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# GRE Math Challenge #8- a, b and c are multiple of 15

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GRE Math Challenge #8- a, b and c are multiple of 15 [#permalink]  05 Aug 2014, 03:42
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00:00

Question Stats:

50% (00:34) correct 50% (00:08) wrong based on 10 sessions
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A bit of Divisibility and Number systems.
[Reveal] Spoiler: OA

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Re: GRE Math Challenge #8- a, b and c are multiple of 15 [#permalink]  19 Sep 2016, 10:03
hi

Thanks
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Re: GRE Math Challenge #8- a, b and c are multiple of 15 [#permalink]  19 Sep 2016, 10:41
I think the answer is D. I took 15,30 and 45 at first and here A is greater. But then I took 15, 30 and 150 30/150 leaves a quotient of 0.2 and a remainder of 0. Hence D
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Re: GRE Math Challenge #8- a, b and c are multiple of 15 [#permalink]  21 Sep 2016, 04:57
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Expert's post
Given: a < b < c

Quantity A: The remainder when b is divided by c
Notice that c is greater than b
So, b divided by c will equal 0 with remainder b
If this isn't 100% clear, here are a few examples.
4 divided by 6 equals 0 with remainder 4.
Likewise, 2 divided by 7 equals 0 with remainder 2.
So, we get.....
Quantity A: b

Quantity B: The remainder when (b + c) is divided by a
IMPORTANT CONCEPT
When positive integer N is divided by positive integer D, the remainder R is such that 0 < R < D
For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
So, we can conclude that....
Quantity B: some integer that's less than a

Since it's given that a < b, we can be certain that quantity A is greater.

[Reveal] Spoiler:
A

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Re: GRE Math Challenge #8- a, b and c are multiple of 15 [#permalink]  19 Dec 2016, 01:17
i think the answer will be D, when I take 15, 30, 45 then for the A quantity remainder will be 15, and for B is 0, then A is BIG, but if I take 15, 30, 150 ( i can take this, cause You didnt tell me that it will be consecutive multiples) then the remainder will be 0 for the quantity A and B, then the answer ll be D! Can you explain it?
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Re: GRE Math Challenge #8- a, b and c are multiple of 15 [#permalink]  26 Aug 2017, 11:35
Yeah why can't the answer be D? If you take a as -15, b as 0 and c as 15...

then quantity A = 0, quantity B = 0

But in more noticeable cases like a = 15, b = 30, c = 45, quantity B is 0 but quantity A is 30
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Re: GRE Math Challenge #8- a, b and c are multiple of 15 [#permalink]  23 Sep 2017, 15:28
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Re: GRE Math Challenge #8- a, b and c are multiple of 15 [#permalink]  26 Sep 2017, 05:16
Saurabh03121992 wrote:
I think the answer is D. I took 15,30 and 45 at first and here A is greater. But then I took 15, 30 and 150 30/150 leaves a quotient of 0.2 and a remainder of 0. Hence D

This is wrong because a 30/150 is not an integer, thus 30 is not divisible by 150 and the remainder is indeed 30 that is still greater than zero, i.e. the remainder of (30+150)/15. Thus, answer is A.

jezzsk8 wrote:
Yeah why can't the answer be D? If you take a as -15, b as 0 and c as 15...

then quantity A = 0, quantity B = 0

But in more noticeable cases like a = 15, b = 30, c = 45, quantity B is 0 but quantity A is 30

This is right instead. 0 divided by any number is 0 with remainder of zero and the definition of multiple does not forbid to look for negative multiples, unless stated we are using positive multiples. So the Answer should be D.

Does anybody have the OA/OE?
Re: GRE Math Challenge #8- a, b and c are multiple of 15   [#permalink] 26 Sep 2017, 05:16
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