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# If x, y, and z are integers greater than 1, and

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Manager
Joined: 11 Aug 2009
Posts: 122
If x, y, and z are integers greater than 1, and [#permalink]

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18 Nov 2009, 21:46
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If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?

(1) y is prime

(2) x is prime
Senior Manager
Joined: 30 Aug 2009
Posts: 287
Location: India
Concentration: General Management
Re: If x, y, and z are integers greater than 1, and (327) [#permalink]

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19 Nov 2009, 00:10
kairoshan wrote:
If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?

(1) y is prime

(2) x is prime

E

option 1 and 2 both can give multiple values for x. even together it doesnt suffice.
Senior Manager
Joined: 31 Aug 2009
Posts: 417
Location: Sydney, Australia
Re: If x, y, and z are integers greater than 1, and (327) [#permalink]

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19 Nov 2009, 02:02
kairoshan wrote:
If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?

(1) y is prime

(2) x is prime

Factor prime factors to simplify equation:
(2)(3^2)(5)(17)(19)(z) = (2^2)(29)(457)xy

1) Insufficient. y is prime means y can be one of 3, 5, 17, 19. X can be the multiple of anything left over times z.
2) Insufficient. X is prime basically switches the logic of statement 1. X can be 3,5,17,19.

1+2) Insufficient because there are still multiple values. It also implies that z = 0 (I think?)

Ans = E
Manager
Joined: 06 Sep 2009
Posts: 113
Re: If x, y, and z are integers greater than 1, and (327) [#permalink]

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19 Nov 2009, 02:22
kairoshan wrote:
If x, y, and z are integers greater than 1, and (327)(510)(z) = (58)(914)(xy), then what is the value of x?

(1) y is prime

(2) x is prime

I spent 2 to 3 minutes struggling and trying to find a solution with the information given.

The fact is: we have three unknown variables and 1 equation.
We should be given 2 "ultimate" information about 2 either of the 3 variables.

Here we go with the POE:
1) not sufficient, since saying that this variable is "prime" is too general. It could be any number from 2 to 29387409218730197319073491.

2) not sufficient either for the same reason.

(1) + (2) --> not sufficient as well, because saying that both X and Y are prime does not help solving this equation, since Z could "compensate" any variations of X and Y, so we have multiple solutions for this equation.

Ans: E
Re: If x, y, and z are integers greater than 1, and (327)   [#permalink] 19 Nov 2009, 02:22
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