The youngest of 4 children has siblings who are 3, 5, and 8 years olde

let the youngest be Y
sum of ages of all the children = 4y+16=4*(avg)
4y+16=84
y=17

Hi All,

This question can be solved by TESTing THE ANSWERS.

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.

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:

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

Testing the answer in my opinion takes a long time.

We know that each one is 3,5,8 years OLDER

X + (3+X) + (5+X) + (8+X) = 21*4
4X + 16 = 84
4X = 68
X = 17

Hi douglasvg,

If you're not using Tactics (such as TEST THE ANSWERS) very often, then it might take you a little longer to use that approach right now (since you're not used to thinking in that way). However, in the long run - and on harder questions - those same Tactics can be extremely valuable.

1) How have you been scoring on your practice CATs (including the Quant and Verbal Scaled Scores)?
2) How is your pacing in the Quant section? Do you have to rush just to finish?

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

On GMATPREP software Im scoring between 45-50 in quant
For hard question I indeed use it, then its a fast way to solve it.

Thank you Empower

X + (3+X) + (5+X) + (8+X) = 21*4
4 X + 16 = 84
4 X = 68
X = 17

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

If the average age of the 4 siblings is 21, we can determine the sum of ages by reversing division by 4.

\(\frac{x}{4}= 21\)
\(x = 4*21\)
\(x = 84\)

From there, we can set up an equation to find the age of the youngest child based on their age relative to their siblings.

If the youngest child = x:

\(x + (x+3) + (x+5) + (x+8) = 84\)
\(4x + 16 = 84\)
\(4x = 68\)
\(x = 17\)

Therefore, the youngest child is 17 (option A).

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.