If a, b, c, and d are positive, is ac + bd > bc + ad?
1. c > d
2. b > a
OA = C
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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.
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.
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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
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
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Rephrase the question:tonebeeze wrote:If a, b, c, and d are positive, is ac + bd > bc + ad?
1. c > d
2. b > a
OA = C
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.
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When I see that all four of the expressions ac, bc, ad and bd, are being added and subtracted here, I'll think of factorizations that look something like (a+b)(c+d) or (a-b)(c-d). We can rewrite the questiontonebeeze wrote:If a, b, c, and d are positive, is ac + bd > bc + ad?
1. c > d
2. b > a
OA = C
Is ac + bd > bc + ad ?
Is ac - ad - bc + bd > 0 ?
Is (a - b)(c - d) > 0 ?
Now you can see immediately that neither statement is sufficient alone, but together we know the sign of both factors and can therefore find the sign of their product, so the answer is C.
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