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by swapna » Tue Feb 09, 2010 5:18 pm
If p and are positive integers and pq=24, what is the value of p?

q/6 is an integer
p/2 is an integer

Answer is e.

I felt a can be used to determine the value of p. But, the book says the possible values of q are therefore 6,12 and 24 and for each of these there is a different value of p(4,2 and 1) hence not sufficient.

MY doubt is how could they take q as 12 or 24, when pq is a two digit integer??
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by ajith » Tue Feb 09, 2010 5:22 pm
swapna wrote:If p and are positive integers and pq=24, what is the value of p?

q/6 is an integer
p/2 is an integer

Answer is e.

I felt a can be used to determine the value of p. But, the book says the possible values of q are therefore 6,12 and 24 and for each of these there is a different value of p(4,2 and 1) hence not sufficient.

MY doubt is how could they take q as 12 or 24, when pq is a two digit integer??
Hi Swapna,

I get your doubt.

pq when mentioned nothing else means p*q where p and q are variables. If they meant the two digit no: 'pq' they will explicitly mention that.

Hence in this case p and q take single digit or double digit values as long as p*q is 24. I hope it is clear
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by money9111 » Tue Feb 09, 2010 10:08 pm
So this question E because we can't narrow down which factor of 24 p would actually be?
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by shashank.ism » Wed Feb 10, 2010 7:46 am
swapna wrote:If p and are positive integers and pq=24, what is the value of p?

q/6 is an integer
p/2 is an integer

Answer is e.

I felt a can be used to determine the value of p. But, the book says the possible values of q are therefore 6,12 and 24 and for each of these there is a different value of p(4,2 and 1) hence not sufficient.

MY doubt is how could they take q as 12 or 24, when pq is a two digit integer??
p and q are positive integers and pq=24,
statement 1 : q/6 =Integer so possibilities q= 6,12,18,24 p=4,2, Not integer, 1
so possible values q=6,12,24, p=4,2,1 respectively .(p,q)=(1,24),(2,12),(4,6) -- not sufficient

statement 2: p/2 = integer so possible values of p and q both being integer are
(2,12),(4,6),(6,4),(8,3),(12,2),(24,1) -- not sufficient

combined: p,q = (2,12),(4,6) -- not sufficient

so E
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by money9111 » Wed Feb 10, 2010 8:08 am
combined: p,q = (2,12),(4,6) -- not sufficient (so i was correct) :-)
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by shashank.ism » Wed Feb 10, 2010 9:43 am
money9111 wrote:combined: p,q = (2,12),(4,6) -- not sufficient (so i was correct) :-)
Yeah you were correct for sure, and no need to describe that. Its quite evident. People can easily figure it out.
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by harsh.champ » Wed Feb 10, 2010 10:37 am
swapna wrote:If p and are positive integers and pq=24, what is the value of p?

q/6 is an integer
p/2 is an integer

Answer is e.

I felt a can be used to determine the value of p. But, the book says the possible values of q are therefore 6,12 and 24 and for each of these there is a different value of p(4,2 and 1) hence not sufficient.

MY doubt is how could they take q as 12 or 24, when pq is a two digit integer??
We see that since both p and q are integers ,q has to be a multiple of 6. which is 6,12,18,24.
we can rule out 18 since 24/18 is not an integer.
So, 1st statement is not sufficient.
As for 2nd statement ,the reasoning is similar as above.Hence,insufficient.

Combining both we get 12,2 and 6,4 hence still insufficient.

Hence ,e.

Yes , in haste we can do the mistake of taking pq as a 2 digit number.
Thanks to ajith for pointing put it out.

Also in GMAT they will specificallt denote whether they measn multiplication of 2 no.s or simply a 2 digit no as in GMAT Preps and other test also they mention it specifically.
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