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Updated on: 01 Jan 2016, 06:54
Originally posted by hb on 21 Jul 2013, 07:08.
Last edited by Nevernevergiveup on 01 Jan 2016, 06:54, edited 2 times in total.
Last edited by Nevernevergiveup on 01 Jan 2016, 06:54, edited 2 times in total.
Edited the question.
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B
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Question Stats:
74% (00:47) correct
26%
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If x is an integer, is x/2 an even integer
(1) x is a multiple of 2
(2) x is a multiple of 4
(1) x is a multiple of 2
(2) x is a multiple of 4
Veritas Answer:
An even integer can be represented algebraically as 2n, where n=any integer. Therefore asking "is \frac{x}{2} an even integer" is the same as asking "is \frac{x}{2=2n}" or is x = 4n.
Statement 1: Fact: x is a multiple of 2. x=2n where n = any integer. This is not sufficient.
Statement 2: Fact: x is a multiple of 4. x=4n. So it is sufficient. The correct answer choice is B.
My answer:
Statement 1: Not Sufficient
Multiples of 2: -14, -12, -10, -8, -6, -4, -2 0, 2, 4, 6, 8, 10, 12, 14......
0/2 = 0 is Neither odd nor even; 4/2 = 2 is even; 6/2 = 3 is odd.
Statement 2: Not Sufficient
Multiples of 4: -24, -20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20, 24.......
0/2 = 0 is neither odd nor even; 4/2 = 2 even; 8/2 = 4 even.
This is not sufficient because zero is also a multiple of 4 and does not provide a yes or no answer.
Statement 1 and Statement 2 together.
Not Sufficient. Hence the answer choice is E.
Can you please advise what is wrong with my understanding ?
An even integer can be represented algebraically as 2n, where n=any integer. Therefore asking "is \frac{x}{2} an even integer" is the same as asking "is \frac{x}{2=2n}" or is x = 4n.
Statement 1: Fact: x is a multiple of 2. x=2n where n = any integer. This is not sufficient.
Statement 2: Fact: x is a multiple of 4. x=4n. So it is sufficient. The correct answer choice is B.
My answer:
Statement 1: Not Sufficient
Multiples of 2: -14, -12, -10, -8, -6, -4, -2 0, 2, 4, 6, 8, 10, 12, 14......
0/2 = 0 is Neither odd nor even; 4/2 = 2 is even; 6/2 = 3 is odd.
Statement 2: Not Sufficient
Multiples of 4: -24, -20, -16, -12, -8, -4, 0, 4, 8, 12, 16, 20, 24.......
0/2 = 0 is neither odd nor even; 4/2 = 2 even; 8/2 = 4 even.
This is not sufficient because zero is also a multiple of 4 and does not provide a yes or no answer.
Statement 1 and Statement 2 together.
Not Sufficient. Hence the answer choice is E.
Can you please advise what is wrong with my understanding ?
Solving this question helps.
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21 Jul 2013, 07:15
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hb
If x is an integer, is x/2 an even integer
Is \(\frac{x}{2}=even=2k\) --> is \(x=2*even=4k\)? So, the question basically asks whether x is a multiple of 4.
(1) x is a multiple of 2. Not sufficient.
(2) x is a multiple of 4. Sufficient.
Answer: B.
As for your solution: Zero is an even integer.
An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even (in fact zero is divisible by every integer).
Hope it's clear.
21 Jul 2013, 07:26
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Bunuel
Thank You. I made a wrong logic regarding zero myself while answering the question. Just for everyone else who maybe reading this at some point, zero is an even integer that is neither negative or positive; it is a multiple of all integers but is never a factor.
