Question

Given below are two statements

Statement I : The set of numbers $(5, 6, 7, p, 6, 7, 8, q)$ has an arithmetic mean of 6 and mode (most frequently occurring number) of 7. Then $p \times q = 16$ . Statement II: Let $p$ and $q$ be two positive integers such that $p + q + p \times q = 94$ . Then $p + q = 20$ .

In light of the above statements, choose the correct answer from the options given below

Accepted Answer

B. Statement I: The set has 8 elements. Mean = 6 $\implies 	ext{Sum} = 48$. $$5 + 6 + 7 + p + 6 + 7 + 8 + q = 48 \implies p + q = 9$$ Since 7 is the unique mode, both $p$ and $q$ (or at least one) must be 7. If $p=7$, then $q=2$, giving $p 	imes q = 14 
eq 16$. Thus Statement I is false. Statement II: $p + q + pq = 94 \implies (p+1)(q+1) = 95 = 5 	imes 19$. Since $p, q$ are positive integers, $\{p+1, q+1\} = \{5, 19\}$, so $\{p, q\} = \{4, 18\}$. Then $p + q = 4 + 18 = 22 
eq 20$. Thus Statement II is false.

Mean and mode / linear system statements

Explanation

Practise this under exam conditions