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

Question

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

Bunuel · Accepted Answer

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.

ENGRTOMBA2018 · Answer

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.

stonecold · Answer

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

Abhishek009 · Answer

Let a = 4 so m = 7

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)

narendran1990 · Answer

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.

ScottTargetTestPrep · Answer

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

Fdambro294 · Answer

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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GMATGuruNY · Answer

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

A

bumpbot · Answer

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

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