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# Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by

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Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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23 Sep 2015, 01:43
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Difficulty:

5% (low)

Question Stats:

85% (00:49) correct 15% (00:47) wrong based on 166 sessions

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Is n/14 an integer?

(1) n is divisible by 28.

(2) n is divisible by 70.

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4486
Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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23 Sep 2015, 14:16
2
Is n/14 an integer?

(1) n is divisible by 28.

(2) n is divisible by 70.

I'm happy to respond.

This question basically hinges on the idea that
If N is divisible by any multiple of k, then N is divisible by k.
This is always true. See this free math lesson video:
http://gmat.magoosh.com/lessons/1248-multiples

Each statement says that n is divisible by a multiple of 14, so each one implies that n is divisible by 14. Both are sufficient. OA = (D).

Does all this make sense?
Mike
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Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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23 Sep 2015, 15:09
3
Is n/14 an integer?

(1) n is divisible by 28.
(2) n is divisible by 70.

Mike's approach is perfect. Here's another way to look at it.

Background information
A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N

Consider these examples:
24 is divisible by 3 because 24 = (2)(2)(2)(3)
Likewise, 70 is divisible by 5 because 70 = (2)(5)(7)
And 112 is divisible by 8 because 112 = (2)(2)(2)(2)(7)
And 630 is divisible by 15 because 630 = (2)(3)(3)(5)(7)
---------------------------------------------------------------------------

Target question: Is n/14 an integer?

REPHRASED target question: Is there a 14 hiding in the prime factorization of n?

Statement 1: n is divisible by 28
In other words, n = (28)(k) where k is some integer
Rewrite 28 to get: n = (2)(2)(7)(k)
We can see that there IS a 14 hiding in the prime factorization of n
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: n is divisible by 70
In other words, n = (70)(k) where k is some integer
Rewrite 70 to get: n = (2)(5)(7)(k)
We can see that there IS a 14 hiding in the prime factorization of n
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent
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Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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17 Jul 2017, 18:40
GMATPrepNow wrote:
Is n/14 an integer?

(1) n is divisible by 28.
(2) n is divisible by 70.

Mike's approach is perfect. Here's another way to look at it.

Background information
A lot of integer property questions can be solved using prime factorization.
For questions involving divisibility, divisors, factors and multiples, we can say:
If N is divisible by k, then k is "hiding" within the prime factorization of N

Consider these examples:
24 is divisible by 3 because 24 = (2)(2)(2)(3)
Likewise, 70 is divisible by 5 because 70 = (2)(5)(7)
And 112 is divisible by 8 because 112 = (2)(2)(2)(2)(7)
And 630 is divisible by 15 because 630 = (2)(3)(3)(5)(7)
---------------------------------------------------------------------------

Target question: Is n/14 an integer?

REPHRASED target question: Is there a 14 hiding in the prime factorization of n?

Statement 1: n is divisible by 28
In other words, n = (28)(k) where k is some integer
Rewrite 28 to get: n = (2)(2)(7)(k)
We can see that there IS a 14 hiding in the prime factorization of n
Since we can answer the REPHRASED target question with certainty, statement 1 is SUFFICIENT

Statement 2: n is divisible by 70
In other words, n = (70)(k) where k is some integer
Rewrite 70 to get: n = (2)(5)(7)(k)
We can see that there IS a 14 hiding in the prime factorization of n
Since we can answer the REPHRASED target question with certainty, statement 2 is SUFFICIENT

Cheers,
Brent

lol "there's a 14 hiding" that bastard
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Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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17 Jul 2017, 18:44
Is n/14 an integer?

(1) n is divisible by 28.

(2) n is divisible by 70.

Is N/14 an integer means is N a multiple of 4 basically or is N divisible by 4 - seems a bit more obvious than it actually is

n/ 7 x 2 =x where x is an integer

OR

n =7 x 2 x K where "K" is some constant

St 1

n = 7 x 2 x 2 x K

OR

n/ 7 x 2 x 2= some integer - it becomes clearer to see that n must be a multiple of 14

St 2

n = 7 x 5 x 2 x k
n= [7 x 2] x 5 x k

D
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Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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30 Jul 2017, 16:40
Is n/14 an integer?

(1) n is divisible by 28.

(2) n is divisible by 70.

We need to determine whether n/14 = integer.

Statement One Alone:

n is divisible by 28.

Since 14 is a factor of 28, n will always be divisible by 14. Statement one alone is sufficient to answer the question.

Statement Two Alone:

n is divisible by 70.

Since 14 is a factor of 70, n will always be divisible by 14. Statement two alone is sufficient to answer the question.

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Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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24 Jan 2018, 18:27
I got the right answer by thinking about it as multiples of 14.

So, 14, 28, 42, 56, 70 and since 28 and 70 are in the multiples of 14, then both 1 and 2 are sufficient.

Is this way of thinking correct?
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Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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24 Jan 2018, 22:01
1
rnz wrote:
I got the right answer by thinking about it as multiples of 14.

So, 14, 28, 42, 56, 70 and since 28 and 70 are in the multiples of 14, then both 1 and 2 are sufficient.

Is this way of thinking correct?

Hi

Yes I think this way of thinking is correct. Any multiple of 14 will have to be divisible by 14, also any multiple of 42 will also be divisible by 14 (since 42 itself is a multiple of 14, so any multiple of 42 will be in turn a multiple of 14 also).
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Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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27 Jan 2018, 20:24
Is n/14 an integer?

(1) n is divisible by 28.

(2) n is divisible by 70.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question, and then recheck the question.

We can modify the original condition and question as follows.

The question asks if n is divisible by 14.

Since we have 1 variable (n) and 0 equations, D is most likely to be the answer. So, we should consider each of the conditions on their own first.

Condition 1)
Since n is divisible by 28, n is divisible by 14.
The condition 1) is sufficient.

Condition 2)
Since n is divisible by 70, n is divisible by 14.
The condition 2) is sufficient.

If the original condition includes “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations” etc., one more equation is required to answer the question. If each of conditions 1) and 2) provide an additional equation, there is a 59% chance that D is the answer, a 38% chance that A or B is the answer, and a 3% chance that the answer is C or E. Thus, answer D (conditions 1) and 2), when applied separately, are sufficient to answer the question) is most likely, but there may be cases where the answer is A,B,C or E.
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Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by  [#permalink]

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27 Mar 2018, 05:30
Is n/14 an integer?

(1) n is divisible by 28.

(2) n is divisible by 70.

Since 28 and 70 both are multiples of 14, and "n" is divisible by both 28 and 70,

Then certainly "n" is divisible by 14.

(D)
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Re: Is n/14 an integer? (1) n is divisible by 28. (2) n is divisible by   [#permalink] 27 Mar 2018, 05:30
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