Solutions
Get detailed explanations to advanced GMAT questions.
Question
If |x| > 3, which of the following must be true?
I. x > 3
II. x^2 > 9
III. |x-1|>2
Option A:
I only
Option B:
II only
Option C:
I and II only
Option D:
II and III only
Option E:
I, II, and III
Difficulty Level
MediumSolution
Option D is the correct answer.
Option Analysis
Given, |x| > 3, which means either x>3 or x<-3
Now check the statements
I. x > 3 – not always true as x can be smaller than -3.Thus option A,C & E is ruled out. Only B & D are left.
II. X^2 > 9 – Always true for x>3 or x<-3 .To check – if x = 4,5,6,7…. or -4,-5,-6,-7, x^2>9
III. |x-1|>2, which means (x-1)>2 —> x>3 (if x-1>0) – True it also means (x-1)<-2—- >x<-1
(if x-1<0) X<-1 satisfies x<-3.
Thus true Both II and III, is true
Related Questions
- If the sum of the consecutive integers from –42 to n inclusive is 372, what is the value of n?
- If the average (arithmetic mean) of the assessed values of x houses is $212,000 and the average of the…
- A string of 10 light bulbs is wired in such a way that if any individual light bulb fails, the entire string…
- (1+0.0001)/(0.04+10) The value of the expression above is closest to which of the following?
- Is the product of a positive integer and a negative integer is less than -10 ?