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# If X,Y, and Z are positive integers. Is (X/Y)^N > 1000?

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If X,Y, and Z are positive integers. Is (X/Y)^N > 1000? [#permalink]  15 Jan 2004, 11:21
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If X,Y, and Z are positive integers. Is (X/Y)^N > 1000?

I) X=Y^3 and N>Y
II) X>5Y and N>X
Senior Manager
Joined: 30 Aug 2003
Posts: 325
Location: dallas , tx
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It is B...?
(1) ... as its says x=y^3 ..say x=64 then y=4 and N>y so it is say 5
then 1 is true..but if x =8 then y=2 then its is less than 1000..insuff

(2) x>5y..say x =20 then y=5*2(y=2) and N>x..so it has to be more than 20.. so 20/10^21 ..got to be more than 1000..
i dont know if i am doin it right??
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shubhangi

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Joined: 15 Dec 2003
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Agree B should be the answer

1) (y^3 / y)^N = y^2N
Let's pick numbers. When y is smallest at 1, then N could be = 2. In this case 1^2(2) = 1 and 1 is thus < 1000
However, if we say y = 10, then N could be equal to 11. In this case 10^2(11) which is more than 1000. 1 is inconclusive

2) (5y / y)^N = 5^N
When y is at its smallest and say y=1 then N could be equal to 6. In this case, 5^6 is larger than 1000 and it would be the case with just any given value for y. Sufficient
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Paul

Senior Manager
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Kudos [?]: 9 [0], given: 0

in the 2nd stat.. x is not equal but greater than 5y..so why have u taken 5y/y??
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shubhangi

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Joined: 15 Dec 2003
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Kudos [?]: 216 [0], given: 0

I assumed that 5x = y as a critical value for the formula. If 5x>y then N is always gonna be more than 5x. It's for simplification purposes
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Best Regards,

Paul

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