If x and y are positive, which of the following must be

Hi,

It states that X and Y are positive numbers. So, How can we consider x + y = 0 which leads to infinity.
Moreover, If I consider x=y=1 then I am getting answer B as 2/2= 1 which is greater.
Could you please tell me what I am doing wrong ?

aarushisingla, of course x+y can never be exactly 0. But we can take it pretty close to 0. x+y could be equal to 0.00000000000000000000001.
Now, this would give you an unusually large value for the question stem. Veritaskarishma and walker are talking about values approaching infinity and not exactly infinity.
Also, the question states "must be greater". You're not trying to find a particular value for which it would be greater. But they're asking if the options would be greater than the stem for ALL the values.

I realise that this is more than a year later LOL.

To test the values, the first thing we want to find is easy numbers we can work quickly with:

The given expression takes the square root of 2 Numbers

And in the Roman numeral II, we have individual square roots of X and Y being taken, then added


So ideally we would want 2 numbers that are themselves perfect squares AND ALSO Sum to a Perfect Square

Immediately the Pythagorean Triplet of 3-4-5 should comes to mind.

Sqrt(9 + 16) = 5

Sqrt(9) + sqrt(16) = 3 + 4 = 7


Also, we are given that X and Y are positive. We should test 2 Cases:

Case 1: when X and Y are positive proper fractions ——> (1/9) and (1/16)

Case 2: when X and Y are greater than > 1 ———-> 9 and 16


III is the easiest to start with

The given expression: 1 / square root of X and Y ———> must always be positive, because X and Y themselves are positive and you can not take the Square Root of a negative value on the GMAT

However, in III

Sqrt(x) - Sqrt(y)
_____________
2

If sqrt(Y) > Sqrt(X) ———-> the value can be (-)Negative

So III can be less than


I and II

Let X = 1/9 ———> Sqrt(1/9) = 1/3
Let Y = 1/16———-> Sqrt(1/16) = 1/4
X and Y Sum ———> Sqrt(1/25) = 1/5


Our given expression will be:
1 / (1/5) = 5


I
(1/5) / 2 = 1/10

Less than


II
(1/3 + 1/4)
_________
2

= 7/24

Less than


So we have found a case for all 3 Roman Numerals in which the value can be less than the Given Expression


(E) NONE

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Hi, I took x=12 and y=4 and I saw that option A was greater than the fraction in question. Can you tell me where am I going wrong?

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