Get detailed explanations to advanced GMAT questions.
If |x| > 3, which of the following must be true?
I. x > 3
II. x^2 > 9
I and II only
II and III only
I, II, and III
Option D is the correct answer.
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
- To raise funds, a racing team sold T-shirts imprinted with the team’s logo. The team paid their supplier a…
- A certain cake has two layers with pieces of fruit on top of each layer. Of all the pieces of fruit on…
- For a certain art exhibit, a museum sold admission tickets to a group of 30 people every 5 minutes from 9:00 in…
- A grocery store purchased crates of 40 oranges each for $5.00 per crate and then sold each orange for $0.20. What was the store’s gross profit on each crate of oranges?
- If snow accumulation increased at a constant rate of 30 millimeters per hour during a certain…