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by sana.noor » Sun May 19, 2013 11:47 pm
For any integer m greater than 1, $m denotes the product of all the integers from 1 to m, inclusive. How many prime numbers are there between $7 + 2 and $7 + 10, inclusive?
(A) None
(B) One
(C) Two
(D) Three
(E) Four

OA is A
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by Atekihcan » Mon May 20, 2013 12:19 am
$7 = 1*2*3*4*5*6*7

($7 + 2) = 1*2*3*4*5*6*7 + 2 = 2*(1*3*4*5*6*7 + 1) = multiple of 2
Similarly, ($7 + 3), ($7 + 4), ..., and ($7 + 7) will be multiple of 3, 4, 5, 6, and 7, respectively.

Now, ($7 + 8) = 1*2*3*4*5*6*7 + 8 = 2*(1*3*4*5*6*7 + 4) = multiple of 2
Similarly, ($7 + 9) and ($7 + 10) will be divisible by 3 and 2, respectively.

So, none of the integers in that range is prime.

Answer : A
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by Brent@GMATPrepNow » Mon May 20, 2013 7:20 am
This question is a variation of 2 official GMAT questions. If you'd like more practice, try these two:

- https://www.beatthegmat.com/laymans-term ... t9968.html
- https://www.beatthegmat.com/help-on-quan ... 26500.html

Cheers,
Brent
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