Is x^3 < 3^y ? (1) 5^x = 1/25 (2) y^5 = -32

ans A..
statement 1 tells us that x is a negative number -2, so LHS will be negative and RHS is always positive so suff..
statement 2 just gives value of y as -2, not suff..

hi ,
statement 1 is suff ..
as LHS becomes negative and RHS will always be positive..

Hello all

My attempt:

This looks like a trap question but anyways

Statement 1:

\(5^x = \frac{1}{25}\)
\(5^x = 5^-2\)
\(x=-2\)

Plugging it into the expression in the question
\(-2^3<3^y\)
\(-8<3^y\)
now whether \(y\) is \(-ve\), \(0\) or \(+ve\) the expression \(3^y\) is always \(positive\)

Thus statement 1 is sufficient to answer the question.

Statement 2:

\(y^5=-32\)
\(y^5=-2^5\)
\(y=-2\)

Plugging it into the expression in the question
\(x^3<3^y\)
\(x^3<3^-2\)
\(x^3<\frac{1}{9}\)
Now in this if \(x\) is \(-ve\) then the inequality holds true but if it is 1 or greater than 1 then it does not.

Thus statement 2 is insufficient to answer the question.

My answer choice is \(A\)

Is x^3 < 3^y ?

(1) 5^x = 1/25
(2) y^5 = -32

Statement 1,
5^x = 1/25 will give
x = -2

Putting in original statement
-8 < 3^y this statement will hold true irrespective of value of Y
say for Example
y = 0 ---- -8<1 True
Y=1 ----- -8<3 True
y= -1 ---- -8< 1/3 True

Hence Statement 1 is sufficient

Statement 2
y^5 = -32 will give
y = -2

Putting in original statement
X^3 < 3^-2
X^3 < 1/9

Validity of this statement will depend on Value of X.
Say for Example X = 0
1<1/9 Not True

X= -1
-1 <1/9 True
Hence statement 2 is not sufficient.

Answer A

Hi adityadon,

Sometimes DS questions are designed with specific Number Properties in mind, so you have think very carefully about the actual question that is asked.

Here, we're asked if X^3 < 3^Y. This is a YES/NO question.

Before we get to the two Facts, there are some Number Properties involved in the wording of this question that are worth noting:

1) X^3 can be positive, negative or 0....depending on the value of X
2) 3^Y can ONLY be positive. It doesn't matter if Y is positive, negative or 0, the result of the calculation will be POSITIVE.

Knowing that second Number Property rule and factoring in what you deduced about Fact 1, what answer should you pick?

GMAT assassins aren't born, they're made,
Rich

Ans: A

Solution:at first look: we need to find value of x and y

1) 5^x= 1/25 means x=-2 so x^3=-8 with this we know that x^3 is always less than 3^y because 3^y is always positive. [Sufficient]

2)y^5=-32 means y=-2 well it does not gives us any information about x so we can't say anything. [Not Sufficient]

Ans: A [Statement 1 alone is sufficient to ans the question,but not statement 2 alone]

Hi Rich ,

Thanks for explanation . I did hurry while solving it and didnt pay attention to 2nd statement . It was a trap indeed.
I have noted down the fact about 1st statement .
Thanks

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