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# When a certain number X is divided by 143, the remainder is 45. Which

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When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

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19 Apr 2016, 03:12
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When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

A. 7
B. 21
C. 34
D. 47
E. 55
[Reveal] Spoiler: OA

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Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

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19 Apr 2016, 04:55
Bunuel wrote:
When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

A. 7
B. 21
C. 34
D. 47
E. 55
...

hi,

firstly you can eliminate B, C and D straightway..
all have a difference of 13, so either all 3 can divide or none can..
since we cannot have three answers, all three can be eliminated...

Now X= 143q + 45 = 11*13*q + 45..so we have to make only 45 div by 13..

A.7
45 + 7 = 42 YES

E. 55
45 + 55 = 100 No

ans A
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When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

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19 Apr 2016, 10:23
Bunuel wrote:
When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

A. 7
B. 21
C. 34
D. 47
E. 55

Posting a different approach

Least possible value of x is 188

188/13 = 182 and remainder 6

Thus we need 7 more to make the number divisible by 13

Hence answer will be 7 !!
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Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

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19 Apr 2016, 15:33
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So the number given is N = 143Q + 45

If this number is divided by 13, the remainder would be R[(143Q + 45)/13]

Since 143 is divisible by 13 , the product 143Q gives no remainder
This means the remainder of 45/13 should be the remainder of the entire number N
which is 6

To make it divisible by 13 , the smallest number that can be added = 13 - 6 = 7

Correct Option : A
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Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

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20 Apr 2016, 14:07
Excellent Question
Now if the Question said subtract the answer was 6 or 6- 13p where p is an integer
here as it says add => the number must be of the form => 7+13P
only A satisfies that..
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Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

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22 Apr 2016, 11:43
since 143 is divisible by 13, x divided by 13 yields a remainder of 45/13 ==> 6
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Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

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04 May 2016, 19:31
the equation becomes- X=143q+45, take the smallest values for q, i.e 0. So now we have 45, nearest multiple is 52(ques. says add), hence the next multiple. 52-45=7.
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Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

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05 May 2016, 05:53
X = 143 x k + 45

143 = 11 x 13

the least integer after 45 to be divisible by 13 is 52 (13 x 4 ) = 45 + 7
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When a certain number X is divided by 143, the reminder is 45 [#permalink]

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03 Oct 2017, 17:44
Mo2men wrote:
When a certain number X is divided by 143, the reminder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

1) 7

2) 21

3) 34

4) 47

5) 55

If X = 143a + 45, and a = 1, then

X = (143(1) + 45) = 188

What number could be added to 188 to make it evenly divisible by 13? Obviously, we need a multiple of 13.

(13*13) = 169 --> +13 is
(13*14) = 182 --> +13 is
(13*15) = 195. Bingo

X = 188. Adding 7 to 188 equals 195, which is divisible by 13.

That is, 188 + 7 = 195

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Formerly genxer123

Last edited by generis on 03 Oct 2017, 17:58, edited 1 time in total.
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Re: When a certain number X is divided by 143, the reminder is 45 [#permalink]

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03 Oct 2017, 17:50
1
KUDOS
genxer123 wrote:
If $$\frac{X}{143}$$ = a + 45, and a = 1, then

X = ((1)143 + 45) = 188

What number could be added to 188 to make it evenly divisible by 13? Obviously, we need a multiple of 13.

(13*13) = 169 --> +13 is
(13*14) = 182 --> +13 is
(13*15) = 195. Bingo

X = 188. Adding 7 to 188 equals 195, which is divisible by 13.

That is, 188 + 7 = 195

I think you mean either $$\frac{X}{143}$$ = a +$$\frac{45}{143}$$ or $$X = 143 a + 45$$
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When a certain number X is divided by 143, the reminder is 45 [#permalink]

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03 Oct 2017, 17:56
Mo2men wrote:

I think you mean either $$\frac{X}{143}$$ = a +$$\frac{45}{143}$$ or $$X = 143 a + 45$$

Both of your suggestions are more clear than what I have, and certainly more aligned with the division theorem as it is typically written. I'll edit. Thanks!
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Re: When a certain number X is divided by 143, the remainder is 45. Which [#permalink]

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03 Oct 2017, 21:18
Bunuel wrote:
When a certain number X is divided by 143, the remainder is 45. Which of the following numbers, if added to X, would result in a number divisible by 13?

A. 7
B. 21
C. 34
D. 47
E. 55

x=143+45
143 is a multiple of 13
the next multiple of 13 above 45 is 52
52-45=7
A
Re: When a certain number X is divided by 143, the remainder is 45. Which   [#permalink] 03 Oct 2017, 21:18
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