Is y – x positive? (1) y 0 (2) x = 1 – y

Question

Is y – x positive?

(1) y > 0
(2) x = 1 – y

Bunuel · Accepted Answer

Is  x-y>0 ?

Or: is  x>y ?

(1) y > 0. Clearly insufficient, as no info about x.

(2) x = 1 – y -->  x+y=1  --> the sum of two numbers equals to 1, we cannot say from this which one is greater. Not sufficient.

(1)+(2)  y>0  and  x+y=1  --> also insufficient: if  x=0.1  and  y=0.9  then the answer is NO but if  x=0.9  and  y=0.1  then the answer is YES.

Answer: E.

yamikikyou · Answer

Statement 1 doesn't give you anything b/c you don't know anything about x.

Statement 2 isn't sufficient alone either:
x = 1 – y ; 5 = 1 - (-4); y - x is negative
x = 1 – y ; -5 = 1 - 6; y - x is positive

Both statements together is also insufficient, b/c
x = 1 – y ; 1/2 = 1 - 1/2; y - x = 0

So I think the answer should be E.

satishreddy · Answer

could you please explain the combined equation in detail by method of substitution, yeah, i could figure out that both the statements are not sufficient individually and when combined, gives an equation X+Y=1 and Y>0 .....iam not able to get a "no" for this equation

scheol79 · Answer

Combined, y>0 and x+y=1. When problem doesn't state that the variables are integers, you must consider fractions.

if y is 1/4 then x is 3/4 therefore x>y false
if y is 3/4 then x is 1/4 therefore x<y true

So combined, it is insufficient.

ulm · Answer

BTW, in GMAT 0 is an even integer, isn't it?
But i'm agree with (E).

TooLong150 · Answer

Forgot about those pesky positive non-integers!

Konstantin1983 · Answer

Bunuel! The question asks if "y-x positive" i.e is y-x>0 ==> is y>x. But if you multiply both sides by -1 to reverse the equation you should flip a sign i.e x-y<0 ==> x

Bunuel · Answer

Yes, the question asks whether y > x, while I wrote x > y. But this changes nothing in solution or answer.

TaN1213 · Answer

Is y – x positive?

(1) y > 0 - clearly insufficient
(2) x = 1 – y

chetan2u, is my approach correct? If yes, is it safe to approach such problems in this manner?
(Thank You )
statement 2: x = 1 – y
adding -y on both sides

x-y = 1-2y
if x-y is negative then y-x is positive.

case 1 :if y = 0,1,... , x-y is negative, y-x is positive
case 2: if y= negative , x-y is positive, y-x is negative
case 3: if 0<y<1, (x-y) is positive , y-x is negative

1 &2 => eliminates case2.
still insufficient
--E--

chetan2u · Answer

Hi...

I think it's correct in this particular case....

Another look at the Q..

Combined..
x=1-y......x+y=1 and y>0
We do not know the relationship between x and y..
X could be >y, x=0.6 & y=0.4......x-y is positive
x could be <y, x=0.4 & y=0.4........y-x is positive
E

dabaobao · Answer

Question: y - x > 0? => y > x?

1) Nothing given about x. Not sufficient
2) y > 1 - y? => 2y > 1? => y > 1/2? Not sufficient
1+2)
y > 1/2? Not sufficient

Kritisood · Answer

experts  chetan2u   Bunuel  what's wrong with this?
(combined)
to prove 
y>x
substitute x = 1 – y
y> 1-y
2y> 1
y>1/2 hence this statement is only true when y>1/2 statement one tells us y>0 hence should be sufficient?

Bunuel · Answer

The question asks: is y > x?

When you substitute THE QUESTION BECOMES is y > 1 - y? Or IS y > 1/2. (1) says that y > 0, which is not sufficient to determine whether y > 1/2.

Cellchat · Answer

y = 1, x = 2 Statement is False
y = 2, x = 1 Statement is True
 Insufficient

y = 0, x = 1 Statement is False
y = 1, x = 0 Statement is True
 Insufficient

y = 0.5, x = 0.5 Statement is False
y = 1, x = 0 Statement is True
 Insufficient 
(E)

Mo2men · Answer

Bunuel

There is a typo. It should by is y>x? You changed the sequence mentioned in the question.

Bunuel · Answer

I already y replied to this here: https://gmatclub.com/forum/is-y-x-posit ... l#p1546184

agrasan · Answer

Is y – x positive?

(1) y > 0
Clearly,  Insufficient  as we know nothing about x.

(2) x = 1 – y
Put x = 1-y in the original equation

y -x > 0 ?
y - 1 + y>0 ?
 y > 1/2 ?

Clearly,  Insufficient  as we know nothing about the range of y.

Combining (1) and (2),
We know that y > 0 and we want to know if y > 1/2, we can't say anything with certainty here; let's say  if y = 1/4 then the equation y - x > 0 or y > 1/2 won't hold.

Hence,  (E)  is the answer.

Is y – x positive? (1) y > 0 (2) x = 1 – y

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions