Problem Solving

kevind147 wrote:If X/Y = 2/3, what is the value of (X-Y)/X?

A. -1/2
B. -1/3
C. 1/3
D. 1/2
E. 5/2

The answer in the book gives a long drawn-out explanation, but can you not just assume that X = 2 and Y = 3 from the equation provided? So (2-3)/2 = -1/2. Is this assumption correct?

It's useful to notice here that every answer choice is an exact number. That must mean that the answer is the same for any x and y you choose, as long as x/y = 2/3. Otherwise the question would have more than one right answer, and of course that can't happen on the GMAT. It is indeed perfectly fine to plug in x = 2 and y = 3 here; whatever answer you get must be the right answer.

You could not, however, reliably use this strategy if the question looked like this:

If X/Y = 2/3, what is the value of (X-Y)/X?

A. -1/2
B. -1/3
C. 1/3
D. 1/2
E. It cannot be determined from the information given.


Because we have answer choice E here, we can't be sure that we will always get the same answer for any x and y we choose. By plugging in x=2 and y=3, you can be sure that the answer is either A or E, but you'd need to do more work after that to choose between them.

That's a long way of saying: whether picking numbers is a reliable strategy depends on the answer choices. As a caution, take a look at question 181 in the OG (11th ed. pg. 176-177) -- here, answer choice E says 'It cannot be determined...", and you won't get the right answer if you just plug in one set of numbers. Plugging in numbers can be a reliable strategy if you know when you can use it, and you know when you can't.

Karan - yes, of course the answer is -1/2, no matter what the answer choices are. My only point is this: if you plug in x = 2, and y = 3, you can be absolutely certain in this question that you will arrive at the correct answer when every answer choice is a number. However, when answer choice E reads "It cannot be determined..." then if you plug in x = 2 and y = 3, all you can be certain of is that the answer choice is either A or E -- you still don't know for certain which answer is correct, and you need to do more work to decide. So plugging in numbers is not nearly as useful a strategy when E reads "It cannot be determined..." because you won't know which answer is right after plugging in numbers the first time. You need to try more numbers, or look at the problem in a different way.

Of course, I'd recommend doing the problem algebraically anyway, since it's very fast, and is completely reliable no matter what the structure of the answer choices. I did, however, want to correct the previous posts which claimed that plugging in x=2 and y=3 was not a correct strategy here - while we certainly have no idea what the values of x and y are here (all we know is their ratio), plugging these values into the original question is still certain to lead to the right answer. This 'plugging in' strategy certainly has its limitations, however, as I pointed out above.

gmat740 wrote:Ian,
With all due respect the answer looks correct to me even if the Option E . It cannot be determined from the information given.

lets take another look to it:

X/Y = 2/3

Yes off course it does not mean X= 2 and Y=3
but it certainly does mean X =2k and Y= 3k

where k is any number either positive or negative

So now

X-Y/X = 2k -3k/2k = -k/2k = -1/2

And this is true for any value of k

This is something which comes from the fundamentals of Ratio's

please do correct me if you find me wrong

Karan

gmat740 wrote: Thank You for you reply

I solved the question algebraically and it is true for all values of k

Let me know whether this approach is correct or not for any question(even if it is having Option E as data not suff)

Yes, your approach is much better than picking numbers, because you can use it no matter what the answer choices, and you could also use it on a DS question, or on a harder question where picking numbers was impractical.

kevind147 wrote:If X/Y = 2/3, what is the value of (X-Y)/X?

A. -1/2
B. -1/3
C. 1/3
D. 1/2
E. 5/2

Cross-multiplying, we have:

3X = 2Y

Thus, we can let X = 2 and Y = 3, so we have:

(2 - 3)/2 = -1/2

Alternate Solution:

(X-Y)/X = X/X - Y/X = 1 - Y/X

Since X/Y = 2/3, Y/X = 3/2, so 1 - Y/X = 1 - 3/2 = -1/2.

Answer: A