Data Sufficiency

If a, b, c, and d are positive, is ac + bd > bc + ad?

1. c > d
2. b > a

OA = C

q asks whther c(a-b)>d(a-b)
from 1 c>d but a-b can be =0 or a-b>0 so not suff
from 2 b>a, here also we knw one part of the equality is +ve, but c may be > or < d so not suff.
taken 1 and 2 together,
both the sides of c(a-b)>d(a-b) are negative and C>D so c(a-b)<d(a-b)
so C is enough.

Edit: awww! missed that, In my case (c-d) could be 0... and both sides would be equal. Yeah, it should be (C).

Really?! I got (B)!...

If a, b, c, and d are positive, is ac + bd > bc + ad?
ac + bd > bc + ad ?
ac - ad > bc - bd ?
a(c-d) > b (c-d) ?
Divide by (c-d) on both sides
a > c ?

1) c > d
Insufficient to answer

2) b > a
a < b Sufficient to answer

tonebeeze wrote:If a, b, c, and d are positive, is ac + bd > bc + ad?

1. c > d
2. b > a

OA = C

Rephrase the question:
ac + bd > bc + ad
ac - bc > ad - bd
c(a-b) > d(a-b).

Question rephrased: Is c(a-b) > d(a-b)?

Statement 1: c>d.
Let c=2, d = 1, and a-b = 20-10 = 10.
Is 2*10 > 1*10? Yes.

Let c=1, d=2, and a-b = 10-20 = -10.
Is 2(-10) > 1(-10)? No.
Since in the first case the answer is Yes, and in the second case the answer is No, insufficient.

Statement 2: b > a.
Let b=20 and a=10 so that a-b = -10.

Let c=1 and d=2.
Is 1(-10) > 2(-10)? Yes.

Let c=2 and d=1.
Is 2(-10) > 1(-10)? No.
Since in the first case the answer is Yes, and in the second case the answer is No, insufficient.

Statements 1 and 2 combined: c>d and b>a.
Thus, a-b < 0.
Since c>d, c(a-b) will be further below 0 than will be d(a-b).
Thus, we know that c(a-b) < d(a-b).
Sufficient.

The correct answer is C.

Be careful when using division to simplify an expression.
Once the question has been rephrased as Is c(a-b) > d(a-b)?, it's dangerous to divide by (a-b) because we don't know the value of (a-b).
If (a-b) = 0, then the quotient will be undefined.
If (a-b) < 0, then the direction of the inequality will have to change from > to <.
Since we don't know the value of (a-b), plugging in values is a safer approach for most test-takers.