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The number m is the average (arithmetic mean) of the positive numbers

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The number m is the average (arithmetic mean) of the positive numbers [#permalink]

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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
[Reveal] Spoiler: OA

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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink]

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New post 23 Aug 2015, 12:55
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shasadou wrote:
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


Say a = 4 (multiple of 4), then m = 4 + 3/4*4 = 7.

m = (a + b)/2;

7 = (4 + b)/2 --> b = 10.

m = 7 is 30% less than b = 10.

Answer: A.
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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink]

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shasadou wrote:
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



Algebraic solution:

Given, m is the average of a and b ---> m = (a+b)/2 ---> a+b=2m

and m = 1.75a ---> a = 4/7m ---> 2m = 4/7m + b ---> m = 0.7b ---> m is 0.3 or 30% less than b.

A is the correct answer.
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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink]

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New post 09 Dec 2016, 09:44
Okay this is a great Question.
Here's my solution=>
2m=a+b
and a(1+75/100)=m
Hence a=(4/7) *m
So b=10m/7
m=(7/10)*m

m=0.7b
Hence 30 percent less than b

Hence A

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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink]

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New post 09 Dec 2016, 11:04
shasadou wrote:
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


Quote:
If m is 75% more than a


Let a = 4 so m = 7

Quote:
The number m is the average (arithmetic mean) of the positive numbers a and b


So, \(\frac{a + b}{2} = m\)

Or, \(\frac{4 + b}{2} = 7\)

Or, \(4 + b = 14\)

Or, \(b = 10\)

Thus, m is 30% less than b, answer will definitely be (A)

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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink]

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New post 21 Dec 2016, 02:45
Given that, m=a+b/2 - (1) Also 'm' is 75% more than 'a', therefore m=1.75a.

Substituting in (1): 1.75a = a+b/2, solving for 'b', b=2.5a. Therefore, (1.75a/2.5a*100) = 0.7, hence (A) is the correct answer.
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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink]

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New post 04 Apr 2018, 17:23
shasadou wrote:
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



We can create the equation:

m = (a + b)/2

and

m = 1.75a

Substituting, we have:

1.75a = (a + b)/2

3.5a = a + b

2.5a = b

Using the percent change formula, we have:

(m - b)/b x 100

(1.75a - 2.5a)/(2.5a) x 100

Multiplying by 100/100, we have:

(175a - 250a)/250a x 100

-75a/250a x 100

-3/10 x 100 = 30% less

Alternate Solution:

We can let a = 100; then m = 175. We can create the equation:

(a + b)/2 = m

(100 + b)/2 = 175

100 + b = 350

b = 250

Using the percent change formula, we have:

(m - b)/b x 100 = (175 - 250)/250 x 100 = -30%, or 30% less.

Answer: A
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Re: The number m is the average (arithmetic mean) of the positive numbers   [#permalink] 04 Apr 2018, 17:23
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