Quick solution: √(x²) is EQUIVALENT to |x|If x ≠0, then √(x²)/x =
A) -1
B) 0
C) 1
D) x
E) |x|/x
So, √(x²)/x = |x|/x = E
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Source: Beat The GMAT — Problem Solving |
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
- Thanked: 5254 times
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So, √(x²)/x = |x|/x = E
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
- Thanked: 5254 times
- GMAT Score:770
Longer solution:If x ≠0, then (√x²)/x =
A) -1
B) 0
C) 1
D) x
E) |x|/x
TEST some numbers.
Let x = 2
This means √(x²)/x = √(2²)/2 = (√4)/2 = 2/2 = 1
Now check the answer choices:
A) -1 NOPE. ELIMINATE
B) 0 NOPE. ELIMINATE
C) 1 Yes. KEEP
D) x NOPE. x = 2 but our expression evaluated to 1. ELIMINATE
E) |x|/x. If x = 2, |x|/x = |2|/2 = 1 KEEP
We're left with C and E.
Now TEST another value.
Let x = -2
This means √(x²)/x = √[(-2)²]/-2 = (√4)/-2 = 2/-2 = -1
Now check the answer choices:
C) 1 NOPE. ELIMINATE
We're left with E, so it must be correct.
Brent Hanneson - Creator of GMATPrepNow.com
