If negative integer a is multiplied by b and the result is greater tha

Question

If negative integer a is multiplied by b and the result is greater than 0 but less than |a|, then which of the following must be true of b?

A.  b > 1

B.  0 < b < 1

C.  -1 < b < 0

D.  b < a

E.  |b| < a

chetan2u · Accepted Answer

If a*b>0, where a<0, so b is also <0 If ab<|a|, square both sides a^2b^20, so b^2-1<0........b^2<1 Range of b is -1\frac{2}{-2}...............b>-1 Since b<0....-1

KSBGC · Answer

I think conceptual understanding is a must to work out this question. Few points can be made based on the information given:

1. a is negative . b must also be negative. 
2. Absolute value of a is greater than the product of a and b.
3. we know that negative times negative yields positive result.

Let assume the value of a and b.

a = -4 and b = -2

so, ab = 8 but it is stated in the question that |a| > ab . So, b can't be a integer rather it's a fraction.

a = -4
b = - \frac{1}{2}

a*b = (-4)*(-1/2)
 = 2
and |a| > 2.

Thus , b is a negative fraction.

Option C is the best answer.

hindu1988 · Answer

Keep in mind - a -ve and |a|>ab>0
implies -- b has to be -ve
For a*b to be less than |a| - b has to be -ve fraction < 1

generis · Answer

Use a negative integer for a in order to simplify the arithmetic Let a=-3 |-3|= 3 (1) the result of a*b is greater than 0 a*b>0 (-3*b)>0 = 0<(-3*b) (2) the result of a*b is less than |a| a*b<|a| (-3*b)<3 (3) Combine: 0<(-3*b)<3 Divide all terms by -3, flip the signs 0>b>-1 = -1

analytica233 · Answer

a < 0 and ab > 0 --> b< 0 ab < |a|. Divide both sides by |a|, we have: -b < 1 <=> b > -1. So 0 < b < 1 (C)

BrushMyQuant · Answer

Given that If negative integer a is multiplied by b and the result is greater than 0 but less than  |a|  and we need to find which of the following must be true of b

Now a negative number integer a, lets say -2 is multiplied by b and the result is > 0 => b is negative

And the result is also < |a|
=> value of ab (without sign) is less than a
=> b is a negative fraction between -1 and 0

So,  Answer will be C 
Hope it helps!

Watch the following video to learn the Basics of Absolute Values

https://www.youtube.com/watch?v=huFiBk8PaGY

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

If negative integer a is multiplied by b and the result is greater tha

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

If negative integer a is multiplied by b and the result is greater tha

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards