Please enter the following details
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?
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.
Your Doubts
Drop Your File Here!
Ask Your Doubt
Drop Your File Here!
Create a FREE account and get:
- All Quant Formulas and shortcuts PDF
- 15 XAT previous papers with solutions PDF
- XAT Trial Classes for FREE
