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

# 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, Last updated: May 28, 2020

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

Answer is true lets give numbers to a&b
b<0 a>0
b=-2 a=1
1- (-2)> 1-2
3>-1

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.

#### John Smith

John Smith

|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.
7

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.

What if a is -ve too?

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.

Um I think it would be |a - b| > a + b

#### 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...

Replied on Jun 11, 2017

That is exactly what I was thinking so even I marked D as correct answer.

Replied on Aug 26, 2017

Yes,I've tried AnnJ method