GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Apr 2019, 06:10

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

Hide Tags

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2906
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
The sum of the possible values of X in the equation |X + 7| + |X – 8|  [#permalink]

Show Tags

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

HideShow timer Statistics

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

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Math Expert
Joined: 02 Aug 2009
Posts: 7558
The sum of the possible values of X in the equation |X + 7| + |X – 8|  [#permalink]

Show Tags

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
_________________
Intern
Joined: 24 Sep 2016
Posts: 17
Re: The sum of the possible values of X in the equation |X + 7| + |X – 8|  [#permalink]

Show Tags

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

Sent from my Mi 4i using GMAT Club Forum mobile app
Intern
Joined: 10 Apr 2017
Posts: 2
Re: The sum of the possible values of X in the equation |X + 7| + |X – 8|  [#permalink]

Show Tags

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

Show Tags

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

_________________
Listen, are you breathing just a little, and calling it a life?
-- Mary Oliver

For practice SC questions with official explanations that were posted and moderated by the SC Team,
go to SC Butler here: https://gmatclub.com/forum/project-sc-butler-get-2-sc-questions-everyday-281043.html
The sum of the possible values of X in the equation |X + 7| + |X – 8|   [#permalink] 27 Jul 2017, 16:14
Display posts from previous: Sort by