Bunuel wrote:
Which equation gives the values of all numbers seven units away from 43?
A. |x + 7| = 43
B. |x – 7| = 43
C. |x – 43| = 14
D. |x – 43| = 7
E. |x + 43| = 7
gmatbusters posted the fastest and easiest way to solve, IMO. If you cannot recall the formulation, or get mixed up, a couple of details might help.
1) watch the SIGN inside the brackets
|x| = the distance OF x from 0
|x - 3| is the distance OF x FROM +3
We measure distance by subtracting. There's one hint:
A
minus sign inside the brackets indicates distance of x from a POSITIVE number.
The distance of x from a negative number is written
x - (-3), which = (x + 3)
In this context, distance from a negative number will be indicated by a plus sign (+) inside the brackets.
Even if you're confused about where 7 and 43 go,
both are positive. Whatever is INSIDE the brackets will be preceded by a minus sign.
Eliminate answers A and E
2) Take the problem at face value. It mentions the numbers 43 and 7, not 14. Ignore C for now
We're down to answers B and D. Solve them. Drawing a number line helps here, I think.
B. |x – 7| = 43
Case 1: x - 7 = 43
x = 50Case 2: -(x - 7) = 43
-x + 7 = 43
-x = 36
x = -36On this number line, boldface type = a discrete dot. There are two points, x = -36 and x = 50. Nothing in between is highlighted.
<--
(-36)-------(0)---------------
(50)-->
Prompt says "all numbers [that are] seven units away from 43." Write in 43 on the number line.
<--
(-36)-----(0)--------(43)--
(50)-->
Well, 50 is indeed 7 units away from 43.
But -36? No, -36 is
many more than seven units away from 43. WRONG.
No need to calculate. It is obvious that -36 is more than seven units away from 43.
Then again, this can be a tough crowd... the distance of -36 from 43 is: 43 - (-36) = 79
Eliminate B
D. |x – 43| = 7
Case 1: x - 43 = 7
x = 50Case 2, -(x - 43) = 7
-x + 43 = 7
-x = -36)
x = 36At this point the logic might be clearer, such that you could investigate 36 and 50 in relation to 43. If not, draw a number line.
<--(0)------
(36)----------------
(50)-->
Back to the prompt: "all numbers that are seven units away from 43." Write in 43
<--(0)------
(36)-----(43)------
(50)-->
36 is seven units away from 43
50 is seven units away from 43
We have gone both directions on the number line.
There are no other numbers that are exactly 7 units away from 43. CORRECT
Answer D
For absolute value as distance, an exceptional introduction is
mikemcgarry ,
GMAT Math: Understanding Absolute ValuesOther superb resources include but are not limited to
chetan2u ,
Absolute Modulus, a Better Understandingand
Bunuel ,
Ultimate GMAT Quantitative Megathread: 10. Absolute Value
_________________
SC Butler has resumed! Get
two SC questions to practice, whose links you can find by date,
here.Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it's the only thing that ever has -- Margaret Mead