Question 17

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

Solution

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Let the middle number be 'a'.

From statement 1, (a-3)(a-2)(a-1)(a)(a+1)(a+2)(a+3) = 702800

On solving this, the value of 'a' that we get is between 7 and 8 and is not a whole number.

from statement 2, (a-3)+(a-2)+(a-1)+(a)+(a+1)+(a+2)+(a+3) = 105

On solving this, we get a = 15.

$$\therefore\ $$ Statement II alone is sufficient to answer the question.

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