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(s + t)2 vs s2 + t2
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15 Apr 2018, 04:42
15 Apr 2018, 04:42
Expert Reply
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Question Stats:
93% (00:20) correct
6% (00:46) wrong based on 30 sessions
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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
Question: 9
Page: 507
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
(s + t)2 vs s2 + t2
[#permalink]
29 Apr 2019, 11:16
29 Apr 2019, 11:16
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.
Answer: D
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Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
(s + t)2 vs s2 + t2
[#permalink]
29 Apr 2019, 11:19
29 Apr 2019, 11:19
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
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
Answer: D
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