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Re: If a < b < 0, which of the following must be true? [#permalink]

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21 Apr 2015, 08:18

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Bunuel wrote:

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

Kudos for a correct solution.

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.
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Thanks, Lucky

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Re: If a < b < 0, which of the following must be true? [#permalink]

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21 Apr 2015, 23:04

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This post received KUDOS

Bunuel wrote:

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

Kudos for a correct solution.

A. a^2<b^2. Put a=-2,b=-1, 4>1.Not true B. b-10<a. Put a=-25,b=-3. -13>-25.Not true C.b+a>a. Put b=-1,a=-2, -3<-2. Not true D. ab<b^2. Put b=-1,a=-2, ab=2 and b^2=1. Not true E.ab<a^2. Always true. Put b=-2,a=-5. ab=10, a^2=25. True Answer E

Re: If a < b < 0, which of the following must be true? [#permalink]

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22 Apr 2015, 00:16

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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.
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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.

Re: If a < b < 0, which of the following must be true? [#permalink]

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21 Dec 2017, 19:17

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