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Y is the sum of five integers a, b, c, d, e. Is Y even? 16 May 2018, 23:01
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Difficulty:

55% (hard)

Question Stats:

58% (02:06) correct 42% (02:01) wrong based on 101 sessions

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Y is the sum of five integers a, b, c, d, e. Is Y even?

(1) Product of a, b, c, d, e is even.

(2) Integers a, b, c, d, e are evenly spaced from each other such that a > b > c > d > e.
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E
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Y is the sum of five integers a, b, c, d, e. Is Y even? 16 May 2018, 23:14
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STATEMENT 1: E*E*O*O*O=E...SUM=O
E*O*O*O*O=E...SUM=E
STATEMENT 2:Evenly spaced..let 1 be the common difference...E+O+E+O+E=E
O+E+O+E+O=O
Ans: e
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Y is the sum of five integers a, b, c, d, e. Is Y even? 17 May 2018, 18:38
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These 2 examples satisfy Statements 1 and 2:

(1,2,3,4,5) ---> their sum is odd
(2,3,4,5,6) ---> their sum is even

Answer: E
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Y is the sum of five integers a, b, c, d, e. Is Y even? 17 May 2018, 23:50
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Solution



Given:
• Y is the sum of five integers a, b, c, d, e

To find:
• Whether the value of Y is even or not

Analysing Statement 1
• As per the information given in Statement 1, product of a, b, c, d, and e is even
    o Now, the product of all these numbers will be even when at least one of them will be even
    o But this does not provide the exact number of even and odd numbers among the five given numbers

Hence, statement 1 is not sufficient to answer

Analysing Statement 2
• As per the information given in Statement 2, integers a, b, c, d, e are evenly spaced from each other such that a > b > c > d > e
    o Now, as there is no specific mention about the gap, it can be even or odd
    o Depending on the gap, the numbers can be all even or all odd or alternatively even or odd

Hence, statement 2 is not sufficient to answer

Combining Both Statements
• Even after combining the statements, we cannot say exactly how many even and odd numbers are present in the given 5 numbers

Hence, the correct answer is option E.

Answer: E
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