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Brent,Rich,check this DS question out..Finding it tricky.

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Brent,Rich,check this DS question out..Finding it tricky.

by dddanny2006 » Sat Nov 16, 2013 4:35 am
If xy!=0,is x>y?

(1)4x=3y
(2)x=y+1 or x=y

St 1 is insufficient.
St 2 is also insufficient

Im finding it tricky to combine the 2 equations

From st1 we know that x/y=3/4 and from st2 we know that x=y+1

Substituting x=y+1 in (x/y=3/4)we get y=-4 and x=-3 and thus x>y.. So its a YES

But now we also have x=y. We simply cant do anything with equations x/y=3/4 and x=y .Substitution makes no sense.Do we consider to x=y INVALID with respect to x/y=3/4 that statement 1 gives us or does this become a NO with regard to the question stem?Ill be direct here.In other-words my question is how do we deal when we have 2 sub-statements of statement 2 of which one sub-statement x=y makes no sense to statement 1 at all while the other statement does go well with statement 1.Please look at the attachment.




Please clarify
Thanks
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Sat Nov 16, 2013 9:25 am
dddanny2006 wrote: If xy ≠ 0, is x > y?

(1)4x = 3y
(2)x = y + 1 or x = y
Let's answer the question step by step.

Target question: Is x > y?

Given: xy ≠ 0. In other words, x ≠ 0 and y ≠ 0

Statement 1: 4x = 3y
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 3 and y = 4, in which case x < y
Case b: x = -3 and y = -4, in which case x > y
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x = y + 1 or x = y
Let's examine each possibility.
case a: if x = y + 1, then x is 1 greater than y, which means x is greater than y
case b: if x = y, then x is not greater than y
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are two cases to consider:
case a: 4x = 3y and x = y + 1. If we solve this, we get x = -3 and y = -4, in which case x is greater than y
case b: 4x = 3y and x = y. If we solve this, we get x = 0 and y = 0. This solution does not satisfy the given condition that x and y ≠ 0. So, we can ELIMINATE CASE B as a possibility.
This leaves only case a as a possible scenario, in which case x is greater than y

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by rahul.sehgal@btgchampion » Sun Nov 17, 2013 8:21 am
good question and thanks Brent for the wonderful explanation as always..
Best Regards,
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by Mathsbuddy » Sun Nov 17, 2013 12:05 pm
(2)x = y + 1 this is a clear statement that x > y

So that just leaves

(1)4x = 3y when x = y -> x = y = 0, which is irrelevant as xy ≠ 0 from the question.

Therefore x > y. True.
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