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# The sum of the possible values of X in the equation |X + 7| + |X – 8|

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The sum of the possible values of X in the equation |X + 7| + |X – 8|  [#permalink]

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26 Jul 2017, 05:23
3
5
00:00

Difficulty:

65% (hard)

Question Stats:

58% (01:59) correct 43% (02:08) wrong based on 136 sessions

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The sum of the possible values of X in the equation |X + 7| + |X – 8| = 16 is:

A. 0
B. 1
C. 2
D. 3
E. None of the above

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The sum of the possible values of X in the equation |X + 7| + |X – 8|  [#permalink]

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26 Jul 2017, 05:32
1
1
GMATinsight wrote:
The sum of the possible values of X in the equation |X + 7| + |X – 8| = 16 is:

A. 0
B. 1
C. 2
D. 3
E. None of the above

hi..

short and sweet method
between -7 and 8, the value will remain CONSTANT.. |0+7|+|0-8|=15..
now any increase in x will result in increase of 2x..

we are looking for 16-15=1
so 2x=1.. x=1/2..
so when x=-7.5.. $$|-7.5+7|+|-7.5-8|=.5+15.5=16$$
x = 8+0.5=8.5..$$|8.5+7|+|8.5-8|=15.5+0.5=16$$

sum = $$8.5+(-7.5)=1$$
B
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Re: The sum of the possible values of X in the equation |X + 7| + |X – 8|  [#permalink]

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26 Jul 2017, 07:32
1
Ans :B

Both terms either can be +ve or - ve
If +ve X=17/2
If - ve X=-15/2
Sum =1

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Re: The sum of the possible values of X in the equation |X + 7| + |X – 8|  [#permalink]

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26 Jul 2017, 12:42
Solving this question on number line is much easier and accurate enough.
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Joined: 22 May 2016
Posts: 2639
The sum of the possible values of X in the equation |X + 7| + |X – 8|  [#permalink]

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27 Jul 2017, 16:14
GMATinsight wrote:
The sum of the possible values of X in the equation |X + 7| + |X – 8| = 16 is:

A. 0
B. 1
C. 2
D. 3
E. None of the above

If you want to solve by removing brackets (not that bad time-wise, 1:50): there are four cases to check.

Let A stand for (X + 7)
Let B stand for (X - 8).

There are four cases to consider for the expressions, just exactly as if the two absolute values were on opposite sides of the equation:

+A +B
-A +B
+A -B
-A -B

Evaluate equation with all four cases:

1. (X + 7) + (X - 8) = 16
X + 7 + X - 8 = 16
2X - 1 = 16
2X = 17
X = $$\frac{17}{2}$$

2. (-X - 7) + (X - 8) = 16
-X - 7 + X - 8 = 16. Stop.
-15 does not equal = 16, let alone give a value for X

3. (X + 7) + (-X + 8) = 16
X + 7 - X + 8 = 16. Stop. Not a solution, same as #2

4. (-X - 7) + (-X + 8) = 16
-X - 7 - X + 8 = 16
-2X + 1 = 16
-2X = 15
X = -$$\frac{15}{2}$$

Check each solution in original equation.

|$$\frac{17}{2}$$ + 7| + |$$\frac{17}{2}$$ - 8| = 16

|$$(\frac{17 + 14)}{2}$$| + |$$\frac{(17-16)}{2}$$| = 16

|$$\frac{31}{2}$$| + |$$\frac{1}{2}$$| =

$$\frac{32}{2}$$ = 16 Correct

The other solution, -$$\frac{15}{2}$$, also works.

The sum of the two solutions?

$$\frac{17}{2}$$ + (-$$\frac{15}{2})$$

= $$\frac{2}{2}$$ = 1

Answer B
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The sum of the possible values of X in the equation |X + 7| + |X – 8|   [#permalink] 27 Jul 2017, 16:14
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# The sum of the possible values of X in the equation |X + 7| + |X – 8|

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