[GMAT math practice question]
Is x > 1?
1) x^2 > x|x|
2) x|x| > x
Is x > 1?
This topic has expert replies
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]
- Max@Math Revolution
- Elite Legendary Member
- Posts: 3991
- Joined: Fri Jul 24, 2015 2:28 am
- Location: Las Vegas, USA
- Thanked: 19 times
- Followed by:37 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify the conditions, if necessary.
Condition 1)
x^2 > x|x|
=> |x|^2 > x|x|
=> |x|^2 - x|x| > 0
=> |x|(|x| - x) > 0
=> (|x| - x) > 0
=> |x| > x
=> x < 0
Thus, condition 1) is sufficient since it yields the unique answer, 'no'.
Condition 2)
x|x| > x
Assume x ≥ 0. x|x| > x => x^2 > x => x^2 - x > 0 => x(x-1) > 0 => x < 0 or x > 1.
We must have x > 1 by the assumption.
Assume x < 0. x|x| > x ⇔ -x2 > x ⇔ x2 + x < 0 ⇔ x(x+1) < 0 ⇔ -1 < x < 0.
In this case, -1 < 0 < 1.
So, condition 2) tells us that -1 < x < 0 or x > 1.
In inequality questions, the law "Question is King" tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
The solution set of the question "x > 1" doesn't include the solution set of the condition 2) "-1 < x < 0 or x > 1". Condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.
The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question. We should simplify the conditions, if necessary.
Condition 1)
x^2 > x|x|
=> |x|^2 > x|x|
=> |x|^2 - x|x| > 0
=> |x|(|x| - x) > 0
=> (|x| - x) > 0
=> |x| > x
=> x < 0
Thus, condition 1) is sufficient since it yields the unique answer, 'no'.
Condition 2)
x|x| > x
Assume x ≥ 0. x|x| > x => x^2 > x => x^2 - x > 0 => x(x-1) > 0 => x < 0 or x > 1.
We must have x > 1 by the assumption.
Assume x < 0. x|x| > x ⇔ -x2 > x ⇔ x2 + x < 0 ⇔ x(x+1) < 0 ⇔ -1 < x < 0.
In this case, -1 < 0 < 1.
So, condition 2) tells us that -1 < x < 0 or x > 1.
In inequality questions, the law "Question is King" tells us that if the solution set of the question includes the solution set of the condition, then the condition is sufficient
The solution set of the question "x > 1" doesn't include the solution set of the condition 2) "-1 < x < 0 or x > 1". Condition 2) is not sufficient.
Therefore, A is the answer.
Answer: A
Math Revolution
The World's Most "Complete" GMAT Math Course!
Score an excellent Q49-51 just like 70% of our students.
[Free] Full on-demand course (7 days) - 100 hours of video lessons, 490 lesson topics, and 2,000 questions.
[Course] Starting $79 for on-demand and $60 for tutoring per hour and $390 only for Live Online.
Email to : [email protected]