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prime numbers between 4 and 18

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by sanju09 » Wed Mar 09, 2011 4:27 am
Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?
A. 21
B. 60
C. 119
D. 180
E. 231


[spoiler]https://www.gmatmaths.com[/spoiler]
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by anshumishra » Wed Mar 09, 2011 4:45 am
sanju09 wrote:Two different prime numbers between 4 and 18 are chosen. When their sum is subtracted from their product, which of the following numbers could be obtained?
A. 21
B. 60
C. 119
D. 180
E. 231


[spoiler]https://www.gmatmaths.com[/spoiler]
All the primes in the given range -> odd
Multiplication of two primes (both odd) = odd
Addition of two primes (both odd) = even

So, M(odd) - A(odd) = odd - even = odd
Choice, B and D out.
The minimum value = 7*5 -(7+5) = 35 - 12 = 23, A out
The maximum value = 17*13 - (17+13) = 221 - 30 = 191, D out

So, C is the answer. {Which is 13*11 - (13+11), although we don't need to calculate it to get the answer}
Thanks
Anshu

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