Number Properties, Percents and Interest Problems

[swerve]

The number \(m\) is the average (arithmetic mean) of the positive numbers \(a\) and \(b\). If \(m\) is \(75\%\) more than a, then m must be

A. \(30\%\) less than \(b\)

B. \( 42\frac{6}{7}\%\) less than \(b\)

C. \(50\%\) less than \(b\)

D. \(66\frac{2}{3}\%\) less than \(b\)

E. \(75\%\) less than \(b\)

The OA is A

Source: Manhattan Prep

[Scott@TargetTestPrep]

The number \(m\) is the average (arithmetic mean) of the positive numbers \(a\) and \(b\). If \(m\) is \(75\%\) more than a, then m must be

A. \(30\%\) less than \(b\)

B. \( 42\frac{6}{7}\%\) less than \(b\)

C. \(50\%\) less than \(b\)

D. \(66\frac{2}{3}\%\) less than \(b\)

E. \(75\%\) less than \(b\)

The OA is A

Source: Manhattan Prep

We can create the equation:

m = (a + b)/2

and

m = 1.75a

Equating the two equations above, we have:

1.75a = (a + b)/2

3.5a = a + b

2.5a = b

Since m = 1.75a = 7a/4, then a = 4m/7. Therefore, we have:

2.5(4m/7) = b

10m/7 = b

m = 7b/10 = 0.7b

In other words, m is 70% of b, and therefore, m is 30% less than b.

Answer: A