AAPL wrote:GMAT Prep
If \(n\) is an integer, is \(n/7\) an integer?
1) \(3n/7\) is an integer.
2) \(5n/7\) is an integer.
OA D
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)
--------------------------------
Okay, onto the question:
Target question: Is n/7 an integer?
Statement 1: 3n/7 is an integer
If 3n/7 is an integer, then we can also say that 3n is DIVISIBLE by 7.
This means that there's a 7 HIDING in the prime factorization of 3n.
Since there's no 7 HIDING in 3, there must be a 7 HIDING in the prime factorization of n.
If there's a 7 HIDING in the prime factorization of n, then
n must be divisible by 7
If n is divisible by 7, then
n/7 is DEFINITELY an integer.
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: 5n/7 is an integer
If 5n/7 is an integer, then we can also say that 5n is DIVISIBLE by 7.
This means that there's a 7 HIDING in the prime factorization of 5n.
Since there's no 7 HIDING in 5, there must be a 7 HIDING in the prime factorization of n.
If there's a 7 HIDING in the prime factorization of n, then
n must be divisible by 7
If n is divisible by 7, then
n/7 is DEFINITELY an integer.
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
