Question

What is the middle number of 7 consecutive whole numbers?
(I) Product of number is 702800.
(II) Sum of the number is 105.

• A. Statement I alone is sufficient to answer the question.
• B. Statement II alone is sufficient to answer the question.
• C. Both statements I and II together are necessary to answer the question.
• D. Both statements I and II together are not sufficient to answer the question.

Answer 1

The Correct Option is B

To determine whether each statement alone is sufficient to find the middle number among 7 consecutive whole numbers, consider each statement separately: 

Statement I: The product of the numbers is 702800.

Let the 7 consecutive numbers be \( x-3, x-2, x-1, x, x+1, x+2, x+3 \). Their product \( (x-3)(x-2)(x-1)x(x+1)(x+2)(x+3) = 702800 \) is very complex to solve algebraically for \( x \) directly. Hence, statement I alone is not sufficient.

Statement II: The sum of the numbers is 105.

The sum of these numbers can be expressed as:

\((x-3)+(x-2)+(x-1)+x+(x+1)+(x+2)+(x+3)=7x\).

Thus, we have \(7x=105\). Solving for \(x\):

\(x=\frac{105}{7}=15\).

Here, \(x\) is the middle number. Therefore, statement II alone is sufficient to find the middle number.

Conclusively, the correct answer is: Statement II alone is sufficient to answer the question.