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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.... _________________

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.