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If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 +

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If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 +  [#permalink]

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New post Updated on: 23 Jan 2018, 21:02
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If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 + 4, is c*d^(ab) an even number?

(1) 3.5d - 2 is even
(2) b/d is even

Originally posted by BelaHaqi on 23 Jan 2018, 19:35.
Last edited by chetan2u on 23 Jan 2018, 21:02, edited 1 time in total.
corrected the OA
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Re: If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 +  [#permalink]

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New post 23 Jan 2018, 21:01
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BelaHaqi wrote:
If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 + 4, is c*d^(ab) an even number?

(1) 3.5d - 2 is even
(2) b/d is even


From the given equations, following comes out..
1) a and b are of same type- both odd or both even
2) similarly c and d - both are odd or both even.
3) if any of c and d is even, our answer is YES
4) b is MULTIPLE of 5 and d is MULTIPLE of 7


Let's see what each statement tells us..
1) 3.5d-2 is even
So d has to be even, otherwise 3.5d-2 will be a decimal.
Ans is YES
Sufficient
2) b/d is even
b is surely even but nothing can be said about d
If b is 70, and d is 7, Ans is ODD
If b is 140 and d is 70, Ans is EVEN..
Insuff

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Re: If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 +  [#permalink]

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New post 24 Jan 2018, 12:57
In statement 1, it has to be even > 2 right . If d = 2 , we get 5 which is odd.

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Re: If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 +  [#permalink]

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New post 24 Jan 2018, 23:06
adityanahan wrote:
In statement 1, it has to be even > 2 right . If d = 2 , we get 5 which is odd.

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Hi Aditya

I think there's no need to write that explicitly in statement 1, because if we take d=2, we get 3.5d - 2 as an odd number, which does NOT satisfy the condition given in statement 1 - that means we have to reject this value of d and take some other value.
If we take d=4 or 8 or 12 etc., then only we get (3.5d - 2) as even, thus from this statement itself, we can conclude that d is a multiple of 4 (and thus even anyway) which will give us c * d^(ab) as even, and thus our question is answered.
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Re: If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 +  [#permalink]

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New post 24 Jan 2018, 23:08
adityanahan wrote:
In statement 1, it has to be even > 2 right . If d = 2 , we get 5 which is odd.

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d has to be a MULTIPLE of 4...
Even 6, 10 will give you 3.5d-2 as odd
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Re: If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 +  [#permalink]

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Re: If a, b, c, and d are all positive integers, a = b/5 + 2 and d = c/7 +   [#permalink] 05 May 2019, 21:17
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