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

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shasadou
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The number m is the average (arithmetic mean) of the positive numbers [#permalink] New post   23 Aug 2015, 12:47
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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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A
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Bunuel
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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink] 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] New post   23 Aug 2015, 17:31
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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] 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] 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] 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] New post   04 Apr 2018, 17:23
Expert Reply
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] New post   08 Dec 2018, 13:29
Bunuel wrote:
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.



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?
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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink] New post   05 May 2020, 02:41
Take a = 4 and then m has to be 7

Eventually b has to be 10 . Now compare
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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink] New post   21 Mar 2021, 03:07
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ScottTargetTestPrep

Hi, how can I decide that here is:

"Using the percent change formula, we have:"
"(m - b)/b x 100 = (175 - 250)/250 x 100 = -30%, or 30% less."

and not
(b - m)/m x 100 = (250 - 175)/175 x 100

thank you:-)
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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink] New post   02 Apr 2021, 00:52
M = (a + b) / 2


3/4 more ———> 7/4 of


M = (7/4)a


Setting equations equal for M:

(7/4)a = (a + b) / 2

7a / 2 = a + b

7a = 2a + 2b

5a = 2b

a = (2/5)b

Substituting into the original mean equation of M = (a + b) / 2

You end up with:

M = (7/10)b

Which means she Mean is 30% less than b

(A)

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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink] New post   02 Apr 2021, 03:48
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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



Since \(m\) is 3/4 greater than \(a\) -- in other words, since \(m\) is equal to 7/4 of \(a\) -- let \(a=4\), with the result that \(m = \frac{7}{4} * 4 = 7\)

average means HALFWAY.
Since m=7 must be halfway between \(a=4\) and \(b\), the following number line is implied:
\(a=4\).....\(m=7\).....\(b=10\)

Of the five answer choices, only A is viable:
\(m=7\) is 30% less than \(b=10\)

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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink] New post   29 Mar 2024, 05:16
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Re: The number m is the average (arithmetic mean) of the positive numbers [#permalink]
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