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# Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P

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SVP
Joined: 05 Jul 2006
Posts: 1516
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Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P [#permalink]  12 Oct 2006, 15:42
Is a two-digit number PQ even?

(1) GCD of P and Q is 1
(2) P is even
Senior Manager
Joined: 31 Jul 2006
Posts: 440
Followers: 3

Kudos [?]: 16 [0], given: 0

Re: GCD [#permalink]  12 Oct 2006, 16:23
Is a two-digit number PQ even?

(1) GCD of P and Q is 1
Could be 32 or 23

(2) P is even
Could be 22 or 21

1 and 2)
If P is Even and GCD is 1 then Q can't be a multiple of 2 (i.e. can't be even)

C.
Intern
Joined: 05 Oct 2006
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C

1) P could be 3 and Q could be 4 (GCD is 1) making PQ even or
P could be 3 and Q coulc be 5 (GCD is still 1) making PQ odd

Not Suff

2) P is even. So if Q is odd, PQ is Odd and if Q is even PQ is even.
Not suff

from 1 and 2
If P is even and if GCD of P and Q is 1 then Q needs to be odd, making PQ odd all the time
Director
Joined: 23 Jun 2005
Posts: 847
GMAT 1: 740 Q48 V42
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Kudos [?]: 36 [0], given: 1

C

Statement 1:
The two digits cannot be both even. INSUFF

Statement 2:
P is even, PQ can be 23 or 24 INSUFF

Together,
Since P is even, Q cannot be even. SUFF
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