES.
Let p = 10 and q = 10. The range of S is less than 9 and p + q $>$ 18, so we conclude NO.

Because this statement does not allow us to answer definitively Yes or No, it is insufficient.

(2) SUFFICIENT: Statement (2) tells us that the average of p and q is less than the average of the set S. Writing this as an inequality:
$\frac{p+q}{2}<\frac{7+8+9+12+p+q}{6}$
$\frac{p+q}{2}<\frac{36+p+q}{6}$
$3(p+q)<36+(p+q)$
$2(p+q)<36$
$p+q<18$

Therefore, statement (2) is SUFFICIENT to determine whether p + q $>$ 18.