If b 0 and ax

Question

If b > 0 and ax < bx < by, is xy > 0? (1) a – b > 0 (2) a < y *kudos for all correct solutions

rohit8865 · Answer

ax < bx == (a-b)x<0-------(m) && bx < by ==b(x-y)<0 (1) putting a-b>0 in eq (m) we get x<0 no info of y insuff (2) y>a no info of a ie a<0 or a>0 insuff Combining we know b>0 from stem and a>b from (1) thus a>b>0 thus a >0 from (2) we get y>a>0 thus y >0 && x<0 from (1) thus xy<0 suff Ans C

Diwakar003 · Answer

(1) a-b > 0 a>b. Since b is positive, a should also be positive. Now using these constraints in the given condition ax < bx < by -> Since a and b are positive, x has to be negative. y can either be positive or negative. So we can't be sure of xy. - Insufficient. (2) a < y - No information about signs of x, y, and a. - Again not sufficient. Combining (1) and (2) From (2) we can tell y is positive. Hence xy <0. Sufficient. Hence C. Cheers!

Mo2men · Answer

Great question Brent. It is hard based on simple concepts and organization of data.

If b > 0 and ax < bx < by, is xy > 0?

(1) a – b > 0

a>b>0.........It means both a & b are Positive.

Hence, x must be Negative to yield that ax<bx

But we do not know anything bout sign of 'y'.

Let b=1 and x=-1 and y=10.........xy<0

Let b=1 and x=-1 and y=-1/2.........xy>0

Insufficient

(2) a < y

No clue about signs x, b, y and a can take many combinations with signs could verify that ax < by

Let a = 1 & y = 2 & x=b=1...... xy>0

Let x=-10 & y=1 & a=2 & b=-1...xy<0

Insufficient

Combining 1 & 2

y> a>b>0 & x<0....... then xy is NOT greater than Zero

Answer: C

BrentGMATPrepNow · Answer

Target question : Is xy > 0? Given : b > 0 and ax < bx < by Since we're told that a - b is POSITIVE, we can take bx < by, and divide both sides by b to get: x < y Statement 1 : a – b > 0 I can see (a - b) "hiding" in the inequality ax < bx, so let's look into this further. Take ax < bx and subtract bx from both sides to get: ax - bx < 0 Factor: x(a - b) < 0 Since we're told that a - b is POSITIVE, we can divide both sides by a-b to get: x < 0 So, x is NEGATIVE Also, a - b > 0, we can add b to both sides to get a > b Is this enough information to answer the target question ? Well, we still don't know anything about y, so it seems unlikely that statement 1 is sufficient. Let's TEST some numbers. Here are two cases that both that satisfy statement 1: Case a: a = 3, b = 2, x = -1 and y = 1. In this case, xy = -1. So, xy < 0 Case b: a = 3, b = 2, x = -1 and y = -0.5. In this case, xy = 0.5. So, xy > 0 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2 : a < y There are several scenarios that satisfy statement 2. Here are two: Case a: a = 3, b = 10, x = 2 and y = 4. In this case, xy = 8. So, xy > 0 Case b: a = 2, b = 1, x = -1 and y = 10. In this case, xy = -10. So, xy < 0 Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1 tells us that x is NEGATIVE and that b < a Since it's given that 0 < b, we can write: x < 0 < b < a Statement 2 tells us that a < y If we add that information to the above inequality, we get: x < 0 < b < a < y In other words, x is NEGATIVE and y is POSITIVE, which means xy < 0 Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer: C RELATED VIDEO https://www.youtube.com/watch?v=Od98BOicIq4

AbhishekGopal · Answer

Hi can you please tell me how x has to be negative since a and b are positive?

rohit8865 · Answer

From stem we know ax> x(a-b)<0---------(A) from (1) we know a-b>0 thus for statement ----(A) to be valid , x must be <0

bumpbot · Answer

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If b > 0 and ax < bx < by, is xy > 0?

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