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1) \(b > 5\) and \(a < 5\) if \(b>5\), then \(|b+5|=b+5\); but \(a<5\) is not enough to determine the sign of \(|a+5|\), so

\(|a+5|=b+5\), so \(b+5=a+5\) or \(b+5=-a-5\). In this latter case \(a+b=-10\), but in the first one we get \(a=b\). But because a>5 and b<5, \(a=b\) is not a valid option. So only \(a+b=-10\) remains. Sufficient

2) b = 10 \(|a+5|=|10+5|=15\) so \(a=10\)or \(a=-20\), not sufficient to determine a+b.

A _________________

It is beyond a doubt that all our knowledge that begins with experience.

Alternatively, you can get rid of the mod sign and then proceed:

If |a+5|=|b+5|,

EITHER a + 5 = b + 5 (In this case a = b)

OR a + 5 = - (b + 5) (In this case a + b = -10)

1) b > 5 and a < 5 This statement tells you that a is not equal to b. Then, a + b = -10. Sufficient

2) b = 10 Here a could be 10 so a + b = 20 OR a + b = -10. Not sufficient.

Answer (A)

Note that |a+5|=|b+5| gives you 4 cases but they are equivalent to 2 cases discussed above: a + 5 = b + 5 a + 5 = - (b + 5) -(a + 5) = b + 5 -(a + 5) = -(b + 5)
_________________

Re: If |a+5|=|b+5| what is the value of a + b [#permalink]

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16 May 2015, 21:38

VeritasPrepKarishma wrote:

gmat2805 wrote:

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

1) b > 5 and a < 5

2) b = 10

Alternatively, you can get rid of the mod sign and then proceed:

If |a+5|=|b+5|,

EITHER a + 5 = b + 5 (In this case a = b)

OR a + 5 = - (b + 5) (In this case a + b = -10)

1) b > 5 and a < 5 This statement tells you that a is not equal to b. Then, a + b = -10. Sufficient

2) b = 10 Here a could be 10 so a + b = 20 OR a + b = -10. Not sufficient.

Answer (A)

Note that |a+5|=|b+5| gives you 4 cases but they are equivalent to 2 cases discussed above: a + 5 = b + 5 a + 5 = - (b + 5) -(a + 5) = b + 5 -(a + 5) = -(b + 5)

Although you mentioned 4 scenarios , why did just consider 2 of them prior to moving to answer choices

When DS questions look complex, they often hide subtle patterns. While you might not immediately 'see' what the pattern is, you can do a bit of work (TEST VALUES) and PROVE the pattern exists.

Here, we're told that |A+5| = |B+5|. We're asked for the value of A+B.

Fact 1: B>5 and A<5

This means that A and B CANNOT be the same number. Let's TEST VALUES and see what happens....

IF... B = 6 |A+5| = 11

Since we were told that A<5, A can only have one solution....A = -16 (since |-16+5| = |-11| = 11). The answer to the question is 6 + (-16) = -10

IF... B = 7 |A+5| = 12

Since we were told that A<5, A can only have one solution....A = -17 The answer to the question is 7 + (-17) = -10

We were NOT told that A and B had to be integers though, so I'll try one more TEST....

IF... B = 5.5 |A+5| = 10.5

Since we were told that A<5, A can only have one solution....A = -15.5 The answer to the question is 5.5 + (-15.5) = -10

The answer is ALWAYS -10 Fact 1 is SUFFICIENT

Fact 2: B = 10

This tells us nothing about the value of A. Fact 2 is INSUFFICIENT.

Note that |a+5|=|b+5| gives you 4 cases but they are equivalent to 2 cases discussed above: a + 5 = b + 5 a + 5 = - (b + 5) -(a + 5) = b + 5 -(a + 5) = -(b + 5)

Although you mentioned 4 scenarios , why did just consider 2 of them prior to moving to answer choices

The first and the fourth cases give us the same equation:

I. a + 5 = b + 5

IV. -(a + 5) = -(b + 5) Multiply the equation by -1 on both sides to get (a + 5) = (b + 5)

The second and third cases give us the same equation:

II. (a + 5) = -(b + 5)

III. -(a + 5) = (b + 5) Multiply the equation by -1 on both sides to get (a + 5) = -(b + 5)

So actually you have only 2 distinct equations.
_________________

The question can also be solved by basic interpretation of the concept of modulus.

Interpreting the Given Info We know that modulus denotes the magnitude of the distance of a number from another number. So for |a + 5| = | b + 5|, we know that distance of a and b from -5 is the same. Thus there are two possible cases:

I. a = b. In this case a and b are at the same distance from -5 and thus a + b can take any value

II. a and b are on the opposite sides of -5 and equidistant from -5. Let's assume the distance be x. So a = -5 -x and b = -5 +x or vice versa. in both the cases we observe that a + b = -10.

In other words the question asks us to find if a = b?.

Statement-I St-I tells us that b > 5 and a < 5 i.e. both are distinct numbers. So we know that a + b = -10.

Hence st-I is sufficient to answer the question

Statement-II St-II tells us that b = 10. However it does not tell us anything about a. Here a = 10 or a = -20. Hence st-II is not sufficient to answer the question.

Re: If |a+5|=|b+5| what is the value of a + b [#permalink]

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28 Sep 2016, 05:41

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Re: If |a+5|=|b+5| what is the value of a + b [#permalink]

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18 Dec 2016, 02:25

EMPOWERgmatRichC wrote:

Hi All,

When DS questions look complex, they often hide subtle patterns. While you might not immediately 'see' what the pattern is, you can do a bit of work (TEST VALUES) and PROVE the pattern exists.

Here, we're told that |A+5| = |B+5|. We're asked for the value of A+B.

Fact 1: B>5 and A<5

This means that A and B CANNOT be the same number. Let's TEST VALUES and see what happens....

IF... B = 6 |A+5| = 11

Since we were told that A<5, A can only have one solution....A = -16 (since |-16+5| = |-11| = 11). The answer to the question is 6 + (-16) = -10

IF... B = 7 |A+5| = 12

Since we were told that A<5, A can only have one solution....A = -17 The answer to the question is 7 + (-17) = -10

We were NOT told that A and B had to be integers though, so I'll try one more TEST....

IF... B = 5.5 |A+5| = 10.5

Since we were told that A<5, A can only have one solution....A = -15.5 The answer to the question is 5.5 + (-15.5) = -10

The answer is ALWAYS -10 Fact 1 is SUFFICIENT

Fact 2: B = 10

This tells us nothing about the value of A. Fact 2 is INSUFFICIENT.

“The heights by great men reached and kept were not attained in sudden flight but, they while their companions slept, they were toiling upwards in the night.” ― Henry Wadsworth Longfellow