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# M16-35

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Math Expert
Joined: 02 Sep 2009
Posts: 46207

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29 May 2017, 04:37
1
AAmulya wrote:
I think this is a high-quality question and I don't agree with the explanation. Question says " when x is divided by a, the remainder is b" so that would mean that x+b is divisible by a.
So the option "x+b is divisible by a" is also correct

How did you come up with that conclusion? It's not true. You could test it yourself.

Say x = 5, a = 3, and b = 2. All conditions are satisfied:

$$x=5$$ is divided by $$a=3$$, the remainder is $$b=2$$.
$$x=5$$ is divided by $$b=2$$, the remainder is $$a-2=1$$.

But x + b = 5 + 2 = 7, which is NOT divisible by a = 3.

Hope it's clear.
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Joined: 11 Jul 2016
Posts: 25
Location: Thailand
GMAT 1: 700 Q48 V38

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26 Jun 2017, 18:09
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 13 Jul 2016
Posts: 2

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19 Sep 2017, 07:44
I think this is a high-quality question and I agree with explanation.
Intern
Joined: 14 Jan 2018
Posts: 2

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14 Jan 2018, 10:23
hensap wrote:
Key takeway that really helps *thanks Bunuel for showing this* is remainder must be less than divisor

Thank you very much for pointing it out so clearly
Intern
Joined: 20 Jun 2017
Posts: 35
GMAT 1: 580 Q36 V32
GMAT 2: 660 Q39 V41
GRE 1: 319 Q159 V160

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24 Jan 2018, 18:14
DJ1986 wrote:
Slightly different approach:

x=aq+b
x=bq+a-2

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2
Divide by 2
b=a-1
Ans D

How do we know we can use the same co-efficient for the quotients?
Math Expert
Joined: 02 Sep 2009
Posts: 46207

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24 Jan 2018, 21:14
Mco100 wrote:
DJ1986 wrote:
Slightly different approach:

x=aq+b
x=bq+a-2

aq+b=bq+a-2
factor out q's
re-arranging gives: 2b=2a-2
Divide by 2
b=a-1
Ans D

How do we know we can use the same co-efficient for the quotients?

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Joined: 26 Feb 2018
Posts: 43
Location: India
WE: Web Development (Computer Software)

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22 May 2018, 13:41
I think this is a high-quality question and I don't agree with the explanation. I don't completely agree with the explanation.
In the first line, the question says "when x is divided by a, the remainder is b" so using the basic division laws, x will be divisible by a when b is added (x + b will be divisible by a)
So the option "x+b is divisible by a" is also correct.

Let me know if I am thinking in the wrong direction
Math Expert
Joined: 02 Sep 2009
Posts: 46207

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22 May 2018, 21:58
PrayasT wrote:
I think this is a high-quality question and I don't agree with the explanation. I don't completely agree with the explanation.
In the first line, the question says "when x is divided by a, the remainder is b" so using the basic division laws, x will be divisible by a when b is added (x + b will be divisible by a)
So the option "x+b is divisible by a" is also correct.

Let me know if I am thinking in the wrong direction

That's not true.

For example, x = 1, a = 5 and b = 1.

x = 1 divided by a = 5 gives the remainder of b = 1 but x + b = 2 is NOT divisible by a = 5.
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Joined: 23 Mar 2018
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29 May 2018, 09:14
It would have been correct had the option said x-b is divisible by a. You need to subtract the remainder from the dividend in order to make it divisible by the quotient.
Re: M16-35   [#permalink] 29 May 2018, 09:14

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# M16-35

Moderators: chetan2u, Bunuel

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