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# If P & Q are positive integers , what is the value of Q

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Intern
Joined: 30 Apr 2007
Posts: 3
If P & Q are positive integers , what is the value of Q [#permalink]

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17 Jun 2007, 02:56
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If P & Q are positive integers , what is the value of Q ?

1. S is the product of two prime numbers greater than 10

2. S=P. Q3 ( Read as Q cube)

SVP
Joined: 01 May 2006
Posts: 1796

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17 Jun 2007, 04:03
(C) for me

We have:
p > 0 and q > 0

q=?

From 1
S = i * j where i > 10 and j > 10 and i, j are primes.

No relationship with P or Q....

INSUFF.

From 2
S = p*q^3

S could be anything and so is q...

INSUFF.

Both 1 and 2
p*q^3 = i*j

Implies that, as i & j are primes:
o p = i*j
o q^3 = 1 <=> q = 1

SUFF.
Manager
Joined: 17 May 2007
Posts: 170

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17 Jun 2007, 05:22

Director
Joined: 14 Jan 2007
Posts: 774

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17 Jun 2007, 05:38
I agree with Fig.
Q should be 1 to satisfy the equation for all primes > 10.
Director
Joined: 13 Mar 2007
Posts: 543
Schools: MIT Sloan

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17 Jun 2007, 09:31
i dont get the expln for C.

can someone pls explain ?
SVP
Joined: 01 May 2006
Posts: 1796

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17 Jun 2007, 10:12
i dont get the expln for C.

can someone pls explain ?

S is composed of 2 prime integers.... q^3 cannot give a prime integer (ex 11^3, 13^3 are not prime integers), so it must be equal to 1 to not interfer and to make it possible for S to be a multiple of 2 primes integers, provided by p here.
Director
Joined: 13 Mar 2007
Posts: 543
Schools: MIT Sloan

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17 Jun 2007, 13:28
Thx Fig !

appreciate ur enthu in the forum evn after ur long done with ur GMAT !
SVP
Joined: 01 May 2006
Posts: 1796

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17 Jun 2007, 13:38
Thx Fig !

appreciate ur enthu in the forum evn after ur long done with ur GMAT !

U are welcome ... Have u planned to pass the GMAT soon?
Director
Joined: 13 Mar 2007
Posts: 543
Schools: MIT Sloan

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18 Jun 2007, 21:32
Fig wrote:
Thx Fig !

appreciate ur enthu in the forum evn after ur long done with ur GMAT !

U are welcome ... Have u planned to pass the GMAT soon?

yes yes .. gives me shivers though !
Senior Manager
Joined: 03 Jun 2007
Posts: 376

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19 Jun 2007, 12:14
This is abad question though. When combining the 2 statements we need to assume both are true. So by stmt 1 we are told that S is a product of 2 prime ints > 10. Using stmt2, q^3 cannot exist at all
Senior Manager
Joined: 19 Feb 2007
Posts: 325

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20 Jun 2007, 09:15
dahcrap wrote:
This is abad question though. When combining the 2 statements we need to assume both are true. So by stmt 1 we are told that S is a product of 2 prime ints > 10. Using stmt2, q^3 cannot exist at all

It can if q=1.

eg: S = 11 * 13

also S = (11* 13) * 1^3
S = P * Q^3

Hope this explains.
Director
Joined: 26 Feb 2006
Posts: 899

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20 Jun 2007, 13:51
Fig wrote:
(C) for me

We have:
p > 0 and q > 0

q=?

From 1
S = i * j where i > 10 and j > 10 and i, j are primes.

No relationship with P or Q....

INSUFF.

From 2
S = p*q^3

S could be anything and so is q...

INSUFF.

Both 1 and 2
p*q^3 = i*j

Implies that, as i & j are primes:
o p = i*j
o q^3 = 1 <=> q = 1

SUFF.

amitsamel wrote:
If P & Q are positive integers, what is the value of Q ?

1. S is the product of two prime numbers greater than 10
2. S = P . Q^3

C. agree with Fig.

if P and Q were positive numbers, the answer would be E. but P and Q are integers, it makes sense Q is 1 and C is the answer.

I too was heading for E but realized the mistake immidiately.
Senior Manager
Joined: 04 Jun 2007
Posts: 366

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10 Sep 2007, 20:23
I still don't see how it's C?

ST. 1 says S is the product of two prime numbers which are both >10
ST. 2 gives us S= P*Q^3

which means P is a prime>10
and Q^3 is a prime>10

hence Q^3 needs to be a perfect cube + a prime> 10
perfect cubes >10 are 27, 64, 125, none of which are primes
there is no perfect cube which is also a prime> 10
how can we take Q to be equal to 1, that would make Q^3= 1 and 1<10

the answer has to be E.
CEO
Joined: 29 Mar 2007
Posts: 2560

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10 Sep 2007, 20:51
Fig wrote:
i dont get the expln for C.

can someone pls explain ?

S is composed of 2 prime integers.... q^3 cannot give a prime integer (ex 11^3, 13^3 are not prime integers), so it must be equal to 1 to not interfer and to make it possible for S to be a multiple of 2 primes integers, provided by p here.

Ah ok now I see. I thought S1 was sayin that S is the product of 2 primes that are both greater than 10.

Was like how can this be C?
Director
Joined: 08 Jun 2007
Posts: 573

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10 Sep 2007, 20:57
Well it got me nuts first. But finally managed C.
Fig gr8 explanation.
Senior Manager
Joined: 04 Jun 2007
Posts: 366

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10 Sep 2007, 21:27
GMATBLACKBELT wrote:
Fig wrote:
i dont get the expln for C.

can someone pls explain ?

S is composed of 2 prime integers.... q^3 cannot give a prime integer (ex 11^3, 13^3 are not prime integers), so it must be equal to 1 to not interfer and to make it possible for S to be a multiple of 2 primes integers, provided by p here.

Ah ok now I see. I thought S1 was sayin that S is the product of 2 primes that are both greater than 10.

Was like how can this be C?

exactly, I am not sure why everyone is agreeing that Q is 1 when ST. 1& 2 implies clearly that Q^3 must be a prime> 10.
1 is not a prime and it is not greater than 10.
Senior Manager
Joined: 27 Aug 2007
Posts: 253

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11 Sep 2007, 08:42
Totally agree with Fig, it is C

since prime number cannot be equal to the number n^3 because it says it is prime...

however, Sometimes I dont understand what is saying the question,
can smn give me advice how to cope with it???
11 Sep 2007, 08:42
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