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(1) \(p\) is a prime number. If \(p=2\) then the answer is NO but if \(p=11\) then the answer is YES. Not sufficient.

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

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

(1) \(p\) is a prime number. If \(p=2\) then the answer is NO but if \(p=11\) then the answer is YES. Not sufficient.

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

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

Answer: C

Hello,

But we still dont know if it is positive, shouldnt the answer be E?
_________________

(1) \(p\) is a prime number. If \(p=2\) then the answer is NO but if \(p=11\) then the answer is YES. Not sufficient.

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

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

Answer: C

Hello,

But we still dont know if it is positive, shouldnt the answer be E?

Only positive numbers can be primes.
_________________

(1) \(p\) is a prime number. If \(p=2\) then the answer is NO but if \(p=11\) then the answer is YES. Not sufficient.

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

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

Answer: C

Hello,

But we still dont know if it is positive, shouldnt the answer be E?

Prime number can be only positive
_________________

(1) \(p\) is a prime number. If \(p=2\) then the answer is NO but if \(p=11\) then the answer is YES. Not sufficient.

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

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

Answer: C

Bunuel can you please tell us all the properties of zero which will be useful in GMAT exam

(1) \(p\) is a prime number. If \(p=2\) then the answer is NO but if \(p=11\) then the answer is YES. Not sufficient.

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

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

Answer: C

Bunuel can you please tell us all the properties of zero which will be useful in GMAT exam

ZERO:

1. 0 is an integer.

2. 0 is an even integer. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder and as zero is evenly divisible by 2 then it must be even.

3. 0 is neither positive nor negative integer (the only one of this kind).

4. 0 is divisible by EVERY integer except 0 itself.

I dont understand why prime numbers are only positive. A prime is a number that has only 2 unique factors. 1 and the number itself. So why isnt -2 or -11 prime ?

I got the answer correct and agree with you Bunuel. I just want to ask that in case of (2) 2p is divisible by 11, can p be a fraction like 11/7, this will still be divisible by 11.

I dont understand why prime numbers are only positive. A prime is a number that has only 2 unique factors. 1 and the number itself. So why isnt -2 or -11 prime ?

It is by definition "A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself. A natural number greater than 1 that is not a prime number is called a composite number." A prime is a whole number, not a fraction.

I got the answer correct and agree with you Bunuel. I just want to ask that in case of (2) 2p is divisible by 11, can p be a fraction like 11/7, this will still be divisible by 11.

2p is divisible by 11 implies that 2p must be an integer. p there can be a fraction, say 11/2, but not 11/7 because in this case 2p is not an integer.
_________________

2) The stem does not say that p is an integer, thus p could be 5.5, 16.5, etc., or it could also be 0 (0 is an integer though), and still follow this rule. Insufficient.

Together, p has to be a prime number that when multiplied by 2 is divisible by 11. Thus, the only possible value for p is 11.

Question really tests properties of zero. The trick is to remember (1) the number 0 is divisible by every number except 0 (0/0 is undefined) and (2) the number 0 is not positive or negative it's neutral.

With (b) 2p is divisible by 11 Using rule (1) above, P can equal 0, 5.5, 11, 16.5, 22, etc. and the statement "2p is divisible by 11" will hold. With p=0, you have 2x0 = 0 divided by 11 = 0.

Is 4p/11 a positive integer? with p=0, 4p/11 is 0. As (2) above mentions the number 0 is not positive (or negative). so, no, it is not a positive integer. All other values of P (5.5, 11, 16.5) would yield a positive integers if plugged in 4p/11, so Yes, it is a positive integer if P is not 0. So, insufficient

I dont understand why prime numbers are only positive. A prime is a number that has only 2 unique factors. 1 and the number itself. So why isnt -2 or -11 prime ?

You can look at this like, -2 is not prime because it has more factors; ie 2, 1, -1, -2 Hence, the basic definition of prime numbers gets violated.
_________________

(1) \(p\) is a prime number. If \(p=2\) then the answer is NO but if \(p=11\) then the answer is YES. Not sufficient.

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

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

Answer: C

i agree with the solution. Shouldn't the final choice be - "B" only 2nd choice is correct

(1) \(p\) is a prime number. If \(p=2\) then the answer is NO but if \(p=11\) then the answer is YES. Not sufficient.

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

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

Answer: C

i agree with the solution. Shouldn't the final choice be - "B" only 2nd choice is correct

The answer is NOT B because the second statement is NOT sufficient on its own. There are TWO different values of p given there giving TWO different answers to the question.
_________________

Tool is great, just thought it would be nice to have the questions marked as correct once they've been answered correctly in test mode (even if previously incorrect)