M40-66

Question

If the ages of three people are all different and their average age is 21 years, is the youngest person older than 13?

(1) The oldest person is 25 years old.
 
(2) One of the three people is 24 years old.

Bunuel · Answer

Official Solution:

If the ages of three people are all different and their average (arithmetic mean) age is 21 years, is the youngest person older than 13? 
 
Note two things: a. since the average of three people is 21, the sum of their ages is 3*21 = 63 and b. the ages of three people are all  different .
 
(1) The oldest person is 25 years old.
 
This implies that the sum of the ages of the two other younger people is 63 - 25 = 38. If the youngest person were 13 or younger, the other one must be 25 or older to reach the sum of 38. However, we are told that the oldest person is 25 years old, so the second oldest cannot be 25 or older. Therefore, the youngest person must be older than 13. Sufficient.
 
(2) One of the three people is 24 years old.
 
This is clearly insufficient. For example, consider the three ages to be (10, 24, 29) for a NO answer, and (14, 24, 25) for a YES answer. Not sufficient.

Answer: A

hc29 · Answer

The first statement mentions that the oldest person is 25 years old.
So the second oldest person can also be 25 years old.
Which would result in the third person being 13 years old.

Now the question asks if one of the persons is  older than 13 years  which should mean the third person should be  at least 14 years old.  So this is not possible to determine from this

Bunuel · Answer

Please read the question carefully:

If  the ages of three people are all different  and their average (arithmetic mean) age is 21 years, is the youngest person older than 13?

Also, note that the ages do not necessarily have to be integers.

Purnank · Answer

Tricky question but easier one.

assuming younger's age is a, middle one is b, and the oldest is c and all are different.
Given a+b+c = 21*3 = 63.

1st - Oldest is that is c = 25. Now a + b = 63-25 = 38. Now question is asking "is the youngest person older than 13?"
yes from this alone we can answer question. what max value that b has to be lesser than 25. so lets take b=24. Put it equation
a+b = 38 we will get a=38-24 = 14 that is greater than 13 Hence Sufficient.

2nd - one of three is 24 year old but doesn't specify who. Hence not sufficient.

Hence A.

honeyaholman · Answer

This is a great question that’s helpful for learning.

honeyaholman · Answer

This is a great question that’s helpful for learning.

bumbleBee3445 · Answer

Consider ages as a,b,c in increasing order.
a+b+c=21*3=63 given.

Q: is a>13?
or rephrase the same as Q: is b+c<50?

1) c=25 is given. Now, b cannot be 25 as they are distinct, and b is smaller. Hence, b+c must be less than 50.  Hence 1) is sufficient.

2) one person is 24 years old. Multiple combinations are possible to get avg as 21.
eg., 18,21,24 or 12,24,27.  we cannot say that the youngest person is > 13. Hence insufficient.

Ans: A

matthewwyatt7 · Answer

I did not quite understand the solution. Why can't there be two 25 year olds? There would still be the oldest person at 25 years old, along with the second oldest at 25 and the youngest at 13?

Bunuel · Answer

Have you checked the highlighted part of the question?

If  the ages of three people are all different  and their average (arithmetic mean) age is 21 years, is the youngest person older than 13?

possimuseius · Answer

I don’t quite agree with the solution. The oldest person being 25 years old does not necessarily mean that the second oldest could not also be 25 years old, since that statement would still hold true, as with two 25 year olds, the oldest person is still 25 years old. If that was the intention of the statement, the statement should've been worded to reflect that.

possimuseius · Answer

yeah i lied i didnt see the distinct age bit my bad fair enough!

bb · Answer

Funny how a one line question can pack so much information.

3D · Answer

This is a great question that’s helpful for learning and I like the solution - it’s helpful.

Kashu18 · Answer

I like the solution - it’s helpful.

liberoexplicabo · Answer

I like the solution - it’s helpful.

vrinda6 · Answer

I did not quite understand the solution. So the way that I solved this was:

Total sum of ages= 21*3= 63

Taking statememt 1:
I get that one of the persons age is 25 years, that gives me 38. Now I can divide the ages of the remaining two individuals in whichever proportion I want to answer the original question.

Taking only statement 2:
One of the persons age is 24, similarly I get 39 which I can use to get the ages of the remaining individuals and get them to answer the original question.

And thats why I answered with Each statement alone is sufficient to answer.

Why is that wrong?

Bunuel · Answer

Your mistake is that in statement 1 you cannot split the remaining 38 any way you want, because  25 is specifically the oldest age , so the other two must both be less than 25 and all three ages must be different, that restriction forces the youngest to be older than 13, since if the youngest were 13 or less, the third person would have to be 25 or more, which is impossible.

In statement 2, 24 is just one person’s age, not necessarily the oldest, so the other two ages can still be arranged to give either a YES or a NO.

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