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

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Math Expert
Joined: 02 Aug 2009
Posts: 7212
What is the value of |a|/a+|b|/b?  [#permalink]

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12 Apr 2018, 08:16
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:21) correct 43% (01:23) wrong based on 127 sessions

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What is the value of $$\frac{|a|}{a}+\frac{|b|}{b}$$?
(1) ab<0
(2) $$\frac{|a|}{a}=-\frac{|b|}{b}$$

New question

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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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12 Apr 2018, 10:02
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.

Director
Joined: 09 Mar 2017
Posts: 522
Location: India
Concentration: Marketing, Organizational Behavior
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Re: What is the value of |a|/a+|b|/b?  [#permalink]

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13 Apr 2018, 04:05
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

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

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13 Apr 2018, 04:26
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

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Joined: 18 Mar 2013
Posts: 11
Concentration: Marketing, Strategy
GMAT 1: 480 Q36 V20
GMAT 2: 490 Q41 V19
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Re: What is the value of |a|/a+|b|/b?  [#permalink]

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13 Apr 2018, 11:29

(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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Joined: 16 Aug 2015
Posts: 6827
GMAT 1: 760 Q51 V42
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Re: What is the value of |a|/a+|b|/b?  [#permalink]

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16 Apr 2018, 07:15
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.

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Re: What is the value of |a|/a+|b|/b? &nbs [#permalink] 16 Apr 2018, 07:15
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