What is the smallest integer that can be divided by the product of a

Question

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

chetan2u · Answer

The integer is nothing but 7*p*p
P can be 2 at the lowest value, so 7*2*2=28
D

Sprincejindal · Answer

To get the smallest integer we need to multiply 7 with the smallest prime number, which is 2. 
2*7 = 14. 
Answer - B

chetan2u · Answer

thats a TRAP.
Be careful while reading Q..
 
in your calculation 14/14 will leave 1 whereas Q says it should yield a prime number

6urra · Answer

First of all can product of a prime number mean prime*1? Its the product of a prime, right?

Secondly doesn't it mean that division by 7 should yield a prime aswell? Thereby making the answer either B or E.

Paulli1982 · Answer

IMO, it is D. 7 x 2 x 2 = 28.

Sprincejindal · Answer

Oh yes, you are right!
So the integer is 2*2*7 and it can be divided with the product of 2*7 to yield 2, which is a prime number. Right?
Thanks!

rocko911 · Answer

How do u know it should be p * p * 7 and not just p*7 ?

the product of a prime number and 7 means A prime number means just one NUMBER .....Like product of 7 and 8........How cn u tell that its product of p * p

chetan2u · Answer

hi

this means when you divide that integer by PRODUCT of p and 7, it should yield another prime number..
why p*p because we have to find the smallest number, so we will take p as the smallest prime number and what is remaining also as p, which should be 2

Jerry1982 · Answer

in case of first you are incorrect 1 is not Prime ,
Second you are partially correct you missed an info : the question asks for the smallest integer and 28< 35 . Hence the answer has to be D.

be generous with kudos if you like the answer

EMPOWERgmatRichC · Answer

Hi All,

We're asked to find the smallest integer that can be DIVIDED by the PRODUCT of a PRIME number and 7 AND will yield a PRIME number as the result. We can answer this question by TESTing THE ANSWERS.

Since we're asked for the SMALLEST number that will fit the above information, we should start with Answer A: 7....

The smallest product that can occur between 7 and a prime is (7)(2) = 14. 7 is NOT divisibly by 14, so we can eliminate Answer A.

Answer B: 14...

While 14 is divisible by 14, the end result is 1 - but that is NOT a prime number. Eliminate Answer B.

Answer C: 24

24/14 is NOT a prime. The next two products to consider would be (7)(3) = 21 and (7)(5) = 35. However, 24/21 and 24/35 are NOT primes. Eliminate Answer C.

Answer D: 28 
28/14 = 2 - and that IS a prime. This matches everything we were told, so this must be the answer.

Final Answer:  D

GMAT assassins aren't born, they're made, 
Rich

ScottTargetTestPrep · Answer

Since the smallest prime number is 2, the smallest product of a prime number and 7 is 2 x 7 = 14, and the smallest integer that yields a prime number when it is divided by 14 is 28 (notice that 28/14 = 2).
 
Answer: D

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What is the smallest integer that can be divided by the product of a

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