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

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If negative integer a is multiplied by b and the result is greater tha  [#permalink]

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New post 29 Jun 2018, 01:12
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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. \(|b| < a\)

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If negative integer a is multiplied by b and the result is greater tha  [#permalink]

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New post 29 Jun 2018, 02:14
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Bunuel wrote:
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. \(|b| < a\)


If a*b>0, where a<0, so b is also <0

If ab<|a|, square both sides
\(a^2b^2<a^2.......a^2b^2-a^2<0....a^2(b^2-1)<0\)
Since a^2>0, so \(b^2-1<0........b^2<1\)
Range of b is -1<b<1....
But b is negative, so -1<b<0


Other way
Substitute a as -2
So -2b<|-2|.............-2b<2..........divide both sides by -2...
\(\frac{-2b}{-2}>\frac{2}{-2}...............b>-1\)
Since b<0....-1<b<0

C
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: If negative integer a is multiplied by b and the result is greater tha  [#permalink]

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New post 29 Jun 2018, 07:05
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Bunuel wrote:
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. \(|b| < a\)



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.
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Re: If negative integer a is multiplied by b and the result is greater tha  [#permalink]

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New post 29 Jun 2018, 08:05
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
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If negative integer a is multiplied by b and the result is greater tha  [#permalink]

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New post 29 Jun 2018, 09:04
1
Bunuel wrote:
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. \(|b| < a\)

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
\(0>b>-1\)
= \(-1<b<0\)

Answer C
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If negative integer a is multiplied by b and the result is greater tha &nbs [#permalink] 29 Jun 2018, 09:04
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