The average (arithmetic mean) of 10, 30, and 50 is 5 more than the ave

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and
(A) 15
(B) 25
(C) 35
(D) 45
(E) 55

Average of 10,30,50 = 30
Average of 20,40 & x = 25
so 60 + x = 75----> x = 15
Answer A

Answer is A (15)

Since 10, 30 and 50 are numbers in equally spaced sets, average is 30

Now 30 is 5 greater than 25 ....Thus average of 20, 40 and (x) is 25 ......This implies, sum of 3 numbers should be 75 to make the average = 25

Thus, answer is 15 = 75 - 20 - 40

10+30+50 = 90

90/3=30.

so mean of 20+40+x should be 25...

25*3=75(total),

60+x=75

x=15.

Algebraic Method (Forming single equation for result)

\(\frac{10 + 30 + 50}{3} = \frac{20 + 40 + x}{3} + 5\)

x = 15

Shortcut (By observation) Method

10, 30, 50 are equally spaced; so average = 30

For the other set, required average would be 30 - 5 = 25

It means total = 75

Required number = 75 - (20+40) = 15

Let’s first determine the average of 10, 30, and 50, using the average formula.

average = sum/quantity

average = (10+30+50)/3

average = 90/3

average = 30

We can now rephrase the question to ask: "30 is 5 more than the average of 20, 40, and what value?" Let’s label the missing value as n and create an equation.

30 = (20+40+n)/3 + 5

25 = (20+40+n)/3

75 = 60 + n

15 = n

The answer is A.

[quote="Bunuel"]The Official Guide for GMAT® Review, 13th Edition - Quantitative Questions Project

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

(A) 15
(B) 25
(C) 35
(D) 45
(E) 55
/quote]

avg of (10, 30, 50) = (10+30+50)/ 3 = 30.

Avg of next set = 25.

There are 3 nos. So sum of those 3 nos. = 25 * 3 = 75.
Third number = 75 - 20-40 = 15

(A) is the answer.

Here is my solution to this one =>

Mean(1) = 30 (Notice that it is an AP series so the median will be the mean)

Mean(2)=\(\frac{60+x}{3}\)

As per question
\(30=\frac{60+x}{3} +5\)
Hence x=15
Hence A

\(a1 : \frac{90}{3} = 30\)
a2: \(25 = \frac{60 + x}{3}\)
x = 15
A

(10+30+50)/3 - (20+40+x)/3= 5
30-(60+x)/3=5
x=90-75=15

Let x = the missing (required number)
Average of 10, 30, and 50 = (10 + 30 + 50)/3 = 90/3 = 30
Average of 20, 40, and x = (20 + 40 + x)/3 = (60 + x)/3

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and
So, 30 = (60 + x)/3 + 5
Subtract 5 from both sides to get: 25 = (60 + x)/3
Multiply both sides by 3 to get: 75 = 60 + x
Solve: x = 15

Answer: A

RELATED VIDEO

Hi

Did you notice that there are many incorrect choices that you could have rejected without actually solving the questions

Look at Set 1 : 10, 30, 50

Set 2: 20, 40 , X

Pay close attention to 10, 50 from set 1 and 20 and 40 from Set 2 both are equal to 60. Now if the third number (X) in set 2 would be 30 or more essentially the average would be more than or equal to average of Set 1.
But this isn't the case . So We can reject Choices C, D,E.

Another way of looking at it

Also we are told that averages reduces 5, will that also mean that sum reduces 15. So in set 2 (X) is scored in such a way that sum reduces by 15.
Now (20, 40) in set 2 are equal to (10,50 ) in set 1, But 30 in set 1 implies that X in set 2 must be 15 less than 30, which is 15
So we can reject choices b,c,d,e without solving .

Conceptually you could solve the question ins 15 secs.
How will i remember this in exam. Just practice solving questions conceptually without actually using ur sctach pad.
Not only will u be able to solve questions quickly you will be able to reject answer choices that are incorrect if u had to guess.

10+30+50=90/3=30

20+40+x= 25*3 (Since it is 5 more than the average)

x=15

The average of {10, 30, 50} is 30 and since this value is 5 more than the average of {20, 40, X} we can conclude that {20, 40 , x } has an average of 25.

Learning: Average is a point at which Excess (difference between all High values and average) meets shortfall.(difference between all Low values and average)

Excess: 40 - 25 = 15. Thus the shortfall must also add up to 15
Shortfall: 25 - 20 = 5. We need the shortfall to be 10.

Thus we can say that Average - X = 10.
25 - X = 10 ; X = 15

(A)

Theory

➡ Average = Sum of all the Values / Total Number of Values
➡ Sum of All the values = Average * Total Number of Values

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

Let the unknown number be x

Average of 10, 30, and 50 = \(\frac{Sum}{3}\) = \(\frac{10+30+50}{3}\) = \(\frac{90}{3}\)

Average of 20, 40 and x = \(\frac{Sum}{3}\) = \(\frac{20+40+x}{3}\) = \(\frac{60+x}{3}\)

Average of 20, 60 and 180 = 5 + Average of 10, 30 and x (given)

=> \(\frac{90}{3}\) = 5 + \(\frac{60+x}{3}\)
=> 90 = 5*3 + 60 + x = 15 + 60 + x = 75 + x
=> x = 90 - 75 = 15

So, Answer will be A.
Hope it helps!

Watch the following video to Learn the Basics of Statistics

Theory

➡ Average = Sum of all the Values / Total Number of Values
➡ Sum of All the values = Average * Total Number of Values

The average (arithmetic mean) of 10, 30, and 50 is 5 more than the average of 20, 40, and

Let the unknown number be x

Average of 10, 30, and 50 = \(\frac{Sum}{3}\) = \(\frac{10+30+50}{3}\) = \(\frac{90}{3}\)

Average of 20, 40 and x = \(\frac{Sum}{3}\) = \(\frac{20+40+x}{3}\) = \(\frac{60+x}{3}\)

Average of 20, 60 and 180 = 5 + Average of 10, 30 and x (given)

=> \(\frac{90}{3}\) = 5 + \(\frac{60+x}{3}\)
=> 90 = 5*3 + 60 + x = 15 + 60 + x = 75 + x
=> x = 90 - 75 = 15

So, Answer will be A.
Hope it helps!

Watch the following video to Learn the Basics of Statistics

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.