What is value of the fraction x/y? 1) x-y = 14 2) 2x = 5y

Question

Dear all,

I have the following question in this test.
What is value of the fraction x/y?

1) x-y = 14
2) 2x = 5y

The official answer is (2) is enough. But what happens if x = y = 0? In this case 2x=5y but we can not know the value of x/y.

Thank you very much.

fluke · Answer

I agree. It should at least mention that y is non-zero.

gmat1220 · Answer

If x = y = 0 then you contradicting the statements 1) and 2). Hence the assumption is wrong.

The premises are not touched. They are assumed to be true.

amit2k9 · Answer

Agreed X and Y should not be zero respectively.

fluke · Answer

Yeah, but when I am answering "B", I am not even looking at Statement 1. I am just looking at the stem and statement 2. Thus, I feel that the answer should be "C", where I am getting 2 simultaneous equations to solve for x and y.

If we go by statement 2 alone and divide LHS and RHS by "y", it would be wrong because y could be 0 and division by 0 is undefined.

gmat1220 · Answer

Pls allow me to explain

. The assumption x = y =0 is not going to tip the answer in favor of C. This is my interpretation of S2. The ratio x : y is 2.5 then the assumption that x = 0 or y = 0 does not hold. If x = 0 then ratio become zero which will contradict S2. S2 tells us x : y is 2.5 If y = 0 then the ratio x : y is meaningless. However S2 tells us x : y is real number. Again this contradicts S2. If you take S1. If x = y = 0 then 0 = 14 which is impossible. Hence the values of x=0 and y=0 contradict S1 and S2 both. I think the designer assumes that the candidate is not going to go against the statements. Otherwise he cannot plot the question. The cases are evaluated based on those statements and in the end - one case may win. If the statements are negated, even 1) + 2) may not be sufficient to answer the question. The answer may be E or C or anything.

TrueLie · Answer

Hi all,

I just recalled a rule from Manhattan books for DS: all premises are correct and never contradict each other. Therefore, if we see something that makes (1) contradicts with (2), then this "something" is wrong

gmat1220 is right. If x=y=0 then 1) will contradict with 2). Therefore this can not happen.

Thank you.

gmat1220 is right. If x=y=0 then 1) will contradict with 2). Therefore this can not happen. Thank you.

gmatpapa · Answer

Fluke, if it is given that x/y is a "fraction", can we assume the fraction does not contain zeros? According to definition, the number may be a proper/improper/ mixed fraction but it is still a number without zeros right? I dont think we can call 2/2 a fraction can we?

fluke · Answer

Let's ask the experts:

Karishma, IanStewart?

KarishmaB · Answer

In GMAT, whenever they use a fraction, they will mention that the denominator is not 0 since division by 0 is not defined. In some questions on the forum, I have pointed it out. 
They should have mentioned that y is not 0. GMAT will mention it. Hence this question is not correct. 
(0, 0) is a valid solution for statement 2 but it does not give us a value for x/y.

gmat1220 · Answer

Karishma
I have a similar question from OG12 wherein the values are contradicting the question stem. Pls take a look at this OG12 #125. While evaluating second statement, I can assume k,l,m to be all zero since the stem uses "all" - for all the number k,l,m. Lets analyze statement 2)

125. If ° represents one of the operations +, –, and ×,
is k ° (l + m) = (k ° l ) + (k ° m)  for all numbers k, l, and m ? 
(1) k ° 1 is not equal to 1 ° k for some numbers k.
(2) ° represents subtraction.

From 2)
When k = l = m = 0 then the answer is YES
op = "minus"
k op (l + m) = (k op l) + (k op m) = 0
LHS = 0 = RHS.

However when k,l and m are non zero then the answer is NO. I have a YES and NO. So the answer should be E. But the official answer is D. Is there is problem with my analysis? Pls weigh in.

KarishmaB · Answer

125. If ° represents one of the operations +, –, and ×,
is k ° (l + m) = (k ° l ) + (k ° m)  for all numbers k, l, and m ? 
(1) k ° 1 is not equal to 1 ° k for some numbers k.
(2) ° represents subtraction.

Question: Is k ° (l + m) = (k ° l ) + (k ° m) for all numbers k, l, and m?

(1) We understand that had ° been '+' or '*', k ° 1 = 1° k for ALL values of k. Hence ° must be subtraction '-'

Ques: Is k - (l + m) = (k - l ) + (k - m) for all numbers k, l, and m?

Ans: Definitely No. This equation does not hold for ALL numbers. 
For some numbers the equation holds (e.g. when k = 0, l= 0, m = 0), for others it doesn't (e.g. k = 1, m = 0, l = 2).

(2) ° represents subtraction.

Ques: Is k - (l + m) = (k - l ) + (k - m) for all numbers k, l, and m?

Ans: Definitely No. This equation does not hold for ALL numbers. 
For some numbers the equation holds (e.g. when k = 0, l= 0, m = 0), for others it doesn't (e.g. k = 1, m = 0, l = 2).

Both statements alone are sufficient to give us a definite answer to the question. The question explicitly says "Is it true for all numbers?" You answer with "No. It is not true for ALL numbers. For some numbers it is true, for others it is not." Valid and clear answer. Answer (D)

(Tip: Focus on what the question is asking. The question didn't ask you - "Is it true?" It asked you - "Is it true for all numbers?"

amit2k9 · Answer

Good observation. Point noted.

What is value of the fraction x/y? 1) x-y = 14 2) 2x = 5y

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What is value of the fraction x/y? 1) x-y = 14 2) 2x = 5y

Prep Toolkit

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