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# (s + t)2 vs s2 + t2

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GRE Prep Club Legend
Joined: 07 Jun 2014
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GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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(s + t)2 vs s2 + t2 [#permalink]  15 Apr 2018, 04:42
Expert's post
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Question Stats:

94% (00:15) correct 5% (01:06) wrong based on 17 sessions
 Quantity A Quantity B $$(s + t)^2$$ $$s^2 + t^2$$

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 9
Page: 507
[Reveal] Spoiler: OA

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Sandy
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Joined: 10 Apr 2015
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Kudos [?]: 2200 [0], given: 27

Re: (s + t)2 vs s2 + t2 [#permalink]  29 Apr 2019, 11:16
Expert's post
sandy wrote:
 Quantity A Quantity B $$(s + t)^2$$ $$s^2 + t^2$$

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

APPROACH #1: Matching operations
Given:
QUANTITY A: (s + t)²
QUANTITY B: s² + t²

Expand and simplify Quantity A:
QUANTITY A: s² + 2st + t²
QUANTITY B: s² + t²

Subtract s² and t² from both quantities:
QUANTITY A: 2st
QUANTITY B: 0

Since we know nothing about s and t, we can't determine which quantity is greater.

RELATED VIDEO FROM MY COURSE

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Brent Hanneson – Creator of greenlighttestprep.com

GRE Instructor
Joined: 10 Apr 2015
Posts: 2311
Followers: 72

Kudos [?]: 2200 [0], given: 27

Re: (s + t)2 vs s2 + t2 [#permalink]  29 Apr 2019, 11:19
Expert's post
sandy wrote:
 Quantity A Quantity B $$(s + t)^2$$ $$s^2 + t^2$$

A. Quantity A is greater.
B. Quantity B is greater.
C. The two quantities are equal.
D. The relationship cannot be determined from the information given.

Drill 1
Question: 9
Page: 507

APPROACH #2: Testing values

Case i: s = 0 and t = 0. We get:
QUANTITY A: (s + t)² = (0 + 0)² = 0² = 0
QUANTITY B: s² + t² = 0² + 0² = 0 + 0 = 0
In this case, the two quantities are equal

Case ii: s = 1 and t = 2. We get:
QUANTITY A: (s + t)² = (1 + 2)² = 3² = 9
QUANTITY B: s² + t² = 1² + 2² = 1 + 4 = 5
In this case, the Quantity A is greater

RELATED VIDEO FROM MY COURSE

_________________

Brent Hanneson – Creator of greenlighttestprep.com

Re: (s + t)2 vs s2 + t2   [#permalink] 29 Apr 2019, 11:19
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