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# For which of the following values of s is (50+s)s an integer?

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For which of the following values of s is (50+s)s an integer?  [#permalink]

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17 Feb 2016, 03:40
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For which of the following values of s is (50+s)/s an integer?

A. 3
B. 4
C. 9
D. 11
E. 50

Kudos for correct solution.

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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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19 Feb 2016, 03:10
Bunuel wrote:
For which of the following values of s is (50+s)/s an integer?

A. 3
B. 4
C. 9
D. 11
E. 50

Kudos for correct solution.

(50+50)/50= 2

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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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23 Feb 2016, 03:33
Bunuel wrote:
For which of the following values of s is (50+s)/s an integer?

A. 3
B. 4
C. 9
D. 11
E. 50

Kudos for correct solution.

This problem has to be solved by checking the options

(50 + s)/s
For this entity to be an integer, 50 + s should be divisible by s

Option A: 53/3 - Not an Integer
Option B: 54/4 - Not an Integer
Option C: 59/9 - Not an integer
Option D: 61/11 - Not an integer
Option E - 100/50 - Integer

Correct Option: E
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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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28 Jul 2016, 12:41
4
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Bunuel wrote:
For which of the following values of s is (50+s)/s an integer?

A. 3
B. 4
C. 9
D. 11
E. 50

Let's apply a useful property of fractions that is OFTEN useful on the GMAT: (a + b)/c = a/c + b/c
When we apply the rule, we get: (50+s)/s = 50/s + s/s
= 50/s + 1
In order for 50/s + 1 to be an integer, 50 must be divisible by s

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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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29 Jul 2016, 10:46
The only way to solve this efficiently is to check for the options.
Also having done this => is there any divisibility rule for 11 that i am unaware about?
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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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29 Jul 2016, 11:00
stonecold wrote:
The only way to solve this efficiently is to check for the options.
Also having done this => is there any divisibility rule for 11 that i am unaware about?

yes, the best way to solve this question is to check for options.

Divisbility Rule of 11 :
The sum of the even digits is subtracted from the sum of the odd digits. The result is either 0 or divisible by 11.

Example :

i) 292215
By rule, (9+2+5) - (2+2+1) = 11

ii) 760672
By rule, (6+6+2) - (7+0+7) = 0

Both the numbers can be divided by 11.
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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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29 Jul 2016, 11:06
abhimahna wrote:
stonecold wrote:
The only way to solve this efficiently is to check for the options.
Also having done this => is there any divisibility rule for 11 that i am unaware about?

yes, the best way to solve this question is to check for options.

Divisbility Rule of 11 :
The sum of the even digits is subtracted from the sum of the odd digits. The result is either 0 or divisible by 11.

Example :

i) 292215
By rule, (9+2+5) - (2+2+1) = 11

ii) 760672
By rule, (6+6+2) - (7+0+7) = 0

Both the numbers can be divided by 11.

Try this one and lemme know the solution

in-a-certain-pond-50-fish-were-caught-tagged-and-returned-165831.html#p1716513
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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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19 Jun 2017, 09:40
Bunuel wrote:
For which of the following values of s is (50+s)/s an integer?

A. 3
B. 4
C. 9
D. 11
E. 50

Kudos for correct solution.

We can simply break this expression up

50/ s +1 = some integer

Therefore

50/s must be an integer

Thus
"E"
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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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17 Jul 2017, 15:21
Ultimately we want to check if 50/s + 1 is an integer and that is only possible with option E, when s = 50.

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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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20 Aug 2018, 01:35
2
For which of the following values of s is (50+s)/s an integer?

only 50 satisfies the equation
(50+50)/50=2

Therefore, E
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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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20 Aug 2018, 09:24
bu plugging in all the options we came to know that only s=50 results in an integer.
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Re: For which of the following values of s is (50+s)s an integer?  [#permalink]

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31 Oct 2019, 13:15
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Re: For which of the following values of s is (50+s)s an integer?   [#permalink] 31 Oct 2019, 13:15
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