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Math Expert V
Joined: 02 Sep 2009
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3
22 00:00

Difficulty:   65% (hard)

Question Stats: 45% (01:06) correct 55% (01:00) wrong based on 195 sessions

### HideShow timer Statistics Is $$\frac{4p}{11}$$ a positive integer?

(1) $$p$$ is a prime number

(2) $$2p$$ is divisible by 11

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Math Expert V
Joined: 02 Sep 2009
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Official Solution:

(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.

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Bunuel wrote:
Official Solution:

(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.

Hello,

But we still dont know if it is positive, shouldnt the answer be E?
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Math Expert V
Joined: 02 Sep 2009
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aimtoteach wrote:
Bunuel wrote:
Official Solution:

(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.

Hello,

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

Only positive numbers can be primes.
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GMAT 1: 660 Q48 V33 GMAT 2: 740 Q50 V40 ### Show Tags

aimtoteach wrote:
Bunuel wrote:
Official Solution:

(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.

Hello,

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

Prime number can be only positive
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Joined: 29 Oct 2014
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Bunuel wrote:
Official Solution:

(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.

Bunuel can you please tell us all the properties of zero which will be useful in GMAT exam
Math Expert V
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1
2
sharma123 wrote:
Bunuel wrote:
Official Solution:

(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.

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.

Check more here: number-properties-tips-and-hints-174996.html
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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 ?
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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.
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ayushkhatri wrote:
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.
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knitgroove04 wrote:
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.
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Hi,
If the question just asked whether 4p/11 is an integer and not positive integer then option (B) would be correct, right?
Math Expert V
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ishan92 wrote:
Hi,
If the question just asked whether 4p/11 is an integer and not positive integer then option (B) would be correct, right?

___________________
Right.
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Bunuel wrote:
Is $$\frac{4p}{11}$$ a positive integer?

(1) $$p$$ is a prime number

(2) $$2p$$ is divisible by 11

1) P would have to be equal to 11. Insufficient.

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.

C
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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
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ayushkhatri wrote:
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.
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Bunuel wrote:
Official Solution:

(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.

i agree with the solution. Shouldn't the final choice be - "B" only 2nd choice is correct
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19941010 wrote:
Bunuel wrote:
Official Solution:

(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.

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.
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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)
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I don't agree with the explanation. B is stated to be sufficient and yet the answer is C Re M05-29   [#permalink] 11 Aug 2016, 13:46

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# M05-29

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