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# When x is divided by 3 the remainder is 2, and when y is divided by 7

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Manager
Joined: 03 Sep 2018
Posts: 177
When x is divided by 3 the remainder is 2, and when y is divided by 7  [#permalink]

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30 Dec 2018, 23:56
1
00:00

Difficulty:

55% (hard)

Question Stats:

43% (03:16) correct 57% (01:00) wrong based on 7 sessions

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When x is divided by 3 the remainder is 2, and when y is divided by $$7$$, the remainder is $$4$$. What is the remainder when $$x+y$$ is divided by $$21$$?

I) $$x^2$$ divided by $$7$$ leaves a remainder of $$4$$.
II) $$y-4$$ is divisible by $$3$$.
Manager
Joined: 03 Sep 2018
Posts: 177
Re: When x is divided by 3 the remainder is 2, and when y is divided by 7  [#permalink]

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31 Dec 2018, 00:05
So what I don't understand is that my algebraic solution would indicate C as the correct answer. Please let me know where I went wrong:

Stem: $$x=3q+2$$ and $$y=7p+4$$ $$–>$$ $$x+y=3q+7p+6$$
Hence, our question becomes: is $$3q+7p=21k$$. This is the case whenever $$3q$$ is divisible by $$7$$ and $$7p$$ is divisible by $$3$$.

Statement I: $$x^2=9q^2+12q+4=7L+4 –> q=7L$$
Still, Not sufficient as no information is given about y

Statement II: $$y-4=3m$$. Now from the stem, we know that $$y=7p+4$$ hence, this statement tells us that $$7p=3m$$
Still, Not sufficient as no information is given about x

Statement I&II combined:
From I) we know that $$3q$$ is divisible by $$7$$, hence, $$3q$$ must be a multiple of $$21$$
From II) we know that $$7p$$ is divisible by $$3$$, hence, $$7p$$ must be a multiple of $$21$$

Thus, $$x+y=(3q+7p)+6= 21b+6$$

Please let me know where I went wrong!
Manager
Joined: 27 Jun 2015
Posts: 54
GRE 1: Q158 V143
Re: When x is divided by 3 the remainder is 2, and when y is divided by 7  [#permalink]

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31 Dec 2018, 00:29
1
Y can have multiple values that is 25 and 46 , hence the option E is correct

Posted from my mobile device
Manager
Joined: 03 Sep 2018
Posts: 177
Re: When x is divided by 3 the remainder is 2, and when y is divided by 7  [#permalink]

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31 Dec 2018, 00:35
vishumangal wrote:
Y can have multiple values that is 25 and 46 , hence the option E is correct

Posted from my mobile device

thanks, I am aware that this is true, however, what is incorrect in my solution?
Math Expert
Joined: 02 Sep 2009
Posts: 58404
Re: When x is divided by 3 the remainder is 2, and when y is divided by 7  [#permalink]

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31 Dec 2018, 01:45
ghnlrug wrote:
When x is divided by 3 the remainder is 2, and when y is divided by $$7$$, the remainder is $$4$$. What is the remainder when $$x+y$$ is divided by $$21$$?

I) $$x^2$$ divided by $$7$$ leaves a remainder of $$4$$.
II) $$y-4$$ is divisible by $$3$$.

Discussed here: https://gmatclub.com/forum/when-x-is-di ... 17389.html
_________________
Re: When x is divided by 3 the remainder is 2, and when y is divided by 7   [#permalink] 31 Dec 2018, 01:45
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