What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?
(A) 7
(B) 14
(C) 24
(D) 28
(E) 35
(A) 7
(B) 14
(C) 24
(D) 28
(E) 35
The wording of this question is a bit too ambiguous for the GMAT. Even though we can reason out what the question is supposed to say, you'll never be put in that position on test day. What's the source?
Better wording would have been:
Like many number property questions, we can attack it two different ways: pick numbers or use number property concepts. Since we have actual numbers in the choices, backsolving should be a quick way to solve this problem.What is the smallest integer that when divided by the product of a prime number and 7 yields a prime number?
First, let's note that the smallest multiple of 7 and a prime is 14. So, we'll use that as our divisor.
The question asks for the "smallest" integer that fits the rule, so let's start at the top:
A) 7/14 = not prime.
B) 14/14 = not prime.
c) 24/14 = not integer.
d) 28/14 = 2 which is prime... done!
The second way to solve would be by reasoning it out (we almost got there already): we want the smallest possible number that fits the rule, so let's pick the smallest possible primes.
7*2 gives us our divisor of 14.
2 is the smallest prime, so to get our final answer x, we simply set up:
x/14 = 2
x = 28... choose D!
GmatKiss wrote:What is the smallest integer that can be divided by the product of a prime number and 7 while yielding a prime number?
(A) 7
(B) 14
(C) 24
(D) 28
(E) 35
