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Source: — Data Sufficiency |
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by SmartAssJun » Wed Aug 29, 2012 8:53 pm
grandh01 wrote:If x,y, and n are positive integers,
is (x/y)^n > 1000

1) x=y^3 and n>y
2) x>5y and n> x

oa is B
Put Statement 1 in the equation => y^2n, n>y(that means n can be 2,3,4...)
It's not necessarily >1000, so it's insufficient.
So x/y is great than or at least 6 and 6^6 >100, so it's sufficient.
So the answer is B.

x>5y indirectly means that x>5 and x/y>5, n>x>5
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by adthedaddy » Wed Aug 29, 2012 11:15 pm
Given: x,y,n are positive integers
To prove: Is (x/y)^n > 1000 ? ...... (1)

Solving by using numbers,

1) x=y^3 & n>y
Let y=2, thus x=y^3=8
n>y => Let n=3

Substituting in (1) above, we get 4^3=64 which is not greater than 1000
whereas if you take y=10, x=1000, n=20 we get it as (100)^20 which is ofcourse greater than 1000
Thus the given condition is NOT SUFFICIENT

2) x>5y and n>x

Let y=1
Thus x>5 and x is a postitive integer.
So, let x=6
n>x => let n=7

Thus, we can write eqn (1) as 6^7 which much greater than 1000.
Similarly for any value of x,y,n eqn(1) is satisfied.

Thus,this condition is SUFFICIENT

Ans: (B)
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by nisagl750 » Thu Aug 30, 2012 12:38 am
grandh01 wrote:If x,y, and n are positive integers,
is (x/y)^n > 1000

1) x=y^3 and n>y
2) x>5y and n> x

oa is B
Statement 1:

Case1 Let Y = 1, X = 1 and N = 2 , LHS<RHS
Case2 Let Y = 5, X = 125, So N = 126, LHS >> RHS
Hence Insufficient

Statement 2:
Consider minimum value of Y i.e. 1
X = 6, N = 7
6^7 >> 1000

Sufficient

Hence B
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by Brent@GMATPrepNow » Fri Aug 31, 2012 6:20 am
grandh01 wrote:If x,y, and n are positive integers,
is (x/y)^n > 1000

1) x=y^3 and n>y
2) x>5y and n> x

oa is B
Target question: Is (x/y)^n > 1000?

Statement 1: x=y^3 and n>y
At this point, we can take our target question and replace x with y^3 to get: Is (y^3/y)^n > 1000?
We can rewrite this as "Is (y^2)^n >1000?"
Since we haven't really restricted the values of n and y, there are several possible cases. Here are two:
case a: y=1 and n=1, in which case (y^2)^n is not greater than 1000.
case a: y=5 and n=10, in which case (y^2)^n is greater than 1000.
So, statement 1 is NOT SUFFICIENT

Statement 2: x>5y and n> x
First take x>5y and divide both sides by x to get x/y > 5 (great, we already have an idea about the value of x/y.)
Next, since x/y > 5, we know that x must be greater than 5. How do we know this? Well, we're told that x, y and n are positive integers. So, the smallest y could be is 1. Since x/y > 5, we know that x must be greater than 5.
Also, since n>x, we know that n must be greater than 5 as well (in fact, we can conclude that n is actually greater than 6, but that doesn't really matter here).
So, we know that x/y > 5 and we know that n>5.
This means that (x/y)^n must be greater than 1000
So, statement 2 is SUFFICIENT

Answer = B

Cheers,
Brent
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by hjafferi » Fri Aug 31, 2012 6:56 am
IMO B

Statement 1 plug in 1,2. This does not provide any concrete info. Statement 1 is not satisfactory
In statement 2lug in the lowest value y can have I.e 1. This results in the expression value in excess of 1000. Hence statement 1 must be correct.
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