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The table shows the differences between the test results and the average by subject. The

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The table shows the differences between the test results and the average by subject. The

by Max@Math Revolution » Tue Jun 02, 2020 1:21 am

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[GMAT math practice question] 6.2

The table shows the differences between the test results and the average by subject. The average is 6, and the variance is 8.8. If a is the test result of Physics and b is that of Chemistry, what is the value of ab?
6.2ps.png

A. 2
B. 5
C. 7
D. 9
E. 11
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Re: The table shows the differences between the test results and the average by subject. The

by Max@Math Revolution » Thu Jun 04, 2020 7:31 pm
=>

Since the sum of all differences is 0, we have 3 – 1 + x + y = 0 or x + y = -2.
Since the variance is 8.8, we have [3^2 + (-1)^2 + x^2 + 0^2 + y^2] / 5 = 8.8, 9 + 1 + x^2 + y^2 = 44, or x^2 + y^2 = 44 - 10 = 34.
Since we have x + y = -2 or y = -x - 2, we have x2 + y^2 = x^2 + (-x - 2)^2 = 2x^2 + 4x + 4 = 34 or 2x2 + 4x – 30 = 0.
Dividing by 2, we have x^2 + 2x - 15 = 0 or (x + 5)(x - 3) = 0.
Then we have x = -5, y = 3 or x = 3, y = -5.
Since the average is 6, we have a = 6 – 5 = 1, b = 6 + 3 = 9 or a = 6 + 3 = 9, b = 6 - 5 = 1.
Thus, we have ab = 9.

Therefore, the answer is D.
Answer: D
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