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10 Aug 2017, 04:39
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D
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Difficulty:
45%
(medium)
Question Stats:
59% (01:22) correct
41%
(01:28)
wrong
based on 303
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If the sum of three integers is even, is the product of the three integers a multiple of 4 ?
(1) All three integers are equal.
(2) All three integers are even.
(1) All three integers are equal.
(2) All three integers are even.
10 Aug 2017, 05:14
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E
Because 0 is an even integer
Because 0 is an even integer
IMO the answer D.
Statement 1: as the the sum of the three integers is even, and as all three integers are equal to each other, we can conclude that all numbers are even integers (even + even + even = even while odd + odd + odd = odd). In this case the multiplication is necessarily a multiple of 4: If one of the number is zero the multiplication also equal to zero and thus a multiple of 4 (zero is a multiple of all integers) and If non of the numbers is equal to zero the multiplication has at least 3 two's (because each of the numbers is even) and thus the product is necessarily a multiple of 4. Sufficient.
Statement 2: this statement state explicitly the conclusion we inferred from the first statement. Thus the analysis is the same. Sufficient.
Answer: D
Statement 1: as the the sum of the three integers is even, and as all three integers are equal to each other, we can conclude that all numbers are even integers (even + even + even = even while odd + odd + odd = odd). In this case the multiplication is necessarily a multiple of 4: If one of the number is zero the multiplication also equal to zero and thus a multiple of 4 (zero is a multiple of all integers) and If non of the numbers is equal to zero the multiplication has at least 3 two's (because each of the numbers is even) and thus the product is necessarily a multiple of 4. Sufficient.
Statement 2: this statement state explicitly the conclusion we inferred from the first statement. Thus the analysis is the same. Sufficient.
Answer: D
