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
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