Problem Solving

BTGmoderatorDC wrote:The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?

A. 17
B. 18
C. 19
D. 21
E. 22

Say the age of the youngest of 4 children is x, thus, the ages of the other three children are (x+3), (x+5) and (x+8), respectively.

The sum of ages of the four children = x + (x+3) + (x+5) + (x+8) = 4x + 16

Average = (4x + 16)/4 = 21

=> x + 4 = 21 => x = 17

The correct answer: A

Hope this helps!

-Jay
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Hi All,

We're told that the YOUNGEST of 4 children has siblings who are 3, 5, and 8 years OLDER than she is and that the average age of the 4 siblings is 21. We're asked for the age of the youngest sibling. This question can be solved by TESTing THE ANSWERS.

Since the average age is 21 and we're trying to figure out the age of the YOUNGEST sibling, we should look for an answer that is several years LESS than 21...

Let's TEST Answer B: 18 years

IF...
Youngest = 18
Siblings = 21, 23 and 26
Sum = 88
Average = 88/4 = 22
This is TOO HIGH (the average is supposed to be 21). Since the average is too high, all 4 of the children are TOO OLD. There's only one answer left that would lower the average...

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

BTGmoderatorDC wrote:The youngest of 4 children has siblings who are 3, 5, and 8 years older than she is. If the average (arithmetic mean) age of the 4 siblings is 21, what is the age of the youngest sibling?

A. 17
B. 18
C. 19
D. 21
E. 22

We can let x = the age of the youngest child; thus, the ages of the three older children are x + 3, x + 5 and x + 8, respectively. We can create the equation:

(x + x + 3 + x + 5 + x + 8)/4 = 21

4x + 16 = 84

4x = 68

x = 17

Answer: A