M01-05

Question

If  x \gt 1  and  y \gt 1 , is  x \gt y ?

(1)  \sqrt{x} \gt y

(2)  \sqrt{y} \lt x

Bunuel · Answer

Official Solution: If x \gt 1 and y \gt 1 , is x \gt y ? Notice that we are told that both x and y are greater than 1. (1) \sqrt{x} \gt y . Since x > 1 , then x > \sqrt{x} . Therefore, x > \sqrt{x} > y and thus x > y . Sufficient. (2) \sqrt{y} \lt x . Since y > 1 , then \sqrt{y} < y . However, x can be between \sqrt{y} and y , on the number line: \sqrt{y}< x < y as well as to the right of y , on the number line: \sqrt{y}< y < x . For example, if y=4 and x=3 then the answer to the question is NO but if y=4 and x=100 then the answer to the question is YES. Not sufficient. Answer: A

Nikkb · Answer

Given : x>1 and y>1, so here we don't have to worry about fractions, negative numbers and value 0 and 1
Now find if x>y

Condition 1:
\(\sqrt{x}\) >y
=> x> \(y^2\)
Now as we know \(y^2\) >y (if y is not equal to 0 and 1)
so => x>\(y^2\) > y
=> x>y . Answer. Sufficient

by putting values:
\(\sqrt{x}\) >y
So we have to find value of \(\sqrt{x}\) is "greater" than y.
Assume y=2 .. => 2.1 > 2
So \(\sqrt{x}\) = 2.1 => x = 4.41 => 4.41 >2 => x>y Sufficient

Condition 2:
\(\sqrt{y}\) < x
=> y <\(x^2\)
=> 3<(3)^2 => but here x=y so Answer x> y answer to main question is No
=> 2< (4)^2 =>Here x> y answer to our main question is yes
=> 9 < (4)^2 => Here x<y so answer to our main question is No
Not sufficient

Answer: A

ddavy · Answer

I think this is a  high-quality  question and I agree with explanation.

IanStewart · Answer

I wonder if anyone can explain something to me that I've been vaguely curious about for a while. Whenever I visit these discussion threads about gmatclub test questions, I always see several posts that read, almost verbatim, sometimes years apart, "I think this is a high-quality question and I agree with the explanation" or "I think this is a poor-quality question and I disagree with the explanation." Why are there so many posts like this? Did gmatclub request this kind of feedback at some point?

This question is very similar to many official questions -- comparing powers of unknowns is a standard GMAT inequality trope -- and it's certainly a high-quality question, and one that will reward study.

This question is very similar to many official questions -- comparing powers of unknowns is a standard GMAT inequality trope -- and it's certainly a high-quality question, and one that will reward study.

Bunuel · Answer

IanStewart

Hi Ian,

Yes, there is an option for each question in a test to mark it as high-quality or poor-quality and mark "I agree with the explanation" or "I don't agree with the explanation".

IanStewart · Answer

That explains it! Thanks Bunuel.

IanStewart · Answer

If x > 1, then x > √x. So from Statement 1, x > √x > y, and x > y, so Statement 1 is sufficient.

For Statement 2, we know x > √y, and since y > 1, we know y > √y. That doesn't help us compare x and y. If y = 4, then since x > √y, we know x > 2, but x can be 3 and can thus be less than y, or x can be 1,000,000 and can thus be greater than y. So the answer is A.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

avikalagarwal · Answer

I think this is a  high-quality  question and I agree with explanation.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

ArtemNYC · Answer

Let's say x=4 and y=3, so is the first condition still fine and sufficient?

Bunuel · Answer

x = 4 and y = 3 does not satisfy  \sqrt{x} \gt y .

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