If a

Question

If a < b < 0, which of the following must be true?

A. a^2 < b^2
B. b − 10 < a
C. b + a > a
D. ab < b^2
E. ab < a^2

Lucky2783 · Accepted Answer

A. a^2 < b^2 --> (a+b)(a-b) < 0 --> (-ive)*(-ive)<0 ; NO B. b − 10 < a --> b-a<10,let a=-1000 and b=-1; then b-a=999 . NO C. b + a > a --> b>0 ; NO D. ab < b^2 --> b*(a-b) <0; (-ive)*(-ive)<0 ; NO E. ab < a^2 --> a*(b-a)<0; (-ive)*(+ive) <0 YESSSSSSSS!!. this is our answer.

Harley1980 · Answer

a) a^2|b| b) b − 10 < a ; b 10 c) b + a > a ; b > 0 false d) ab < b^2 false because |b| < |a| e) ab < a^2 true because |a|>|b| And answer is E

KS15 · Answer

A. a^21.Not true B. b-10-25.Not true C.b+a>a. Put b=-1,a=-2, -3<-2. Not true D. ab

SherLocked2018 · Answer

picking no for a and b : 
 a b OpA 
-2 -1 4<1 NT
-1.5 -.5 2.25<.25 NT
-20 -1 400<1 NT

similarly work out the table for other options.. Thus we see that putting these nos of a and b in A, B, C, D give Not True(NT) or maybe true ans. E gives true always. Thus E.

Bunuel · Answer

VERITAS PREP OFFICIAL SOLUTION:

E. In this problem you should see that a and b are both negative numbers, and that a has a greater absolute value (it's further from zero) than b does. So when you square a, you'll end up with a larger positive number than when you multiply a by a lesser-absolute-value b. So choice E must be true. Choosing numbers can help exemplify:

a = -10, b = -5

Would mean that a^2 = 100 and ab = 50, so a^2 is bigger.

Even if you try with fractions (always a good idea to consider), a = -3/4 and b = -1/2 yields:

a^2 = 9/16 (greater than 1/2)

ab = 3/8 (less than 1/2)

Proving E to be true. For the incorrect answers:

A) Since a has a larger absolute value, when it's squared it will be larger than b-squared.

B) Because you don't know the relative values of a and b, you can't determine that moving b 10 places to the left will reduce it past a.

C) Adding a negative number (b) to a will make it smaller, not larger, than the original a.

D) See demonstration above.

bumpbot · Answer

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If a < b < 0, which of the following must be true?

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GMAT Problem Solving (PS) Questions

If a < b < 0, which of the following must be true?

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