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What is the value of |a|/a+|b|/b?

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What is the value of |a|/a+|b|/b?  [#permalink]

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New post 12 Apr 2018, 09:16
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What is the value of \(\frac{|a|}{a}+\frac{|b|}{b}\)?
(1) ab<0
(2) \(\frac{|a|}{a}=-\frac{|b|}{b}\)

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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: What is the value of |a|/a+|b|/b?  [#permalink]

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New post 12 Apr 2018, 11:02
1
chetan2u wrote:
What is the value of \(\frac{|a|}{a}+\frac{|b|}{b}\)?
(1) ab<0
(2) \(\frac{|a|}{a}=-\frac{|b|}{b}\)

New question


If a number x is positive, then |x| = x and thus |x|/x = 1
If a number y is negative, then |y| = -y and thus |y|/y = -1

(1) ab < 0 . This means out of a/b, one is negative and other is positive.
So one of |a|/a and |b|/b will be '1' and the other will be '-1'. So the sum will be '0'. Sufficient.

(2) |a|/a = -|b|/b
This means |a|/a + |b|/b = 0. Sufficient.

Hence D answer
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Re: What is the value of |a|/a+|b|/b?  [#permalink]

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New post 13 Apr 2018, 05:05
chetan2u wrote:
What is the value of \(\frac{|a|}{a}+\frac{|b|}{b}\)?
(1) ab<0
(2) \(\frac{|a|}{a}=-\frac{|b|}{b}\)

New question

Possible cases :
Case 1: -1 -1 = -2
Case 2: -1 +1 =0
Case 3: 1 +1 = 2
Case 4: 1- 1 = 0

St. 1 says a and b have opposite signs. Cases 2 & 4. Both gives a sum of 0.
Sufficient

St.2 directly gives the sum 0.
Sufficient

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Re: What is the value of |a|/a+|b|/b?  [#permalink]

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New post 13 Apr 2018, 05:26
chetan2u wrote:
What is the value of \(\frac{|a|}{a}+\frac{|b|}{b}\)?
(1) ab<0
(2) \(\frac{|a|}{a}=-\frac{|b|}{b}\)

New question


Great question chetan2u

(2) \(\frac{|a|}{a}=-\frac{|b|}{b}\)

Apply directly in the question

\(\frac{|a|}{a}+\frac{|b|}{b}\) = \(-\frac{|b|}{b}+\frac{|b|}{b}\) = 0

Sufficient

(1) \(ab<0\)

Here it means a & b have different sign

Case 1: a > 0 & b < 0 : then |a| = a & |b| = -b. Therefore, \(\frac{a}{a}+\frac{-b}{b}\) = 1 -1 = 0

Case 1: a < 0 & b > 0 : then |a| = -a & |b| = b. Therefore, \(\frac{-a}{a}+\frac{b}{b}\) = -1 + 1 = 0

Sufficient

Answer: D
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Re: What is the value of |a|/a+|b|/b?  [#permalink]

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New post 13 Apr 2018, 12:29
Answer is (D)

(i) ab<0 means either a or b - ve. that implies., |a|/a + |b|/b = 0 using a -ve or b -ve. Sufficient.
(ii) simplying equation, we can determine |a|/a + |b|/b = 0. Suffiient.
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Re: What is the value of |a|/a+|b|/b?  [#permalink]

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New post 16 Apr 2018, 08:15
chetan2u wrote:
What is the value of \(\frac{|a|}{a}+\frac{|b|}{b}\)?
(1) ab<0
(2) \(\frac{|a|}{a}=-\frac{|b|}{b}\)

New question


Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

|x|/x = 1 if x > 0 and |x|/x = -1 if x < 0.


Condition 1)
ab < 0
⇔ a > 0, b < 0 or a < 0, b > 0
⇔ |a|/a = 1, |b|/b = -1 or |a|/a = -1, |b|/b = 1
⇔ |a|/a + |b|/b = 0 for both sides
Thus the condition 1) is sufficient.

Condition 2)
|a|/a = -|b|/b
⇔ |a|/a + |b|/b = 0
Thus the condition 2) is sufficient.

Therefore, D is the answer.
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Re: What is the value of |a|/a+|b|/b? &nbs [#permalink] 16 Apr 2018, 08:15
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