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A survey wants to collect data specifically from students earn a score
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25 Feb 2022, 08:00
25 Feb 2022, 08:00
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A survey wants to collect data specifically from students earn a score of T, which is between 145 and 165 in the quantitative section of the GRE. Which of the following inequalities can be used to express these search parameters?
(A) |T - 145| < 10
(B) |T + 155| < 10
(C) |T - 165| < 10
(D) |T + 155| > 10
(E) |T - 155| < 10
(A) |T - 145| < 10
(B) |T + 155| < 10
(C) |T - 165| < 10
(D) |T + 155| > 10
(E) |T - 155| < 10
Re: A survey wants to collect data specifically from students earn a score
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25 Feb 2022, 20:14
25 Feb 2022, 20:14
1
T is between 145 and 165 in the quantitative section of the GRE.
\(145 < T < 165\)
Subtract 155 from the inequality
\(145 - 155 < T - 155 < 165 - 155\)
\(-10 < T - 155 < 10\)
\(|T - 155| < 10\)
Answer \(E\)
\(145 < T < 165\)
Subtract 155 from the inequality
\(145 - 155 < T - 155 < 165 - 155\)
\(-10 < T - 155 < 10\)
\(|T - 155| < 10\)
Answer \(E\)
General Discussion
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Joined: 02 Jan 2020
Status:GRE Quant Tutor
Posts: 1131
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)
Re: A survey wants to collect data specifically from students earn a score
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09 Dec 2023, 02:19
09 Dec 2023, 02:19
1
Score has to be between 145 and 165
Let's take each answer choice and check which one satisfies this equation
Theory:
|X| < A
=> -A < X < A
|X| > A
=> X < -A and X > A
(A) |T - 145| < 10
=> -10 < T - 145 < 10
=> -10 + 145 < T < 10 + 145
=> 135 < T < 155 => FALSE
(B) |T + 155| < 10
=> -10 < T + 155 < 10
=> -10 -155 < T < -155 + 10
=> -165 < T < -145 => FALSE
(C) |T - 165| < 10
=> -10 < T - 165 < 10
=> -10 + 165 < T < 165 + 10
=> 155 < T < 175 => FALSE
(D) |T + 155| > 10
We do not need to check this as this is > Inequality and will have a very broad range going towards negative and positive side
T + 155 < -10 and T + 155 > 10
=> T < -165 and T > -145 => FALSE
(E) |T - 155| < 10
=> -10 < T - 155 < 10
=> -10 + 155 < T < 155 + 10
=> 145 < T < 165 => TRUE
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
Let's take each answer choice and check which one satisfies this equation
Theory:
|X| < A
=> -A < X < A
|X| > A
=> X < -A and X > A
(A) |T - 145| < 10
=> -10 < T - 145 < 10
=> -10 + 145 < T < 10 + 145
=> 135 < T < 155 => FALSE
(B) |T + 155| < 10
=> -10 < T + 155 < 10
=> -10 -155 < T < -155 + 10
=> -165 < T < -145 => FALSE
(C) |T - 165| < 10
=> -10 < T - 165 < 10
=> -10 + 165 < T < 165 + 10
=> 155 < T < 175 => FALSE
(D) |T + 155| > 10
We do not need to check this as this is > Inequality and will have a very broad range going towards negative and positive side
T + 155 < -10 and T + 155 > 10
=> T < -165 and T > -145 => FALSE
(E) |T - 155| < 10
=> -10 < T - 155 < 10
=> -10 + 155 < T < 155 + 10
=> 145 < T < 165 => TRUE
So, Answer will be E
Hope it helps!
Watch the following video to learn the Basics of Absolute Values
