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If 5 ≥ |x| ≥ 0, which of the following must be true?

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by BTGmoderatorDC » Sun Oct 22, 2017 2:10 am
If 5 ≥ |x| ≥ 0, which of the following must be true?

I. x ≥ 0
II. x > -5
III. 25 ≥ x^2 ≥ -25

A. None
B. II only
C. III only
D. I and III only
E. II and III only

Why isn't Option D the correct answer? Can some experts explain?

OA C
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by prabsahi » Sun Oct 22, 2017 6:04 am
lheiannie07 wrote:If 5 ≥ |x| ≥ 0, which of the following must be true?

I. x ≥ 0
II. x > -5
III. 25 ≥ x^2 ≥ -25

A. None
B. II only
C. III only
D. I and III only
E. II and III only

Why isn't Option D the correct answer? Can some experts explain?

OA C



The above 5 ≥ |x| ≥ 0 means
x takes values betwenn -5 to 5
(-5,-4,-3,-2,-1,0,1,2,3,4,5)

Now lets look at the options:

I. x ≥ 0
Not possible as X can be 6,7 or negative numbers as wel
II. x > -5
Again from the set not possible
III. 25 ≥ x^2 ≥ -25

>>implies x^2 ≥ -25 which is always trues since x square will always be postive and greater tha equal to zero
>>25 ≥ x^2 implies value of x lies between -5 to 5 (inclusive)

So correct choice is III.Option C.
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by [email protected] » Sun Oct 22, 2017 10:41 am
Hi lheiannie07,

When a question asks 'which of the following MUST be true?', you can interpret that to mean "which of the following is ALWAYS true no matter how many different examples you come up with?"

Here, we know that X can be any value from -5 to +5 (inclusive).

I. x ≥ 0

X could be -5, so Roman Numeral 1 is NOT always true.
Eliminate Answer D.

II. x > -5

X could be -5, so Roman Numeral 2 is NOT always true.
Eliminate Answers B and E.

III. 25 ≥ x^2 ≥ -25

Roman Numeral 3 covers the entire range of possible squared terms (from -5 to +5). Thus, Roman Numeral 3 IS always true.

Final Answer: C

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by Scott@TargetTestPrep » Wed Nov 20, 2019 5:59 pm
BTGmoderatorDC wrote:If 5 ≥ |x| ≥ 0, which of the following must be true?

I. x ≥ 0
II. x > -5
III. 25 ≥ x^2 ≥ -25

A. None
B. II only
C. III only
D. I and III only
E. II and III only

Why isn't Option D the correct answer? Can some experts explain?

OA C

We see that -5 ≤ x ≤ 5

Simplifying III, we have:

5 ≥ |x| ≥ -5

Thus, we see that only III is true.

Answer: C

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