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M28-04

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M28-04  [#permalink]

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New post 16 Sep 2014, 01:28
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A
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D
E

Difficulty:

  35% (medium)

Question Stats:

64% (00:28) correct 36% (00:47) wrong based on 44 sessions

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Re M28-04  [#permalink]

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New post 16 Sep 2014, 01:28
Official Solution:


Both statements are saying the exact same thing: \(|a|+|b|=0\), this to be true, both \(a\) and \(b\) must equal to zero.

Why is that? Absolute value is always non-negative - \(|\text{some expression}| \geq 0\), which means that absolute value is either zero or positive. We have that the sum of two absolute values, or the sum of two non-negative values equals to zero: \(\text{non-negative} + \text{non-negative} = 0\), obviously both must be zero this equation to hold true.


Answer: D
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Re: M28-04  [#permalink]

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New post 18 Apr 2017, 18:20
Bunuel wrote:
Official Solution:


Both statements are saying the exact same thing: \(|a|+|b|=0\), this to be true, both \(a\) and \(b\) must equal to zero.

Why is that? Absolute value is always non-negative - \(|\text{some expression}| \geq 0\), which means that absolute value is either zero or positive. We have that the sum of two absolute values, or the sum of two non-negative values equals to zero: \(\text{non-negative} + \text{non-negative} = 0\), obviously both must be zero this equation to hold true.


Answer: D


In other words, is this the logic? Re-arrange the statements to be:

(1) |a| + |b| = 0

(2) |b| + |a| = 0

If you add two positive values and they equal zero, then both values have to be zero
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Re: M28-04  [#permalink]

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New post 18 Apr 2017, 21:22
joondez wrote:
Bunuel wrote:
Official Solution:


Both statements are saying the exact same thing: \(|a|+|b|=0\), this to be true, both \(a\) and \(b\) must equal to zero.

Why is that? Absolute value is always non-negative - \(|\text{some expression}| \geq 0\), which means that absolute value is either zero or positive. We have that the sum of two absolute values, or the sum of two non-negative values equals to zero: \(\text{non-negative} + \text{non-negative} = 0\), obviously both must be zero this equation to hold true.


Answer: D


In other words, is this the logic? Re-arrange the statements to be:

(1) |a| + |b| = 0

(2) |b| + |a| = 0

If you add two positive values and they equal zero, then both values have to be zero


Two non-negative values. The sum of positive numbers cannot be 0.
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: M28-04  [#permalink]

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New post 10 Jul 2018, 22:19
Bunuel
I understand the arrangement of the equation made above but I was considering the following:
(1) if a>0, a=-b; -b+b=0
BUT if a<0, -a=-b; a=b; and then the sum is a+a=2a (or b+b=2b)
in this case the answer would be not sufficient. Where is the mistake here?
Thank you
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Re: M28-04  [#permalink]

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New post 11 Jul 2018, 00:05
1
NatalieStarr wrote:
Bunuel
I understand the arrangement of the equation made above but I was considering the following:
(1) if a>0, a=-b; -b+b=0
BUT if a<0, -a=-b; a=b; and then the sum is a+a=2a (or b+b=2b)
in this case the answer would be not sufficient. Where is the mistake here?
Thank you


If a > 0 and b > 0, then |a| = -|b| transforms to a = -b --> a + b = 0. This case is not possible: the sum of two positive values cannot be 0.
If a > 0 and b < 0, then |a| = -|b| transforms to a = -(-b) --> a = b. This case is not possible: positive a (a > 0) cannot equal to negative b (b < 0).
If a < 0 and b < 0, then |a| = -|b| transforms to -a = -(-b) --> a + b = 0. This case is not possible: the sum of two negative values cannot be 0.
If a < 0 and b > 0, then |a| = -|b| transforms to -a = -b --> a = b. This case is not possible: negative a (a < 0) cannot equal to positive b (b > 0).

The only case left is a = b = 0.
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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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Re: M28-04 &nbs [#permalink] 11 Jul 2018, 00:05
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