rishianand7 wrote:a is the sum of x consecutive positive integers. b is the sum of y consecutive positive integers. For which of the following values of x and y is it impossible that a = b?
(A) x = 2; y = 6
(B) x = 3; y = 6
(C) x = 7; y = 9
(D) x = 10; y = 4
(E) x = 10; y = 7
Even integers and odd integers ALTERNATE.
A:
x = 2 = sum of 1 even and 1 odd = ODD.
y = 6 = sum of 3 evens and 3 odds = ODD.
Here, x and y both yield ODD sums.
B:
x = 3 = sum of 1 even and 2 odds = EVEN or sum of 2 evens and 1 odd = ODD.
y = 6 = sum of 3 evens and 3 odds = ODD.
Here, it is possible that x and y both yield ODD sums.
C:
x = 7 = sum of 3 evens and 4 odds = EVEN or sum of 4 evens and 3 odds = ODD.
y = 9 = sum of 4 evens and 5 odds = ODD or sum of 5 evens and 4 odds = EVEN.
Here, is is possible that x and y both yield EVEN sums or that x and y both yield ODD sums.
D:
x = 10 = sum of 5 evens and 5 odds = ODD.
y = 4 = sum of 2 evens and 2 odds = EVEN.
Here, it is NOT possible that x and y yield equal sums.
E:
x = 10 = sum of 5 evens and 5 odds = ODD.
y = 7 = sum of 3 evens and 4 odds = EVEN or sum of 4 evens and 3 odds = ODD.
Here, it is possible that x and y both yield ODD sums.
The correct answer is
D.
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