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Averages and means

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by serendipiteez » Thu May 23, 2013 8:43 am
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

30% less than b
42.85% less than b
50% less than b
66.67% less than b
75% less than b

Answer A

I reach until the point where I get [spoiler]2.5a = b[/spoiler] but I do not know how to proceed from that point to get the answer.
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by srcc25anu » Thu May 23, 2013 9:55 am
Once you have 2.5a = b take easy numbers to see the relation between a, b and m.

lets say a = 4
m = 7a/4 or m = 7
b = 2.5a or b = 10

Now m is 30% less than B.
Hence A
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by Atekihcan » Thu May 23, 2013 10:06 am
If you are picking numbers, pick at the beginning.
Say, a = 100
So, m = 100 + 75% of 100 = 175

Now, (a + b)/2 = m
So, b = (2m - a) = 2*175 - 100 = 350 - 100 = 250

So, required percentage = [(b - m)/b]*100 = (250 - 175)*100/250 = 75*100/250 = 30

Answer : A

Algebraic Approach:
m = (a + b)/2 and m = 1.75a
So, (a + b)/2 = 1.75a
So, (a + b) = 3.5a
So, b = 2.5a = 5a/2
So, a = 2b/5

Now, m = (a + b)/2 = (2b/5 + b)/2 = (7b/5)/2 = 7b/10
Required percentage = [(b - m)/b]*100 = [(b - 7b/10)/b]*100 = [(3b/10)/b]*100 = (3/10)*100 = 30
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by GMATGuruNY » Thu May 23, 2013 11:54 am
serendipiteez 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

30% less than b
42.85% less than b
50% less than b
66.67% less than b
75% less than b

Answer A
Let a=4.
Since m is 75% greater than a, m = 4 + (3/4)4 = 7.
Since m is the AVERAGE of a and b, m is HALFWAY between a and b:
a=4.....m=7.....b=10.

Looking at the answer choices, we can see that A is correct:
m=7 is 30% less than b=10.

The correct answer is A.
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