Hi,

\((r^2)x>0\)...
Here r^2 will always be POSITIVE or ZERO...

so we have to know following...
a) Is r "0 or non-zero "?
b) Is x +, - or zero?

lets see the statements-

1) r^5=1
we know r is non-zero..
But nothing about x...
If x is + ans is YES otherwise NO..
Insuff

2) x>0
we know x is+, but nothing about r..
If r is 0, ans is NO otherwise YES
Insuff

combined-
r is non-zero and x >0 so ans is YES irrespective of actual values..
Suff

C
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For (r^2)x>0, we need to fulfill two conditions:-

either r or s must not be 0

x>0 because r^2 will always be +ve

1) r^5=1
r= 1 (as it carries odd power). But there is no information about x. Not sufficient.

2) x>0
No information about r. not sufficient.

Combining both statements fulfills our conditions. Hence sufficient.

C is the answer
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in the question stem r may be (0,+)
and x may be (0,+,-)
if r=0, then x=0(NO), +(NO), -(NO)
again, if r=+, then x=0(NO), +(yes), -(NO)

1) r=(+), but there is no information about x. so, insufficient
2) x>0, but there is no information about r. so, insufficient

combining 1 and 2:
r=(+) and x=(+)..........YES (sufficient)
answer is "C".
Thanks...
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r^2 is always a positive value unless r = 0.

Statement 1 says r is not equal to zero. But it is silent on x.
x could be zero, or negative, then entire value will be zero or negative.
If x is positive, entire value will be positive

So not sufficient

Statement 2 is silent on r. Not sufficient.

When we combine, we know that x is not equal to zero and r^2 is always positive. So confirmed "Yes" can be said against the question.

C is the answer.

There are two variables (r and x) in the original condition. In order to match the number of variables and the number of equations, we need 2 equations. Hence, the correct answer is C.


- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.
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Target question: Is (r²)(x) > 0?

Statement 1: r⁵ = 1
This tells us that r = 1, however we don't know the value of x.
Let's TEST some values.
Case a: r = 1 and x = 1, in which case (r²)(x) = (1²)(1) = 1. Here, (r²)(x) is GREATER than 0
Case b: r = 1 and x = -1, in which case (r²)(x) = (1²)(-1) = -1. Here, (r²)(x) is NOT GREATER than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x > 0
Okay, x is POSITIVE, however we don't know the value of r.
Let's TEST some values.
Case a: r = 1 and x = 1, in which case (r²)(x) = (1²)(1) = 1. Here, (r²)(x) is GREATER than 0
Case b: r = 0 and x = 1, in which case (0²)(x) = (0²)(1) = 0. Here, (r²)(x) is NOT GREATER than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that r = 1, which means r² = 1
Statement 2 tells us that x is POSITIVE
This means that (r²)(x) = (1³)(POSITIVE) = SOME POSITVE #. In other words, (r²)(x) is GREATER than 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer =

Cheers,
Brent
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