M05-29

Hello,

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

Only positive numbers can be primes.

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

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.

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation.

I think this is a high-quality question and I agree with explanation. Excellent question! I missed the positive word in the question stem.

Bunuel, In second statement when P=0 then 2P will be 0, how can we consider then 0 is divisible by 11.

0 is divisible by all integers (except 0 itself). Divisible means divisible without a remainder, so x is divisible by y, means that x/y = integer. Since 0/11 = 0 = integer, then 0 is divisible by 11.

Hope it's clear.

I think this is a high-quality question and I agree with explanation. This is a great question that makes sure you pay attention to the details.

Hi Bunuel,

During my mock exam I saw very clearly that there was 0, but the 2nd sentence says 2p is divisible by 11. And during the exam I was thinking: does GMAT mean 0 is divisible by 11 in these types of questions? I was stuck on a technicality. Then I thought that "divisible by 11" would mean the same as 2p is a multiple of 11. And I have seen plenty of problems where multiples of 11 are numbers more than or equal to 11 (so not 0). According to the logic given in your explanation, 0 is divisible by any number (I am also aware that GMAT does not test 0/0 cases). So, If I want to avoid any any doubts on the exam, should I think that whenever the problem says divisible by some number 0 is always an alternative?

And also, I would be glad to hear about the multiples of numbers. Am I correct at least about this matter (or is 0 multiple of any number)?

0 is divisible by all integers (except 0 itself). Divisible means divisible without a remainder, so integer x is divisible by integer y, means that x/y = integer. Since 0/11 = 0 = integer, then 0 is divisible by 11 (0 is a multiple of 11).

Next, multiples of 11 are ..., -22, -11, 0, 11, 22, 33, ... Good news is that on the GMAT all divisibility/remainder questions are limited to positive integers only. So, a question will tell you in advance that all unknowns are positive integers. Though you still should know properties of 0 and that negative integers also can be multiples of a number just in case.

Hope it's clear.
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As per statement 2, can p be equal to a negative integer also?

Yes, for example, if p = -11.

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.