M05-29

Question

If p is an integer, is  \frac{4p}{11}  a positive integer?

(1)  p  is a prime number
 
(2)  2p  is an integer divisible by 11

Bunuel · Accepted Answer

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. Check more here: number-properties-tips-and-hints-174996.html

Bunuel · Answer

Official Solution:

If p is an integer, is  \frac{4p}{11}  a positive integer? 
 
In order for  \frac{4p}{11}  to be a positive integer,  p  must be a positive multiple of 11, such as 11, 22, 33, and so on.
 
(1)  p  is a prime number:
 
If  p=11  then the answer is YES but if  p  is any other prime than the answer is NO. Not sufficient.
 
(2)  2p  is an integer divisible by 11: 
 
Since 2 is not divisible by 11, for  2p  to be divisible by 11,  p  must be divisible by 11. Therefore,  p  can be any multiple of 11, such as ..., -33, -22, -11, 0, 11, 22, 33, and so on. This statement alone is not sufficient.
 
(1)+(2) (1) says that  p  is prime, and (2) says that  p  is a multiple of 11. The only prime number that is also a multiple of 11 is 11 itself. Therefore,  p=11  and  \frac{4p}{11}=4 , which is a positive integer. Sufficient.

Answer: C

aimtoteach · Answer

Hello,

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

Bunuel · Answer

Only positive numbers can be primes.

sharma123 · Answer

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

knitgroove04 · Answer

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.

Bunuel · Answer

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.

damduy · Answer

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

gupta87 · Answer

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

culsivaji · Answer

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

patto · Answer

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

mzaid · Answer

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

Bunuel · Answer

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.

aloysiusgaul · Answer

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.

Foreheadson · Answer

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)?

Bunuel · Answer

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.
_________________

DamanDeep · Answer

As per statement 2, can p be equal to a negative integer also?

Bunuel · Answer

Yes, for example, if p = -11.

Bunuel · Answer

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

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