GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Children who ride the roller coaster must be between 24 and 52 inches
[#permalink]
17 Mar 2021, 07:08
17 Mar 2021, 07:08
Expert Reply
9
Bookmarks
00:00
Question Stats:
60% (01:45) correct
40% (01:42) wrong based on 40 sessions
Hide Show timer Statistics
Children who ride the roller coaster must be between 24 and 52 inches tall. If x represents the height in inches of a child who may ride the roller coaster, which of the following absolute value inequalities represents all possible values of x?
| x – 24 | < 52
| x – 28 | < 14
| x – 38 | < 14
| x – 14 | < 38
| x – 28 | < 52
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
| x – 24 | < 52
| x – 28 | < 14
| x – 38 | < 14
| x – 14 | < 38
| x – 28 | < 52
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
Moderator
Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1115
Given Kudos: 9
Location: India
Concentration: General Management
Schools: XLRI Jamshedpur, India - Class of 2014
GMAT 1: 700 Q51 V31
GPA: 2.8
WE:Engineering (Computer Software)
Children who ride the roller coaster must be between 24 and 52 inches
[#permalink]
28 Dec 2021, 02:15
28 Dec 2021, 02:15
1
Given that Children who ride the roller coaster must be between 24 and 52 inches tall and x represents the height in inches of a child
=> 24 < x < 52
Now, we need to open the option choices and see which one gives that range.
before we do that let's understand a formula which we can use
|x| < a => -a < x < a (Watch this video to understand the basics of Absolute value)
A. | x – 24 | < 52
=> -52 < x-24 < 52
=> -52 + 24 < x < 52 + 24
=> -28 < x < 76. This is bigger than the range we are looking for. so, NOT POSSIBLE
B. | x – 28 | < 14
=> -14 < x-28 < 14
=> -14 + 28 < x < 14 + 28
=> 14 < x < 42. Not the range we are looking for. So, NOT POSSIBLE
C. | x – 38 | < 14
=> -14 < x-38 < 14
=> -14 + 38 < x < 14 + 38
=> 24 < x < 52. This is the Range we were looking for.
We don't need to solve further but I am solving to complete the solution.
D. | x – 14 | < 38
=> -38 < x-14 < 38
=> -38 + 14 < x < 14 + 38
=> -24 < x < 52. Not the range we are looking for. So, NOT POSSIBLE
E. | x – 28 | < 52
=> -52 < x-28 < 52
=> -52 + 28 < x < 52 + 28
=> -24 < x < 80. Not the range we are looking for. So, NOT POSSIBLE
So, Answer will be C
Hope it helps!
Watch the following video to learn how to Solve Inequality + Absolute value Problems
=> 24 < x < 52
Now, we need to open the option choices and see which one gives that range.
before we do that let's understand a formula which we can use
|x| < a => -a < x < a (Watch this video to understand the basics of Absolute value)
A. | x – 24 | < 52
=> -52 < x-24 < 52
=> -52 + 24 < x < 52 + 24
=> -28 < x < 76. This is bigger than the range we are looking for. so, NOT POSSIBLE
B. | x – 28 | < 14
=> -14 < x-28 < 14
=> -14 + 28 < x < 14 + 28
=> 14 < x < 42. Not the range we are looking for. So, NOT POSSIBLE
C. | x – 38 | < 14
=> -14 < x-38 < 14
=> -14 + 38 < x < 14 + 38
=> 24 < x < 52. This is the Range we were looking for.
We don't need to solve further but I am solving to complete the solution.
D. | x – 14 | < 38
=> -38 < x-14 < 38
=> -38 + 14 < x < 14 + 38
=> -24 < x < 52. Not the range we are looking for. So, NOT POSSIBLE
E. | x – 28 | < 52
=> -52 < x-28 < 52
=> -52 + 28 < x < 52 + 28
=> -24 < x < 80. Not the range we are looking for. So, NOT POSSIBLE
So, Answer will be C
Hope it helps!
Watch the following video to learn how to Solve Inequality + Absolute value Problems
General Discussion
Re: Children who ride the roller coaster must be between 24 and 52 inches
[#permalink]
17 Mar 2021, 07:32
17 Mar 2021, 07:32
1
24 < x < 52
Subtract 38 from each ( This we can determine by looking at answer choices )
24 - 38 < x - 38 < 52 - 38
-14 < x - 38 < 14
|x - 38| < 14
Answer C
Subtract 38 from each ( This we can determine by looking at answer choices )
24 - 38 < x - 38 < 52 - 38
-14 < x - 38 < 14
|x - 38| < 14
Answer C
