If x>0, which of the following must be true?

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Re: If x>0, which of the following must be true?

by Brent@GMATPrepNow » Sun Mar 15, 2020 12:27 pm

BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:47 am
If x > 0, which of the following must be true?

A. 1 < x
B. 0 < x < 2
C. -1 < x < 1
D. -10 < x
E. 1/100 < x

Answer: D
Source: Economist GMAT

Given: 0 < x
We also know that -10 < 0

So, we can COMBINE the inequalities to get: -10 < 0 < x
From here, we can conclude that -10 < x
Answer: D

Brent Hanneson - Creator of GMATPrepNow.com

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swerve: Legendary Member; Posts: 2499; Joined: Sun Oct 29, 2017 2:04 pm; Followed by:6 members

Re: If x>0, which of the following must be true?

by swerve » Tue Mar 17, 2020 7:42 am

BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:47 am
If x > 0, which of the following must be true?

A. 1 < x
B. 0 < x < 2
C. -1 < x < 1
D. -10 < x
E. 1/100 < x

Answer: D
Source: Economist GMAT

All we know is that \(x\) is some positive number. Right away we can see that D must be true: if \(x\) is positive then it MUST be true that it's greater than \(-10\). Still let's check each option.

A. \(1 < x\). We don't know whether the number is greater than \(1\), it could be a positive number less than or equal to \(1\). Discard. \(\Large{\color{red}\chi}\)

B.\( 0 < x < 2\). The same here: we don't know whether the number is less than \(2\), it could be more than or equal to 2. Discard. \(\Large{\color{red}\chi}\)

C. \(-1 < x < 1\). The same as A. Discard. \(\Large{\color{red}\chi}\)

E. \(\dfrac{1}{100} < x\). We don't know whether the number is greater than \(\dfrac{1}{100}\), it could be a positive number less than or equal to \(\dfrac{1}{100}\). Discard. \(\Large{\color{red}\chi}\)

Therefore, the correct answer is D.

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Re: If x>0, which of the following must be true?

by Scott@TargetTestPrep » Wed Mar 18, 2020 3:48 pm

BTGModeratorVI wrote: ↑
Sat Mar 14, 2020 6:47 am
If x > 0, which of the following must be true?

A. 1 < x
B. 0 < x < 2
C. -1 < x < 1
D. -10 < x
E. 1/100 < x

Answer: D
Source: Economist GMAT