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10 Feb 2022, 07:00
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
(low)
Question Stats:
81% (01:22) correct
19%
(00:54)
wrong
based on 75
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The average (arithmetic mean) of four numbers is 4a + 16. When a fifth number is added, the average becomes 5a + 20. The fifth number is
A. a - 4
B. a + 4
C. 4a + 4
D. 4a + 16
E. 9a + 36
A. a - 4
B. a + 4
C. 4a + 4
D. 4a + 16
E. 9a + 36
10 Feb 2022, 07:05
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16a+64+x = 25a + 100
x = 9a + 36
x = 9a + 36
10 Feb 2022, 07:22
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Bunuel
The average (arithmetic mean) of four numbers is 4a + 16. When a fifth number is added, the average becomes 5a + 20. The fifth number is
A. a - 4
B. a + 4
C. 4a + 4
D. 4a + 16
E. 9a + 36
A. a - 4
B. a + 4
C. 4a + 4
D. 4a + 16
E. 9a + 36
The average (arithmetic mean) of the original four numbers is 4a + 16.
This tells us that: (the sum of the original four numbers)/4 = 4a + 16
Multiply both sides of the equation by 4 to get: sum of the original four numbers = 16a + 64
When a fifth number is added, the average becomes 5a + 20.
So we can write: (sum of all five numbers)/5 = 5a + 20
Multiply both sides of the equation by 5 to get: sum of all five numbers = 25a + 100
Let k = the fifth number.
Notice that: sum of all five numbers = sum of the original four numbers + k
Substitute to get: 25a + 100 = 16a + 64 + k
Subtract 64 from both sides of the equation: 25a + 36 = 16a + k
Subtract 16a from both sides of the equation: 9a + 36 = k
Answer: E
