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# If x, y, and z are positive prime numbers such that the

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Intern
Joined: 19 Nov 2004
Posts: 44
If x, y, and z are positive prime numbers such that the [#permalink]

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19 Dec 2004, 19:08
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15. If x, y, and z are positive prime numbers such that the product of x, y, and z is 42, what is the value of y?

(1) x + z = y^2
(2) x < y < z

I have no idea how to approach this problem
Director
Joined: 07 Nov 2004
Posts: 683

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21 Dec 2004, 07:15
D

Prime factors of 42 are 2, 3, 7.

s1: x+z = y^2
The only solution for this is 2+7 = 9
=> y =3 (remember the question only asks for y, so the exact values of x and z are not needed.
Sufficient

s2: x<y<z
we know that 2<3<7
so y=3
Sufficient
Senior Manager
Joined: 25 Dec 2003
Posts: 359
Location: India

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21 Dec 2004, 07:41
As soon as you see an even number, you should know that one of the prime number is 2.

The stem says that x*y*z=42 (this means one of the prime is 2). the other ones are 3 and 7 (prime factors).

From this point you can find others by substitution.

1) x + z = y^2 --> we know x is 2 and other numbers are prime. Other numbers that satisfiy this criteria are 3 and 7. Hence y=3. Suffcnt.

(2) x < y < z ---> we know x =2, and in the lis of 2,3,7, y takes the value 3. Hence suffcnt.

ANS : D
_________________

Giving another SHOT

21 Dec 2004, 07:41
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