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Re: Math DS (m05q29) [#permalink]
25 Oct 2009, 09:45

eyunni wrote:

Is 4Q/11 a positive integer?

(1) Q is a prime number (2) 2Q is divisible by 11

1: Q could be 2 or 3 or 5 or 7 or 11 or 13. NSF.. 2: Q could be -ve, 0 or +ve. For ex: -11 or -5.50 or 0 or 5.50 or 11 or any multiples of 11. NSF..

1&2: Q must be a prime and 2Q must be divisible by 11.

Q must be a prime eliminates the chances that Q is a -ve, 0 and fraction. Given that Q is a prime and 2Q must be divisible by 11 eliminate the chances that Q is other than 11.

Therefore Q = 11 and 4Q/11 is a +ve integer i.e. 4.

Thats a good question though....
_________________

Re: Math DS (m05q29) [#permalink]
26 Jun 2010, 17:12

C

1) Q can be 11 => it works or Q can be 3 => is not good, hence insufficient 2) 2Q is divisible by B, but we don't know if the result of this division is a positive integer, hence insufficient

(1) q is a prime number --> if q=2 then the answer is NO but if q=11 then the answer is YES. Not sufficient.

(2) 2q is divisible by 11 --> \frac{2q}{11}=integer --> 2*\frac{2q}{11}=\frac{4q}{11}=2*integer=integer, but we don't know whether this integer is positive or not: consider q=0 and q=11. Not sufficient.

(1)+(2) Since q is a prime number and 2q is divisible by 11, then q must be equal to 11 (no other prime but 11 will yield integer result for \frac{2q}{11} ) --> \frac{4q}{11}=4. Sufficient.