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

Question

Is n/14 an integer?

(1) n is divisible by 28.

(2) n is divisible by 70.

mikemcgarry · Answer

Dear shasadou , 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: https://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 :-)

BrentGMATPrepNow · Answer

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

Answer = D

Cheers,
Brent

Nunuboy1994 · Answer

lol "there's a 14 hiding" that bastard

Nunuboy1994 · Answer

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=     x 5 x k

D

ScottTargetTestPrep · Answer

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.

Answer: D

rnz · Answer

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?

amanvermagmat · Answer

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).

MathRevolution · Answer

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.

Therefore, D is the answer.

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.

AkshdeepS · Answer

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)

An78w · Answer

@Banuel -

When it is said that n is divisible by 28, does it necessarily mean that the quotient will be an integer?

I thought that the statements given were traps.

Statement 1 - n is divisible by 28. n could be 35 (28x1.25). Here 35 is divisible by 28 (statement doesn't say that it gives an integer). But 35/14 doesn't give an integer. Whereas if n were 140, n/14 would be an integer. Hence I thought it was not sufficient.

Same case for statement 2.

Pls help

Bunuel · Answer

Integer x is divisible by integer y ALWAYS means that x/y = integer (y is a factor of x).

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards