Is 0

Question

Is 0 < (x−y)/(x−2y) < 1? (1) x > y (2) x > 2y Kudos for a correct solution .

sterling19 · Answer

Both statements are  insufficient  (even when combined).
The answer depends on whether the numbers are positive or negative.

If x = 5 and y = 2, then  (5-2) / (5-4) = 3  which is greater than 1.
If x = 5 and y = -2, then  (5-(-2)) / (5-(-4)) = 7/9  which is less than 1.

The correct answer is  E .

jaxndaxt145 · Answer

I say E as well.

rephrase the equation:

0(x-2y)<x-y<1(x-2y)
0<x-y<x-2y
y<x<x-y

1) x>y
2>1 ----- (1)<(2)<(2-1) ---- 1<2<1 DOESN'T WORK
2>-1 ---- (-1)<(2)<(2- (-1)) ---- -1<2<3 WORKS
NS - depends on values chosen

2) X>2Y can use same numbers as above
2>-2
NS - depends on values chosen

Same information provided for each statement. Together NS

Ans - E

buddyisraelgmat · Answer

Ans - E
Rephrasing the Question, we get
x-2y > x-y >0
-2y > -y > -x
Is x> y > 2y

1) Not suff
2) Not Suff

When combining, we dont know the relation between y & 2y - The results can vary if we quickly plug in +ve, -ve integers or decimals

Hence E

KI2 · Answer

I think it is E.

Statement 1 is not sufficient as there are many numbers possible.
Statement 2 is also not sufficient. Similar to statement 1.

Both statements together do not add any additional information, so E

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION

Correct Answer: E

Explanation: In order to answer the question, we will need to determine whether the numerator is greater than the denominator.

This tells us only that the numerator is positive.
This tells us only that the denominator is positive.
Together, we know that the numerator and denominator are positive, but we don't know which is larger. For example, if x and y are 1 and -1, the answer to the question stem is YES, because plugging in those values give us 2/3 , which is between 0 and 1. But, if x and y are 5 and 2, the answer to the question stem is NO, because we get 3, which is not between 0 and 1. Insufficient.

mvictor · Answer

i solved it in ~ 2mins by picking numbers.

x-y/x-2y will be between 0 and 1 if both expressions are of the same sign, and the second one will be greater than the first one.

1. x>y. not sufficient.
x=6, y=-5 -> yes.
x=6, y=2 -> no.
A and D - eliminated.

2. x>2y.
x=6, y=1 -> no
x=6, y=-5 -> yes.

2 outcomes, not sufficient, B out.

1+2
x=6 and y=-5 -> yes
x=6, and y=1 -> no.

eliminate C, and pick E.

chetan2u · Answer

what does the Q stem tell us about x and y.. two things are required for the ans to be yes or no... 1) \frac{(x−y)}{(x−2y)} should be positive.. so both num and denominator have to be of same sign... 2) for \frac{(x−y)}{(x−2y)} to be between 0 and 1, num has to be smaller than denominator.. x-y y.... y need not be -ive. and nothing can be said about signs of num and denominator...insuff (2) x > 2y... we can say both num and deno are positive, but cannot say about the sign of y..insuff. combined nothing new.. insuff E

Fdambro294 · Answer

In these type of Inequality data sufficiency questions, the issue will usually turn on whether the variables are positive or negative.

Looking at the statements, together seems to be a C Trap that the test makers are trying to lure you into picking.

S1 and S2 together tell us that the numerator and denominator will be both be positive.

S1: x > y

x - y > 0

S2: x > 2y

x - 2y > 0

The test-makers are trying to lure you into picking C, since we know that the fraction will be positive. However, we do not know whether the it will be a proper positive fraction that falls between 0 and 1.

In order to get a YES when both statements are combined, the magnitude of the numerator must be less than the magnitude of the denominator.

Or

[x - y] < [x - 2y]

Concept 1: if a number is positive, multiplying it by a positive constant greater than 1 will INCREASE the value on the number line.

Case 1: let X > 0 and Y > 0

In this case ——-> 2Y > Y > 0

And X is great than both of them:

X > 2Y > Y > 0

The absolute value can be interpreted as the distance on the number line. Hence, our rephrased question:

Is: [x - y] < [x - 2y] ?

Can be interpreted as: “on the number line, is the distance from X to Y LESS THAN the distance from X to 2Y?”

In case 1, in which both variables are positive, we an answer this NO, since:

X > 2Y > Y > 0

x will be closer to 2y on the number line

Case 2: X > 0 and Y < 0

Concept: if we multiply a negative value by a positive constant greater than 1, the magnitude will increase and the VALUE will DECREASE

Hence, if Y is negative ——> 0 > Y > 2Y

And we know from the statements that X is greater than both so we have

X > 0 > Y > 2Y

From this case, we can say YES: the distance from X to Y on the number line IS less than the distance from X to 2Y

Since we have Yes and No answers even when the statements are combined, the answer is

E

Bunuel

Is 0 < (x−y)/(x−2y) < 1?

(1) x > y
(2) x > 2y

Kudos for a correct solution.

Posted from my mobile device

Is 0 < (x−y)/(x−2y) < 1?

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