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
If 5 ≥ |x| ≥ 0, which of the following must be true?
This topic has expert replies
-
- Moderator
- Posts: 7187
- Joined: Thu Sep 07, 2017 4:43 pm
- Followed by:23 members
- prabsahi
- Senior | Next Rank: 100 Posts
- Posts: 53
- Joined: Wed Jun 04, 2014 10:50 am
- Thanked: 6 times
- Followed by:2 members
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.
If you want to fly,you have to give up the things that weighs you down!
PS
PS
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
GMAT assassins aren't born, they're made,
Rich
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
GMAT assassins aren't born, they're made,
Rich
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7222
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
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
Scott Woodbury-Stewart
Founder and CEO
[email protected]
See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews