BTGmoderatorDC wrote: ↑Mon Jan 25, 2021 5:07 pm
Is n/14 an integer?
(1) n is divisible by 28.
(2) n is divisible by 70.
OA
D
Source: Manhattan Prep
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
