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26 Jul 2017, 05:23
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
57% (01:59) correct
43%
(02:00)
wrong
based on 626
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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
A. 0
B. 1
C. 2
D. 3
E. None of the above
27 Jul 2017, 16:14
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GMATinsight
If you want to solve by removing brackets (not 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.
-X + X = 0. We cannot get 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. When we solve this way, this step is imperative.
|\(\frac{17}{2}\) + 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. (Check it.)
The sum of the two solutions?
\(\frac{17}{2}\) + (-\(\frac{15}{2})\)
= \(\frac{2}{2}\) = 1
Answer B
26 Jul 2017, 05:32
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GMATinsight
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
