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The number m is the average (arithmetic mean) of the positive numbers
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23 Aug 2015, 12:47
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
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
Re: The number m is the average (arithmetic mean) of the positive numbers
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23 Aug 2015, 12:55
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
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
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23 Aug 2015, 17:31
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
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.
General Discussion
Re: The number m is the average (arithmetic mean) of the positive numbers
[#permalink]
09 Dec 2016, 09:44
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
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
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09 Dec 2016, 11:04
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
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
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21 Dec 2016, 02:45
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.
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]
04 Apr 2018, 17:23
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
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]
08 Dec 2018, 13:29
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
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
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05 May 2020, 02:41
05 May 2020, 02:41
Take a = 4 and then m has to be 7
Eventually b has to be 10 . Now compare
Eventually b has to be 10 . Now compare
Re: The number m is the average (arithmetic mean) of the positive numbers
[#permalink]
21 Mar 2021, 03:07
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:-)
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:-)
Re: The number m is the average (arithmetic mean) of the positive numbers
[#permalink]
02 Apr 2021, 00:52
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)
Posted from my mobile device
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)
Posted from my mobile device
Re: The number m is the average (arithmetic mean) of the positive numbers
[#permalink]
02 Apr 2021, 03:48
02 Apr 2021, 03:48
1
Kudos
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
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
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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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