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If p, q and r are three consecutive integers, in that order and p > 1,

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If p, q and r are three consecutive integers, in that order and p > 1, [#permalink]

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If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?

(1) The average of p, q and r is a multiple of 2
(2) qr/p is an integer .
[Reveal] Spoiler: OA
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If p, q and r are three consecutive integers, in that order and p > 1, [#permalink]

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New post 04 Feb 2018, 13:50
DHAR wrote:
If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?

(1) The average of p, q and r is a multiple of 2
(2) qr/p is an integer .


As this question deals with integer properties, we'll go for a Logical approach.

Three consecutive integers can be even, odd, even in which case their product is divisible by 4 or
odd, even, odd in which case it is divisible by 4 only if the middle number (q) is divisible by 4.
We'll look for a statement which gives us this information.

(1) p + q + r = p + (p + 1) + (p + 2) = 3p +3 so the average is p + 1. Then p + 1 = q is even. But is q divisible by 4?
Insufficient!

(2) if qr = (p + 1)(p + 2) = p^2 + 3p + 2 is divisible by p then 2 must be divisible by p. Since p > 1, then p = 2.
Sufficient!

(B) is our answer.


EDIT: I'm surprised that the OA is (E). Don't think I missed anything...
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Last edited by DavidTutorexamPAL on 04 Feb 2018, 23:15, edited 1 time in total.
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Re: If p, q and r are three consecutive integers, in that order and p > 1, [#permalink]

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New post 04 Feb 2018, 14:14
How is it Option E?

Isn't the answer Option D?
Could anyone explain?
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Re: If p, q and r are three consecutive integers, in that order and p > 1, [#permalink]

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DavidTutorexamPAL wrote:
DHAR wrote:
If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?

(1) The average of p, q and r is a multiple of 2
(2) qr/p is an integer .


As this question deals with integer properties, we'll go for a Logical approach.

Three consecutive integers can be even, odd, even in which case their product is divisible by 4 or odd, even, odd in which case it is not.
We'll look for a statement which gives us this information.

(1) p + q + r = p + (p + 1) + (p + 2) = 3p +3 so the average is p + 1. If this is even, then p is odd.
Sufficient!

(2) if qr = (p + 1)(p + 2) = p^2 + 3p + 2 is divisible by p then 2 must be divisible by p. Since p > 1, then p = 2.
Sufficient!

(D) is our answer.

DHAR : I thought that, if sufficient, (1) and (2) were supposed to give identical answers to the question? In this case (1) gives No and (2) gives Yes... otherwise, nice question!

EDIT: I'm surprised that the OA is (E). Don't think I missed anything...


Hi

Even if the order is odd, even, odd - still the product can be divisible by 4 if the middle number is a mutliple of 4. Eg., 3, 4, 5 or 7, 8, 9.
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Re: If p, q and r are three consecutive integers, in that order and p > 1, [#permalink]

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New post 04 Feb 2018, 21:50
DHAR wrote:
If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?

(1) The average of p, q and r is a multiple of 2
(2) qr/p is an integer .


Let the numbers be p, p+1, p+2 respectively. Their average will be the middle number only.
Average = (p + p+1 + p+2)/3 = p+1.
We have to determined whether p*(p+1)*(p+2) is divisible by 4.

(1) Average = p+1 is even. So p is odd.
Even if p is odd, still the product p*(p+1)*(p+2) might or might not be divisible by 4.

eg, 3*4*5 is divisible by 4 but 5*6*7 is NOT divisible by 4.
So this statement is Not Sufficient.


(2) qr/p is an integer, so the product of q*r is divisible by p.
Product of (p+1)*(p+2) = (p^2 + 3p + 2) is given to be divisible by p.
Now p^2 and 3p are both multiples of p, so these two terms will anyway be divisible by p. But 2 is also divisible by p, This can only happen if p=2 and nothing else (because p>1 given).

So from this condition we can determine that the only case possible here is p, q, r as 2, 3, 4 respectively. And their product, as we can see, is divisible by 4. So this statement is Sufficient.


Hence answer should be B.
(OA is E, either I am missing something or request to please check the OA)
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Re: If p, q and r are three consecutive integers, in that order and p > 1, [#permalink]

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New post 04 Feb 2018, 23:12
amanvermagmat wrote:
Hi

Even if the order is odd, even, odd - still the product can be divisible by 4 if the middle number is a mutliple of 4. Eg., 3, 4, 5 or 7, 8, 9.


You're right! Slipped up there... fixed my reply, thanks.
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Re: If p, q and r are three consecutive integers, in that order and p > 1, [#permalink]

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New post 04 Feb 2018, 23:17
DHAR wrote:
If p, q and r are three consecutive integers, in that order and p > 1, is their product divisible by 4?

(1) The average of p, q and r is a multiple of 2
(2) qr/p is an integer .


The question is till flawed. From (1) p = odd and from (2) p = even. On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem.
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Re: If p, q and r are three consecutive integers, in that order and p > 1,   [#permalink] 04 Feb 2018, 23:17
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If p, q and r are three consecutive integers, in that order and p > 1,

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