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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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stolyar
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Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P [#permalink] Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P   16 Jun 2003, 02:15
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Is a two-digit number PQ even?

(1) GCD of P and Q is 1
(2) P is even



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Re: Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P [#permalink] Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P   16 Jun 2003, 22:45
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stolyar wrote:
Is a two-digit number PQ even?

(1) GCD of P and Q is 1
(2) P is even



So, the number is not even, right?
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Re: Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P [#permalink] Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P   23 Apr 2007, 10:31
stolyar wrote:
Is a two-digit number PQ even?

(1) GCD of P and Q is 1
(2) P is even



how do u find out if statement 1 is suff or not?
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Re: Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P [#permalink] Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P   23 Apr 2007, 11:24
I just did some simple substitutions:

GCD is 1 therefore we could have either 23 or 32 since the GCD of 2 and 3 is 1


those numbers are odd and even, but since they cannot both be even (the GCD would be at least 2)

if we know the first digit is even, then the 2nd digit must be odd which makes the number odd
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Re: Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P [#permalink] Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P   23 Apr 2007, 13:59
stolyar wrote:
Is a two-digit number PQ even?

(1) GCD of P and Q is 1
(2) P is even


From Stat1:
if P is even, Q must be odd and vice versa. Also P and Q cannot be multiples of each other.

That implies Q can be even or odd.
Therefore not sufficient.

From stat2:
P is even
Q is still unkown.
Therefore not sufficient.

Combining 1 and 2
If P is even , Q has to be odd.
Hence PQ is odd or not event.

Hence C
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Re: Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P [#permalink] Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P   24 Apr 2007, 01:31
goalsnr wrote:

From Stat1:
if P is even, Q must be odd and vice versa. Also P and Q cannot be multiples of each other.


The way I understood from state 1, AT LEAST one of the digits should be odd AND, yes, digits should not have common divisors other than 1.

So, PQ can be 11, 12, 31, 45, 79 and so on.

Anyone has anything against this kind of analysis?



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Re: Is a two-digit number PQ even? (1) GCD of P and Q is 1 (2) P [#permalink]
24 Apr 2007, 01:31
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