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

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Senior Manager
Joined: 21 Oct 2013
Posts: 414
If x>0, which of the following must be true?  [#permalink]

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13 Aug 2014, 10:18
2
1
4
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Difficulty:

5% (low)

Question Stats:

74% (00:39) correct 26% (00:48) wrong based on 337 sessions

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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

OE
Make the algebra disappear - plug in numbers that fit the problem. Start by picking one of the many good choices that the limitation x>0 allows. By plugging in x=5, for instance, you can POE answer choices B and C.
A fraction will definitely eliminate A, but what about E?
Try a small enough fraction to POE it! For example x=1/1000.

Hi, I found this question hard. Is OE the best way to solve this Q?
Math Expert
Joined: 02 Sep 2009
Posts: 56303
Re: If x>0, which of the following must be true?  [#permalink]

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13 Aug 2014, 10:29
1
1
goodyear2013 wrote:
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

OE
Make the algebra disappear - plug in numbers that fit the problem. Start by picking one of the many good choices that the limitation x>0 allows. By plugging in x=5, for instance, you can POE answer choices B and C.
A fraction will definitely eliminate A, but what about E?
Try a small enough fraction to POE it! For example x=1/1000.

Hi, I found this question hard. Is OE the best way to solve this Q?

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.

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.

C. -1 < x < 1. The same as A. Discard.

E. 1/100 < x. We don't know whether the number is greater than 1/100, it could be a positive number less than or equal to 1/100. Discard.

Answer: D.
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Joined: 12 Sep 2015
Posts: 3852
Location: Canada
Re: If x>0, which of the following must be true?  [#permalink]

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26 Jan 2018, 09:39
Top Contributor
goodyear2013 wrote:
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

The key word here is MUST

So, if we can show that an answer choice NEED NOT BE TRUE, then we can eliminate it

Given: x > 0 (x is positive)
So, x COULD equal 50
Now check the answer choices...

Answer choice B says that x < 2.
If x = 50, then answer choice B is NOT true.
ELIMINATE B

Answer choice C says that x < 1.
If x = 50, then answer choice C is NOT true.
ELIMINATE C

All of the other answer choices work. So, let's try another possible value of x

If x is positive, x COULD equal 0.0001
Now check the answer choices...

Answer choice A says that 1 < x.
If x = 0.0001, then answer choice A is NOT true.
ELIMINATE A

Answer choice E says that 1/100 < x.
If x = 0.0001, then answer choice E is NOT true.
ELIMINATE E

By the process of elimination, the correct answer is D

Cheers,
Brent
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CEO
Joined: 12 Sep 2015
Posts: 3852
Location: Canada
Re: If x>0, which of the following must be true?  [#permalink]

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26 Jan 2018, 09:43
1
Top Contributor
goodyear2013 wrote:
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

Alternatively....

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

RELATED VIDEO (combining ratios)

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Re: If x>0, which of the following must be true?   [#permalink] 26 Jan 2018, 09:43
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# If x>0, which of the following must be true?

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