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Children who ride the roller coaster must be between 24 and 52 inches
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17 Mar 2021, 07:08
17 Mar 2021, 07:08
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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
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Children who ride the roller coaster must be between 24 and 52 inches
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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
