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# Is n an integer less than 5?

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Math Expert
Joined: 02 Sep 2009
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Is n an integer less than 5?  [#permalink]

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02 Oct 2015, 01:53
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35% (medium)

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65% (01:05) correct 35% (01:14) wrong based on 310 sessions

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Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.

Kudos for a correct solution.

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Re: Is n an integer less than 5?  [#permalink]

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02 Oct 2015, 01:57
1
Bunuel wrote:
Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.

Kudos for a correct solution.

1) 5n is a positive int, so n could be any values above 0.. insuff
2) n/5 is positive int, so n has to be 5,10... always greateer than or equal to 5.. so uff as ans would be NO

ans B
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Re: Is n an integer less than 5?  [#permalink]

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02 Oct 2015, 12:21
Bunuel wrote:
Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.

Kudos for a correct solution.

From Statement (1)
5n is a +ve number, n can have any values 1,2,5.15 etc.

Not sufficient.

From statement (2)
n/5 is a +ve integer min value of n is 5,
hence n is always greater than 5.

Sufficient.

Ans - B
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Re: Is n an integer less than 5?  [#permalink]

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02 Oct 2015, 20:38
1
Bunuel wrote:
Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.

Kudos for a correct solution.

Solution -

Stmt1 - 5n is a positive integer. -> n is a positive integer greater than or equal to 0. n can be decimal(1/5) or integer(>1). Not Sufficient.
Stmt2 - n/5 is a positive integer. ->n is a multiple of 5. This stmt clearly says that n>=5. Sufficient.

Ans B
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Re: Is n an integer less than 5?  [#permalink]

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03 Oct 2015, 05:32
2
Bunuel wrote:
Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.

Kudos for a correct solution.

St1: clearly not sufficient, n could be any value >0
St2: n must be a multiple of 5 -Sufficient
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Re: Is n an integer less than 5?  [#permalink]

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03 Oct 2015, 05:40
Bunuel wrote:
Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.

Kudos for a correct solution.

Question : Is n < 5?

Statement 1: 5n is a positive integer.
This statement doesn't limit the value of n in positive range and for any value of n, 5n will be an Integer as Given that n is an Integer. Hence,
NOT SUFFICIENT

Statement 2: n/5 is a positive integer.
i.e. n must be a multiple of 5 and greater than 0 for being positive
i.e. Possible values of n = 5, 10, 15, 20, 25, ----- etc.
But n may be equal to 5 or may be Greater than 5 but Never less than 5 hence
SUFFICIENT

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Re: Is n an integer less than 5?  [#permalink]

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06 Oct 2015, 05:41
Bunuel wrote:
Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

Question Type: Yes/No Is n an integer less than 5? Notice that the question requires two components to provide the answer “yes”: n must be an integer and n must be less than 5.

Statement 1: 5n is a positive integer. This statement is not sufficient. If you Play Devil’s Advocate you can get both integers and non-integers for n. For example, n could equal 1, which is an integer less than 5. Or n could = 1/5 and 5n = 1. This would give you a “no” since 1/5 is not an integer.

You could also manipulate the “algebra” on this one. If 5n = positive integer, then n = (positive integer)/5 That allows n to equal something like 5/5 (which is 1) or 1/5 (which is not an integer). This statement is not sufficient. Eliminate choices A and D.

Statement 2: n/5 is a positive integer. In order for n/5 to be a positive integer, n must be at least equal to 5 and must be a multiple of 5. For example, 5/5 = 1 and 10/5 = 2, etc. So this statement is sufficient because the answer is “no.” n is an integer but is not less than 5.

Again, you could also perform the “algebra” by saying that n/5 = (positive integer). This means that n = 5(positive integer). And since the lowest positive integer is 1, then n at a minimum is 5(1). Accordingly, n cannot be less than 5. Because you can answer definitively “no” to this question then this statement is
sufficient and the answer is B.
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Re: Is n an integer less than 5?  [#permalink]

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12 Sep 2017, 13:15
1
Top Contributor
Bunuel wrote:
Is n an integer less than 5?

(1) 5n is a positive integer.
(2) n/5 is a positive integer.

Kudos for a correct solution.

Target question: Is n an integer less than 5?

Statement 1: 5n is a positive integer
Let's TEST some values.
There are several values of n that satisfy statement 1. Here are two:
Case a: n = 1. Here, 5n = (5)(1) = 5, and 5 IS a positive integer. In this case, n IS an integer less than 5
Case b: n = 6. Here, 5n = (5)(6) = 30, and 30 IS a positive integer. In this case, n is NOT an integer less than 5
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: n/5 is a positive integer
If n/5 is positive then n is positive
Also, if n/5 is an integer, then we can conclude that n is divisible by 5
If n is a positive number that's divisible by 5, then some possible values of n are: 5, 10, 15, 20, 25, 30,.....
NOTICE that all of the possible values of n are greater than or equal to 5.
In other words, it is NOT POSSIBLE for n to be an integer less than 5
So, the answer to the target question is "No, n is definitely NOT an integer less than 5"
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

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Re: Is n an integer less than 5?  [#permalink]

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05 Jan 2019, 15:27
This should be marked as a 500 level question, imo.

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Re: Is n an integer less than 5?  [#permalink]

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26 Nov 2019, 21:45
Question asks, n <5 , where n is an integer ?

1) 5n = +ve

n= -1, 5n = -5
n= 0, 5n = 0
n= 1, 5n = 5, so n must be <5 & >0. INSUFFICIENT

2) n/5 = integer. This satisfies only when n=5. SO n is not less than 5. SUFFICIENT.
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Re: Is n an integer less than 5?  [#permalink]

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27 Nov 2019, 06:43
This is a fairly easy question on integer properties. In such a question, a smart approach would be to prove that the smallest value of n is equal to 5, so that we can answer the question with a NO.

From statement 1, 5n is a positive integer. This does not tell us anything about n, conclusively. For example, if n = $$\frac{1}{5}$$, 5n = 1 satisfies statement 1. But, n is not even an integer.

If n = 10, 5n = 50 also satisfies statement 1. Here, n is an integer greater than 5.
Statement 1 is insufficient. Possible answer options are B, C or E. Answer options A and D can be eliminated.

From statement 2, $$\frac{n}{5}$$ is a positive integer. We can therefore rewrite the equation as,
n = 5*positive integer.

Now, we know that the smallest positive integer is 1. Therefore, the smallest value for n will be 5*1 = 5. Since the smallest value of n is 5, it’s clear that n is NOT an integer less than 5. This is sufficient to answer the question with a definite NO.

Statement 2 is sufficient. Answer options C and E can be eliminated, the correct answer option is B.

Hope that helps!
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Re: Is n an integer less than 5?   [#permalink] 27 Nov 2019, 06:43
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