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The average (arithmetic mean) of 3a + 4 and another number is 2a.

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by BTGModeratorVI » Sat Jun 13, 2020 5:42 am

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The average (arithmetic mean) of 3a + 4 and another number is 2a. What is the average of the other number and a ?

A. 2a
B. a - 4
C. a - 2
D. a + 2
E. a + 4

Answer: C
Source: Kaplan
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Re: The average (arithmetic mean) of 3a + 4 and another number is 2a.

by Brent@GMATPrepNow » Sat Jun 13, 2020 10:44 am
BTGModeratorVI wrote: ↑
Sat Jun 13, 2020 5:42 am
 The average (arithmetic mean) of 3a + 4 and another number is 2a. What is the average of the other number and a ?

A. 2a
B. a - 4
C. a - 2
D. a + 2
E. a + 4

Answer: C
Source: Kaplan
Let x = the other number

The average (arithmetic mean) of 3a + 4 and another number is 2a.

We can write: [m][fraction](3a + 4) + x/2[/fraction] = 2a[/m]

Multiply both sides of the equation by [m]2[/m] to get : [m]3a + 4 + x = 4a[/m]

Subtract [m]3a[/m] from both sides to get : [m]4 + x = a[/m]

Subtract [m]4[/m] from both sides to get : [m]x = a-4[/m]


What is the average of the other number (x) and [m]a[/m] ?
The average [m]= [fraction]x + a/2[/fraction][/m]

Substitute [m]x[/m] with [m]a-4[/m] to get: average [m]= [fraction](a-4) + a/2[/fraction][/m]

Simplify to get: average [m]= [fraction]2a-4/2[/fraction][/m]

Rewrite this follows: average [m]= [fraction]2(a-2)/2[/fraction][/m]

Simplify to get: average [m]= a-2[/m]

Answer: C
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