Question 5

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


Statement 1:

It is given that the mode of the set is 7. Thus, either p or q(or both) will be 7.

Now, p*q will be a multiple of 7. But it is given that p*q = 16. Thus, this statement is false.

Statement 2:

It is given that p + q + p*q = 94

If p + q = 20, then p*q = 74.

Thus, either (p,q) will be (2,37), (37,2), (1,74) or (74,1).

Since none of the values will give a sum of 20, this statement is also false.

Thus, the correct option is B.

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