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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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23 Aug 2015, 11:47
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Difficulty:

55% (hard)

Question Stats:

62% (02:22) correct 38% (02:36) wrong based on 399 sessions

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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

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

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23 Aug 2015, 11:55
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1
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.

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

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23 Aug 2015, 16:31
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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

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.

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

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09 Dec 2016, 08:44
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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09 Dec 2016, 10:04
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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21 Dec 2016, 01:45
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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04 Apr 2018, 16:23
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.

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

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08 Dec 2018, 12:29
Bunuel 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.

I'm starting to realize I have a problem picking smart numbers... Can you explain your reasoning for choosing a=4? Is it b/c 75% = 3/4 so you use the number in the denominator?
Re: The number m is the average (arithmetic mean) of the positive numbers   [#permalink] 08 Dec 2018, 12:29
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