Question 58

# Consider four natural numbers: x, y, x + y, and x - y. Two statements are provided below:I. All four numbers are prime numbers.II. The arithmetic mean of the numbers is greater than 4.Which of the following statements would be sufficient to determine the sum of the four numbers?

Solution

Natural numbers = $$x , y , (x+y) , (x-y)$$

Statement I : As all the numbers are prime, therefore, either x or y has to be 2 because otherwise (x+y) cannot be prime.

Case 1 : If x = 2, then (x-y) cannot be prime

Case 2 : If y = 2, numbers = $$(x-2) , x , (x+2)$$

These numbers are prime, hence all possibility = 3,5,7

$$\therefore$$ Sum = 2+3+5+7 = 17

Using statement II, we cannot find the required sum, as no specific value of mean is given.

Thus, statement I alone is sufficient.