If |a| < |b|, and a > b, which of the following is necessarily true? - ProProfs

If |a| < |b|, and a > b, which of the following is necessarily true?

A. |a + b| > |b| + |a|
B. |a + b| < a - b
C. |a| + |b| > 2|b|
D. |a - b| > a + b
E. |a| - |b| > |a - b|

This question is part of SAT Math Questions
Asked by Wyatt Williams on Dec 15, 2016

Request Answer   Share    ... Answer AnonymouslyAnswer Later Copy Link Answered on Sep 16, 2017

Works only D

if a=3 and b= -10 so in B

|3-10|=7and 3-(-10)=13 so 7<13.B is correct. But in D it is also correct:

|3+10|=13 and 3-10=-7 13>-7

So we should take both <0

if a=-1 and b=-2 then D is correct

|-1+2|=1and -1-2=-3 1>-3

but B is wrong:

|-1-2|=3 and -1+2=1 3>1 but it said that should be 3<1 which is of course wrong

so D is the only correct answer   Reply Answered on Apr 04, 2017

Answer is true lets give numbers to a&b
b<0 a>0
b=-2 a=1
1- (-2)> 1-2
3>-1   Reply Answered on Jan 20, 2017

Incorrect, as a can be a negative number with a smaller magnitude, in which case 2 does not work out. The correct answer is PART 4, as a+b will always be negative, while |a+b| is always positive.   Reply John Smith

John Smith  Answered on Dec 15, 2016

|a + b| < a - b

Because the absolute value of a is less than that of b, a is a lesser magnitude than b. However, a > b, so a must be a positive number and b a negative number. So, you can plug in numbers: a = some positive number of magnitude less than b, or a = 3, b = -10. Plug them in, and only B works out.   Reply Ncorrect, as a can be a negative number with a smaller magnitude, in which case 2 does not work out. The correct answer is PART 4, as a+b will always be negative, while |a+b| is always positive.   Reply What if a is -ve too?   Reply Disagree with the idea that a must be positive. For example, a can be -2, b can be -10, and the rules from the question still apply.   Reply Um I think it would be |a - b| > a + b   Reply AnnJ

AnnJ

Replied on Jun 02, 2017

But what if both of them ar <0. For exampe a = -2, and b = -3? Then only D works out...   Reply Replied on Jun 11, 2017

That is exactly what I was thinking so even I marked D as correct answer.   Reply Replied on Aug 26, 2017

Yes,I've tried AnnJ method   Reply Search for Google images Select a recommended image
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