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## Comment on

Introduction to Square Roots## Can you please help me with

Is x > y ?

(1) ✓x > y

(2) x² > y

## Tricky question! Just curious

Tricky question! Just curious, what's the source?

TARGET QUESTION: Is x > y?

STATEMENT 1: ✓x > y

There are several values x and y that satisfy statement 1. Here are two:

CASE A: x = 9 and y = 2 (notice that ✓9 = 3, and 3 is greater than 2. In this case, x > y

CASE B: x = 1/4 and y = 0.3 (notice that ✓(1/4) = 1/2, and 1/2 is greater than 0.3. In this case, x < y

Since we cannot answer the TARGET QUESTION with certainty, statement 2 is NOT sufficient.

STATEMENT 2: x² > y

There are several values x and y that satisfy statement 2. Here are two:

CASE A: x = 3 and y = 2 (notice that 3² = 9, and 9 is greater than 2. In this case, x > y

CASE B: x = 3 and y = 4 (notice that 3² = 9, and 9 is greater than 4. In this case, x < y

Since we cannot answer the TARGET QUESTION with certainty, statement 2 is NOT sufficient.

STATEMENTS 1 and 2 COMBINED

It's easy to show values of x and y that satisfy BOTH statements where x > y. For example, the following values of x and y satisfy BOTH statements:

x = 100 and y = 1

x = 16 and y = 1

x = 25 and y = -3

x = 1 and y = -30

etc

In all of the above cases, x > y

So, the correct answer MAY be C.

That said, the answer will E if there are values of x and y that satisfy BOTH statements AND where x < y

Is it possible to find such values for x and y?

No.

The tricky part is finding finding a situation where ✓x > y YET x < y

Important concept: in most cases, the square root of a number is less than the original number. For example:

✓9 < 9

✓4 < 4

✓36 < 36

The only time ✓x is GREATER THAN x is when 0 < x < 1. For example:

✓(1/4) > 1/4

✓(1/25) > 1/25

etc

So, if 0 < x < 1 then ✓x > x

The problem is that, if 0 < x < 1 then x² < x

So, any value on this range will satisfy statement 1, but will NOT satisfy statement 2.

As such, we CANNOT find values for x and y that satisfy BOTH statements such that x < y

So, it MUST be the case that, when both statements are combined, x > y

Answer: C

## Thanks Brent :)

## Hi Brent,

I couldn't find your answer to this question:

https://gmatclub.com/forum/if-x-and-y-are-positive-which-of-the-following-must-be-82080.html

Please let me know if it is already somewhere, if not, I would appreciate if you help and answer it, :

My answer is D. I and II only

There is too much debates there, it was confusing for me.

Thanks

Aladdin

## Hi Aladdin,

Hi Aladdin,

Here's my step-by-step solution: https://gmatclub.com/forum/if-x-and-y-are-positive-which-of-the-followin...

Cheers,

Brent

## Thank you so much.

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