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The average (arithmetic mean) of four numbers is 4a + 16. When a fifth
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29 Apr 2022, 02:00
29 Apr 2022, 02:00
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Question Stats:
92% (01:12) correct
7% (02:03) wrong based on 28 sessions
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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
Part of the project: GRE Quantitative Reasoning Daily Challenge - (2022) EDITION
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GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials for a TOP Quant Score - Q170!!! (2021)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: The average (arithmetic mean) of four numbers is 4a + 16. When a fifth
[#permalink]
29 Apr 2022, 06:40
29 Apr 2022, 06:40
1
Carcass wrote:
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
Re: The average (arithmetic mean) of four numbers is 4a + 16. When a fifth
[#permalink]
30 Apr 2022, 11:40
30 Apr 2022, 11:40
1
4*(4a+16) + y = 5*(5a+20) ----> solving for y we get 9a+36.
Hence correct ans is option E
Hence correct ans is option E
