M7MBA wrote: ↑

Wed Sep 09, 2020 6:50 am

Is \(\dfrac{n}{14}\) an integer?

(1) \(n\) is divisible by \(28.\)

(2) \(n\) is divisible by \(70.\)

Answer: D

Source: Manhattan GMAT

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)
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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