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31 Dec 2024, 10:11
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
80% (03:11) correct
20% (01:58) wrong based on 5 sessions
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If \(x + 2y = a \) and \( x – 2y = b\), which of the following expressions is equal to \(xy\)?
A. \(ab\)
B. \(\frac{a+b}{2}\)
C. \(\frac{a-b}{2}\)
D. \(\frac{a^2-b^2}{4}\)
E. \(\frac{a^2-b^2}{8}\)
A. \(ab\)
B. \(\frac{a+b}{2}\)
C. \(\frac{a-b}{2}\)
D. \(\frac{a^2-b^2}{4}\)
E. \(\frac{a^2-b^2}{8}\)
01 Jan 2025, 10:32
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OE
The easiest way to solve this is to plug in numbers. Let x = 2 and y = 1. Then xy = 2, a = 4, and b = 0. Now, plug in 4 for a and 0 for b and see which of the five choices is equal to 2. Only Choices C and E work:
C. \(\frac{a-b}{2} = \frac{4-0}{2} = 2\)
D. \(\frac{a^2-b^2}{8} = \frac{4^2-0^2}{8} = \frac{16}{8} = 2\)
To determine whether Choice C or E is the correct answer, plug in different numbers. If x = 3 and y = 1, then xy = 3, a = 5, and b = 1.
Now Choice C doesn’t work:
\(\frac{a-b}{2} = \frac{5-1}{2} = \frac{4}{2} = 2\) not equal to 3
Choice E does work: \(\frac{a^2-b^2}{8} = \frac{25-1}{8} = \frac{24}{8} = 3.\)
Answer: E
The easiest way to solve this is to plug in numbers. Let x = 2 and y = 1. Then xy = 2, a = 4, and b = 0. Now, plug in 4 for a and 0 for b and see which of the five choices is equal to 2. Only Choices C and E work:
C. \(\frac{a-b}{2} = \frac{4-0}{2} = 2\)
D. \(\frac{a^2-b^2}{8} = \frac{4^2-0^2}{8} = \frac{16}{8} = 2\)
To determine whether Choice C or E is the correct answer, plug in different numbers. If x = 3 and y = 1, then xy = 3, a = 5, and b = 1.
Now Choice C doesn’t work:
\(\frac{a-b}{2} = \frac{5-1}{2} = \frac{4}{2} = 2\) not equal to 3
Choice E does work: \(\frac{a^2-b^2}{8} = \frac{25-1}{8} = \frac{24}{8} = 3.\)
Answer: E
