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tonebeeze: Master | Next Rank: 500 Posts; Posts: 158; Joined: Mon Nov 02, 2009 5:49 pmFollowed by: 3 members; Thanked: 2 times

by tonebeeze » Mon Apr 25, 2011 4:48 pm

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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Source: Beat The GMAT — Data Sufficiency | Mon Apr 25, 2011 4:48 pm

rohu27: Legendary Member; Posts: 586; Joined: Tue Jan 19, 2010 4:38 amFollowed by: 5 members; Thanked: 31 times; GMAT Score:730

by rohu27 » Mon Apr 25, 2011 5:08 pm

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.

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MAAJ: Master | Next Rank: 500 Posts; Posts: 243; Joined: Sun Jul 12, 2009 7:12 amFollowed by: 2 members; Location: Dominican Republic; Thanked: 31 times; GMAT Score:480

by MAAJ » Tue Apr 26, 2011 6:01 am

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

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 26, 2011 6:33 am

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.

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Ian Stewart: GMAT Instructor; Posts: 2623; Joined: Mon Jun 02, 2008 3:17 amFollowed by: 355 members; Location: Montreal; Thanked: 1090 times; GMAT Score:780

by Ian Stewart » Tue Apr 26, 2011 10:57 am

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

1. c > d
2. b > a

OA = C

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 question

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.

For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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