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|a+5|=|b+5| what is the value of a + b?

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by gmattesttaker2 » Tue May 06, 2014 8:18 pm
Hello,

Can you please help with this:


If |a+5|=|b+5| what is the value of a + b?
1.b > 5 and a < 5

2.b = 10


OA: A


Since |a+5|=|b+5|
=> |a+5| - |b+5| = 0

1) b > 5 and a < 5

Let a = 4 => |a+5| = 9

b+5 has to be +9 or -9

=> b = 4 or -14 . However, both of these are not valid values since b > 5

The OA mentions about picking b = 10 as the starting point.

I was wondering what would be the best way to solve since we have 2 conditions here i.e. b > 5 and a < 5


Thanks a lot,
Sri
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Source: — Data Sufficiency |
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by theCodeToGMAT » Wed May 07, 2014 3:16 am
| a + 5 | = | b + 5 |
=> a + 5 = b + 5 ==> a = b

or
=> a + 5 = -b - 5 ==> a + b = -10

To find: a + b

Statement 1:
b > 5 & a < 5
that means a !=b
SUFFICIENT

Statement 2:
b = 10
doesn't tell us what's the value of "A"
INSUFFICIENT

[spoiler]{A} [/spoiler]
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by GMATGuruNY » Wed May 07, 2014 10:57 am
gmattesttaker2 wrote:Hello,

Can you please help with this:


If |a+5|=|b+5| what is the value of a + b?
1.b > 5 and a < 5

2.b = 10
Statement 1: b>5 and a<5
Test the value given in statement 2.
Case 1: b=10
|a+5| = |10+5|
|a+5| = 15
If a+5 = 15, then a=10.
If a+5 = -15, then a=-20.
Since a must be less than 5, b=10 implies that a=-20.
In this case, a+b = -20+10 = -10.

Test a value closer to the given threshold (b>5).
Case 2: b=6
|a+5| = |6+5|
|a+5| = 11
If a+5 = 11, then a=6.
If a+5 = -11, then a=-16.
Since a must be less than 5, b=6 implies that a=-16.
In this case, a+b = -16+6 = -10.

Since a+b is equal to the SAME VALUE in each case, SUFFICIENT.

Statement 2: b=10
Case 1 implies that if b=10, a=10 or a=-20.
If a=10 and b=10, then a+b = 10+10 = 20.
If a=-20 and b=10, then a+b = -20+10 = -10.

Since a+b can be equal to DIFFERENT VALUES, INSUFFICIENT.

The correct answer is A.
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