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Math Expert V
Joined: 02 Sep 2009
Posts: 58327
For which of the following values of n is (100+n)/n NOT an  [#permalink]

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Question Stats: 98% (00:32) correct 2% (00:37) wrong based on 1917 sessions

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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

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Math Expert V
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Posts: 58327
Re: For which of the following values of n is (100+n)/n NOT an  [#permalink]

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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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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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1
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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2
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.
Math Expert V
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Posts: 58327
Re: For which of the following values of n is (100+n)/n NOT an  [#permalink]

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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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2
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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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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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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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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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.

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

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(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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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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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]

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When we substitute values from the answer choices, we come know that only for Number 3 we do not get an integer.

Hence, Answer is C

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

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memorizing the basic divisibility rules comes in very handy when answering this question. For example: If the digits in a number equal a multiple of 3 when added together, you know that is the only way the number in question is divisible by 3.

Therefore, (100+3)/3 will not equal a number divisible by 3, based on the divisibility rule of 3. Answer choices A, B, D, & E should be easily eliminated as long as youre very familiar with basic divisibility rules.

By memorizing the divisibility rules, you shouldn't even need to pick up a pencil to solve this problem.
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Re: For which of the following values of n is (100+n)/n NOT an  [#permalink]

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4
(100+n)/n = 100/n + n/n = 100/n + 1
From the options it is clear that 3 is the only number that does not result in an integer.

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

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An integer is a whole number.
Substitute answer options into 100+n/n

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

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

C) (100 + 3)/3 = 103/3 = 34.33 - Not an integer (34 R 2)

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

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

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

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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

For which of the following values of n is (100+n)/n NOT an integer?
$$\frac{100+n}{n} = \frac{100}{n} +1$$

100/1 = 100
100/2 = 50
100/3 = 33.33 NOT AN INTEGER
100/4 =25
100/5 = 20

IMO C
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E-mail : kinshook.chaturvedi@gmail.com Re: For which of the following values of n is (100+n)/n NOT an   [#permalink] 16 Sep 2019, 08:51
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