1. 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?
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By: anil on 05 May 2019 02.37 am
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 $$ herefore$$ 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.
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