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If line segments AB and CD have lengths of
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17 Apr 2022, 23:38
17 Apr 2022, 23:38
Expert Reply
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Question Stats:
50% (00:56) correct
50% (01:33) wrong based on 16 sessions
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If line segments AB and CD have lengths of \(10 + \sqrt{7}\) and \(5 − \sqrt{7}\) respectively, AB is greater than CD by how much?
A. \(5 − 2\sqrt{7}\)
B. \(5 + 2\sqrt{7}\)
C. \(15 + 2\sqrt{7}\)
D. 5
E. 15
A. \(5 − 2\sqrt{7}\)
B. \(5 + 2\sqrt{7}\)
C. \(15 + 2\sqrt{7}\)
D. 5
E. 15
Part of the project: GRE Quantitative Reasoning Daily Challenge - (2022) EDITION
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: If line segments AB and CD have lengths of
[#permalink]
18 Apr 2022, 06:14
18 Apr 2022, 06:14
1
Carcass wrote:
If line segments AB and CD have lengths of \(10 + \sqrt{7}\) and \(5 − \sqrt{7}\) respectively, AB is greater than CD by how much?
A. \(5 − 2\sqrt{7}\)
B. \(5 + 2\sqrt{7}\)
C. \(15 + 2\sqrt{7}\)
D. 5
E. 15
A. \(5 − 2\sqrt{7}\)
B. \(5 + 2\sqrt{7}\)
C. \(15 + 2\sqrt{7}\)
D. 5
E. 15
The question: AB is greater than CD by how much?
In other words: What is the value of \(AB - CD\)?
\(AB - CD = (10 + \sqrt{7}) - (5 − \sqrt{7})\)
\( = 10 + \sqrt{7} - 5 + \sqrt{7}\)
\( = 5 + 2\sqrt{7}\)
Answer: B
Re: If line segments AB and CD have lengths of
[#permalink]
18 Apr 2022, 10:56
18 Apr 2022, 10:56
1
Difference between AB and CD is ---> 10+\sqrt{7} - (5− \sqrt{7}) ----> 10 + \sqrt{7} - 5 + \sqrt{7} ---> 5 + 2 \sqrt{7}
Hence ans is option B
Hence ans is option B
