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Which of the following would result in a remainder of 7 when divided

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Which of the following would result in a remainder of 7 when divided [#permalink]

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New post Updated on: 15 Feb 2016, 01:42
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Which of the following would result in a remainder of 7 when divided by 12?

I. 151
II. 3,443
III. 5,995

A) I only
B) I and II
C) I and III
D) II and III
E) I, II and III

[Reveal] Spoiler:
How come the answer is C? 5995 Divided by 12 doesn't leave a remainder 7. Any idea people?
[Reveal] Spoiler: OA

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Originally posted by enigma123 on 07 Nov 2011, 13:47.
Last edited by Bunuel on 15 Feb 2016, 01:42, edited 1 time in total.
Renamed the topic and edited the question.
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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 07 Nov 2011, 16:33
151 = 12 * 12 + 7
3443 = 286 * 12 + 11
5995 = 499 * 12 + 7

Therefore, the answer is C.
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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 07 Nov 2011, 23:24
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for divisibility by 12,check for 3 and 4.
since after dividing remainder is 7,meaning after dividing by 3 remainder = 1
and after dividing by 4 remainder = 3.

so check for 151 giving 1 and 3 respectively.

also for 5995 (sum of the digits = 28) hence dividing by 3 remainder = 1 (3*9=27)
also for 4 (6000 is divisible,similarly 5996 is divisible,hence 5992 is divisible)

thus 5995-5992=3 will be remainder after dividing by 4.

thus C it is.So,without actual dividing you can test like this.
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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 08 Nov 2011, 16:05
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say x div by 12, should check whether x div by 3 and 4. (x is div by 3 if sum of all digits of x is div by 3, and x is div by 4, if the number formed by tens and ones, is div by 4)

since remainder is 7, we have x=12q+7 (rearrange the equation: x-7=12q)

151-7=12q => 144=12q => q=12 yes
3443-7=3436 => 3436=12q => 3+4+3+6 =16 not div by 3 so not div by 12 no
5995-7=5988 => 5988=12q => 5+9+8+8=30 which is div by 3, and 88 is div by 4, so it's div by 12 yes

answer C
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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 08 Nov 2011, 22:37
Thanks Jack for the clear explanation
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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 12 Nov 2011, 21:57
normal division looks much simpler ... and wont take much time as well :)
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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 15 Feb 2016, 01:29
enigma123 wrote:
Which of the following would result in a remainder of 7 when divided by 12?

I. 151

II. 3,443

III. 5,995

A) I only

B) I and II

C) I and III

D) II and III

E) I, II and III

How come the answer is C? 5995 Divided by 12 doesn't leave a remainder 7. Any idea people?


the question is asking which will have a remainder 1 when divided by 3?
answer C
less than 15 seconds :-D
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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 16 Feb 2016, 21:50
It al comes down to basic in the end,I guess.
x=12q+7
151=12q+7
144=12q
q=12
like wise can be found for other two.
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Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 20 Mar 2016, 15:31
If a number has a remainder of 7 when divided by 12 it will have a remainder of 1 when divided by 3 --> 1 2 3 4 5 6 7. So all you have to do is divide all numbers by 3.
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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 20 Mar 2016, 19:00
sq01 wrote:
If a number has a remainder of 7 when divided by 12 it will have a remainder of 1 when divided by 3 --> 1 2 3 4 5 6 7. So all you have to do is divide all numbers by 3.


Hi, sq01 and Nez,

It may not be correct idea to check only by 3 and take that as the answer..
You may have got the correct answer but may not be some other day in some other Q..

When 3 leaves a remainder of 1, the number div by 12 can leave a remainder of 1,4,7, or 10..
for example if one of the choice was 121. 121 leaves a remainder of 1 when div by 3, so you would mark tht as he answer.
But that would be wrong, since 121 leaves a remainder of 1, when div by 12..

therefore check for 3 and 4..
3 should leave a remainder 1, and 4 should leave a remainder of 3..
so if the number +1 is div by 4, that is our answer..

121 +1=122 this is not div by 4 as last two digits are not div by 4..
151 +1 = 152, 52 is div by 4, this is one of our answer.

Hope it helps

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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 21 Mar 2016, 03:19
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Re: Which of the following would result in a remainder of 7 when divided [#permalink]

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New post 26 Jan 2018, 09:34
My technique was the followin:

1. We need to confirm that these numbers have a reminder of 7 when divided by 12:

\(x/12=k+7\)
\(x=12k+7\)

what if we add 5 to each answee and check that the answer is divisible by 12?


\(x+5 = 12k + (7+5) = 12(k+1)\)

I. 151 -> 151+5 = 156 correct:divisible by 4 and by 3
II. 3,443 -> 3448 -> wrong: the sum of the digits is not multiple of 3
III. 5,995 -> 6,000 clearly correct

Best,

Andres
Re: Which of the following would result in a remainder of 7 when divided   [#permalink] 26 Jan 2018, 09:34
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