M60-07

Question

If  x > y > 0 , is  y < 2?

1)  1/x = 1/2

2)  (1/x)+(1/y) =1

MathRevolution · Answer

Official Solution:

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 2 variables (\(x\) and \(y\)) and 1 equation \(( x > y\)), D is most likely to be the answer.

Condition 1)

\(1/x = 1/2\) implies that \(x = 2\). Since \(x > y\), we must have \(y < 2\).

Condition 1) is sufficient.

Condition 2)

The original condition \(x > y > 0\) implies that \(1/x < 1/y\).

Using \(1/x + 1/y = 1\) and \(1/x < 1/y\) together, we can see that \(1/y > 1/2\).

Thus, \(0 < y < 2\).

Condition 2) is sufficient.

Therefore, the answer is D.

Answer: D

manisha1234 · Answer

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

awjpca · Answer

Hi, could you please expand on how the two equations result in the inequality 1/y>1/2?

Thank you

Caroline1606 · Answer

I would also be grateful if you could expand on this!

aruncharles77 · Answer

1/X +1/Y =1. And 1/X<1/Y. One of the 2 numbers has got to be greater than 1/2 right for both the equations to be possible? Now since 1/X<1/Y, 1/Y is the number that is greater than 1/2. That's how you get 1/Y>1/2. So the second equation is also SUFFICIENT

mossa · Answer

I think this is a  poor-quality  question and I don't agree with the explanation. I believe that this question is flawed as both statements can be true at the same time in order to get the same solution. As I understand, statements can not contradict in GMAT, please check.

tulullus · Answer

I think this is a  poor-quality  question and the explanation isn't clear enough, please elaborate. Please elaborate on how statement 2 is sufficient by itself. 
Thanks in advance.

ninadantro · Answer

the statement 1 is sufficient.

But for Statement 2 i dont agree with the solution.
If we solve the statement 2 we get (x+y)/xy=1 ---> (x+y)-xy=0 this tells us that x=y=2 or x=y=0 and neither of it holds true as in the question it is given as x>y>0 and not x≥y. So the 2nd statement contradicts the info given in the question fact itself.

please correct me if I am wrong

RenKan90 · Answer

I agree. This is a poor quality question. Statement one and statement two contradict. If X=2 then 1/x = 1/2 and if 1/x = 1/2 and 1/x + 1/y = 1 then Y must equal two. Therefore statement one and statement two contradict. This is not possible on the GMAT. Poor quality.

kutsch · Answer

That's how I attempted to solve for statement 2 as well and ran into the same issue. Really threw me off how the statement appeared to contradict- so I went with "A" as my answer.

Would also appreciate if someone could clarify this.

Vickey123 · Answer

Oh, okay, I think I have a better solution.
So we all understand why the 1st condition is sufficient, right? If no, then please see below, how it works.

1 condition.
1/x = 1/2 ----> x=2. And if x=2, and x is greater than y, we can easily answer question "is y<2?"
So 1st condition alone is Sufficient or us.

2 condition:
If x>y>0, is y<2?
To make everything looks better and easier to understand
(1/x)+(1/y)=1 is the same as:
1/y=1/x - 1 ----->
1/y=(x-1)/x ------>
y = x/(x-1) perfect
Now we just need to think logically,
whatever integer number we use, then we will always get that y will be equal 1,...., because just watch:
let's take 100, then y=100/(100-1)=100/99
let's take 30, then y=30/(30-1)=30/29
let's take 1000, then y=1000/(1000-1)=1000/999
you see the pattern, right?
So if we take not an integer number, but let's say 1/2 (same as 0.5), then y=0.5/(0.5-1)=1 , but this is not correct, because we know that x>y. So we should use only integer numbers.
Since we will use only integer numbers, we can clearly seem that whatever number we take, y will always be below 2. So again the 2nd condition is enough for us.

Kshitij2007 · Answer

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

it is given that x>y. That means when you take their reciprocal, the inequality reverses, i.e. 1/x<1/y.

Let that be eqn 1.

Eqn 2 is the 2nd condition.That is 1/x + 1/y= 1.

Eqn 2 gives us 1/x= 1- 1/y.

Substitute this in Eqn 1.

1/x<1/y

1-1/y<1/y

1< 2/y

y<2.

hence proven.

I think this is a very high quality question and tricky as well.

Bambi2021 · Answer

For statement 2:

If 1/x + 1/y = 1

then one of them must be greater than 1 and one of them must be smaller than 1, because we know that both are greater than 0.

This means x must be greater than 1 and y must be smaller than 1, because x > y.

Kimberly77 · Answer

Thanks for explanation  MathRevolution . Not quite understand how is 1/y>1/2 and thus, 0<y<2 ?

BottomJee · Answer

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

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