What is the value of x + y?

Question

(1) xy = 24
(2) x/y = 8/3

OA is E.

i understand why it can't be A, B or D but i am having problems to figure out why it would not be "C". i would say, with the information given by (1) AND (2) the values for x = 8 and y = 3, which fits both indications. am i missing something about the perspective if some of the values (or both?!) are negative? i just don't get it.

thx for a reply!

VeritasPrepRon · Accepted Answer

Hi gmatfeelizzle, Bunuel's explanation above is correct, as always. Of course, on data sufficiency questions such as these, there are always three traps you must be mindful of. These traps show up in all kinds of DS questions and therefore should always be considered, even if they can be quickly disregarded in many questions.

The first trap is non-integer. It's easy to say that x*y = 24 must be 1-24, 2-12, 3-8 or 4-6, but it could just as easily be 1.5 and 16. Be wary of choices that don't have to be integers, which is the default case in math
The second trap is negatives. This is exactly where this question gets you. X/Y = 8/3 means that X is 8 and Y is 3... unless X is -8 and Y is -3, in which case you'll get the exact same value. 
The third trap is zero. This number shows up all the time in data sufficiency and must be considered whenever you have data sufficiency questions. It is probably the most common trap used by the GMAT. It is especially common if the question is asking about positive or negative numbers, multiples or the keyword nonnegative. If you see nonnegative, immediately consider 0.

In this case the trap was negatives, but these three possibilities are the trinity of traps (or trapnity?).

Hope this helps!
-Ron

Bunuel · Answer

What is the value of x + y?

(1) xy = 24
(2) x/y = 8/3

Each statement alone is clearly insufficient.

(1)+(2) From (2) we have that  x=\frac{8y}{3} , thus from (1)  xy =\frac{8y}{3}*y =24  -->  y^2=9  -->  y=3  or  y=-3 . If  y=3 , then  x=8  and  x+y=11  but if  y=-3 , then  x=-8  and  x+y=-11 . Two different answers, hence insufficient.

Answer: E.

Hope it's clear.

Virgilius · Answer

Great post gmatfeelizzle and we'll gladly help you out with your query. So let's get started :

We are looking for the value of x + y.
Now in value-based DS question, you should expect to get one and only one value per question. If, when solving the question, you stumble on two distinct values, then the answer will most likely be E.

Statement 1 :\(x*y = 24\)
This statement alone is insufficient because we can think of a multitude of possibilities for both x and y that yield the result given (24) but when plugged into x + y, it will yield different results. For instance :
x = 4 and y = 6 =>\(x + y = 10\)
x = 3 and y = 8 =>\(x + y = 11\)
And so on. You should also think about negative integers as well (since the DS question stem doesn't seem to indicate any signum constraint on the variables we're manipulating).

Statement 2 : \(\frac{x}{y} =\frac{8}{3}\)
Again the statement alone is insufficient for the same reasons as statement 1. We can think of many values for x and y that yield 8/3 but when plugged into x + y, it will yield different results.

Let's combine (1) and (2).

From 2 we get : \(x = \frac{8}{3}*y\)
Substituting in 1 yields : \(x*y = 24\)=> \(\frac{8}{3}*y*y = 24\) => \(y^2 = 24*\frac{3}{8}\) => \(y^2 = 9\)
At this point, you are tempted to say that\(y = 3\), but since we have no signum constraints on the variables in hand, y can be 3 just as it can be -3.

Remember that even powers hide the base's sign !!!

So if \(y = 3\), then \(x = \frac{8}{3}*y = 8\). Yielding : \(x + y = 11\)
If \(y = -3\), however, then \(x = \frac{8}{3}*y = -8\). Yielding : \(x + y = -11\)

So even when combining the two statements, you get different results !! And that clashes with the basic outcome of a value-based DS question : if the question is solvable, then the value is unique ! Otherwise, the answer will almost always be E.

Which is actually the case in this question.

The answer was deliberately lengthy so as to answer your query about why "C" isn't the right answer.

Hope that helped. :-D

gmatfeelizzle · Answer

thank you guys for all your answers!

right, i made the mistake overseeing that the absolute value of (-8)/(-3) is just the same as the absolute value of 8/3, which made me pick answer choice C too quickly.

i really am impressed how fast and precisley your answers helped me to figure out where i was wrong! looking forward for some more tricky questions to discuss with you :-)

just one more question: do you think this question is correctly classified as a 600 - 700 questions or is it rather a below 600 one?

just one more question: do you think this question is correctly classified as a 600 - 700 questions or is it rather a below 600 one?

Virgilius · Answer

This is most likely a sub-600 question. But that's just my opinion...

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What is the value of x + y?

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