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# For which of the following values of n is (100+n)/n NOT an

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For which of the following values of n is (100+n)/n NOT an [#permalink]

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23 Jul 2012, 04:19
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For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Practice Questions
Question: 2
Page: 152
Difficulty: 550
[Reveal] Spoiler: OA

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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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23 Jul 2012, 04:19
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SOLUTION

For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

$$\frac{100+n}{n}=\frac{100}{n}+\frac{n}{n}=\frac{100}{n}+1=\frac{100}{n}+integer$$.

Now, in order $$\frac{100}{n}+integer$$ NOT to be an integer $$\frac{100}{n}$$ must NOT be an integer, so $$n$$ must NOT be a factor of 100. Hence $$n=3$$.

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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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23 Jul 2012, 21:56
Back solve. Immediately we realize 1,2,and 5 will yield integers. Also, 103 cannot be divisible by 3 since 1 + 0 + 3 is not divisible by 3.
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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24 Jul 2012, 21:41
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this resolves to 100/n+1 this implies... plugging in 3 does not yield an integer.

Ans- C[/color]
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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25 Jul 2012, 02:18
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100+n/n ==> 100/n + 1, thus, if 100/n is not an integer then the sum will not be Integer...Plugging in numbers.. .we see that 3 satisfies.. Also, 100=2*2*5*5..thus, if the numbers in the answers are not one of these individual numbers/product of these numbers, will be the answer.
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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27 Jul 2012, 06:41
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SOLUTION

For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

$$\frac{100+n}{n}=\frac{100}{n}+\frac{n}{n}=\frac{100}{n}+1=\frac{100}{n}+integer$$.

Now, in order $$\frac{100}{n}+integer$$ NOT to be an integer $$\frac{100}{n}$$ must NOT be an integer, so $$n$$ must NOT be a factor of 100. Hence $$n=3$$.

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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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12 Apr 2013, 08:42
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At first glance it was obvious to me to eliminate A, B and E answer choices. A quick way to avoid doing much mental math from that point on was to go back to smaller numbers that I knew were divisible and then make a judgement based on that. I started with 3. I stepped back to 99, a very clear multiple of 3. Add 99+3 = 102 which is clearly...not 103. We have our answer with no long division and really nothing more than identifying a clear multiple and adding 3. This allows for a solution in under 30 seconds for me. Hope this helps your speed.
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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11 May 2014, 08:29
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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30 Jun 2014, 21:28
Thinking : Divisibility
Eliminate 5 ,2 1 as these results an ineteger
Solved it by applying number 3 as 103/3 = Decimal
But can solve by just Divisibility rule: sum of all digits should be divisible by 3
mean 1+0+3= 4 cannot be divisble
Here apply the concept then can solve more accurate:):)
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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02 Jul 2014, 02:41
Just look at the options

100 is divisible by all except 3

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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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09 Sep 2014, 10:45
Bunuel wrote:
For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Practice Questions
Question: 2
Page: 152
Difficulty: 550

Apply divisibility rules ..... 1+0+3 =4 not divisible by 3
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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03 Dec 2015, 12:39
Hello from the GMAT Club BumpBot!

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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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19 May 2016, 10:21
Bunuel wrote:
For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Solution:

This problem is easiest solved by plugging in each answer choice.

A) (100 + 1)/1 = 101/1 = 101

Answer choice A yields an integer.

B) (100 + 2)/2 = 102/2 = 51

Answer choice B yields an integer.

C) (100 + 3)/3 = 103/3 = 34, remainder 2

Answer choice C DOES NOT yield an integer.

Although we believe answer choice C is correct, we should still test the other answer choices.

D) (100 + 4)/4 = 104/4 = 26

Answer choice D yields an integer.

E) (100 + 5)/5 = 105/5 = 21

Answer choice E yields an integer.

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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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01 Apr 2017, 07:16
(100+n)/n

Replace n with the values and see that only 3 does not divide 100+n because 100+n=103
And to be divisible by 3, the sum of the digits must be divisible by 3 and here 1+0+3= 4 which is not divisible by 3.
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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01 Apr 2017, 08:10
Bunuel wrote:
For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

Straightaway answer will be (C) 3

$$\frac{(100+n)}{n}$$

$$\frac{(100+3)}{3}$$

$$34.33$$

Thus, correct answer will be (C) 3
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Re: For which of the following values of n is (100+n)/n NOT an [#permalink]

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01 Apr 2017, 08:26
Top Contributor
Bunuel wrote:
For which of the following values of n is (100+n)/n NOT an integer?

(A) 1
(B) 2
(C) 3
(D) 4
(E) 5

The GMAT loves this nice identity: $$\frac{a+b}{c} = \frac{a}{c} + \frac{b}{c}$$

So, $$\frac{100+n}{n} = \frac{100}{n} + \frac{n}{n}$$

= $$\frac{100}{n} + 1$$

Since 1 is already an integer, we can see that 100/n + 1 will be an integer whenever 100/n is an integer.
In other words, 100/n + 1 is an integer whenever 100 is divisible by n.

Conversely, 100/n + 1 is NOT an integer whenever 100 is NOT divisible by n.
Since 100 is NOT divisible by 3, the correct answer is C

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Re: For which of the following values of n is (100+n)/n NOT an   [#permalink] 01 Apr 2017, 08:26
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