DS problem

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btg_13423: Newbie | Next Rank: 10 Posts; Posts: 1; Joined: Sat Oct 05, 2013 7:26 am

by btg_13423 » Tue Nov 26, 2013 5:14 am

If the average age of three people is 21 years, is the youngest older than 13?

(1) The oldest is 25.
(2) One person is 24.

Last edited by btg_13423 on Sun Nov 22, 2015 2:55 pm, edited 1 time in total.

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Source: Beat The GMAT — Data Sufficiency | Tue Nov 26, 2013 5:14 am

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by Brent@GMATPrepNow » Tue Nov 26, 2013 7:36 am

btg_13423 wrote:
If the average age of three people is 21 years, is the youngest older than 13?

(1) The oldest is 25.
(2) One person is 24.

When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

How's this . . .

Target question: Is the youngest older than 13?

Given: The average age of three people is 21 years
If the average (arithmetic mean) the 3 ages is is 21, then the SUM of all 3 ages must = (3)(21) = 63
If we let A, B and C be the ages, in ascending order, then A + B + C = 63

Statement 1: The oldest is 25
So, C = 25
This means that A + B + 25 = 63
In other words, A + B = 38
Let's see what happens if we minimize the value of A.
To MINIMIZE the value of A, we must MAXIMIZE the value of B.
Since 25 is the greatest age, we know that B < 25
So, the MAXIMUM value of B is 24, in which case the MINIMUM value of C is 14 (since A + B = 38).
In other words, C must be greater than or equal to 14
So, the youngest person is definitely older than 13
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: One person is 24
Consider these 2 possible cases:
case a: the ages are 3, 24, 36 in which case the youngest person is NOT older than 13
case b: the ages are 14, 24, 25 in which case the youngest person IS older than 13
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Tue Nov 26, 2013 7:50 am

Brent@GMATPrepNow wrote:
btg_13423 wrote:
If the average age of three people is 21 years, is the youngest older than 13?

(1) The oldest is 25.
(2) One person is 24.
When posting questions, please use the spoiler function to hide the correct answer. This will allow others to attempt the question without seeing the final answer.

How's this . . .

Target question: Is the youngest older than 13?

Given: The average age of three people is 21 years
If the average (arithmetic mean) the 3 ages is is 21, then the SUM of all 3 ages must = (3)(21) = 63
If we let A, B and C be the ages, in ascending order, then A + B + C = 63

Statement 1: The oldest is 25
So, C = 25
This means that A + B + 25 = 63
In other words, A + B = 38
Let's see what happens if we minimize the value of A.
To MINIMIZE the value of A, we must MAXIMIZE the value of B.
Since 25 is the greatest age, we know that B < 25
So, the MAXIMUM value of B is 24, in which case the MINIMUM value of C is 14 (since A + B = 38).
In other words, C must be greater than or equal to 14
So, the youngest person is definitely older than 13
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: One person is 24
Consider these 2 possible cases:
case a: the ages are 3, 24, 36 in which case the youngest person is NOT older than 13
case b: the ages are 14, 24, 25 in which case the youngest person IS older than 13
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer = A

Cheers,
Brent

Brent,
I have doubt with Answer A,
This question is of type Yes/No

Coming to statement 1:
We know that, A+B = 38
We also know that Oldest age is 25.

So, We can split into 13+25 =38
(In Question No-where it is mentioned that all the three people have different ages. Even two could have same age right.)
Now answer is NO. Youngest age is not greater than 13

Or

14+24
Here answer is Yes. Youngest age is greater than 13

Hence Statement 1 is Insufficient na ?

Could you please explain me where I went wrong.

Thanks in advance.
Regards,
Uva.

Known is a drop Unknown is an Ocean

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Mathsbuddy: Master | Next Rank: 500 Posts; Posts: 447; Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member; Thanked: 25 times

by Mathsbuddy » Tue Nov 26, 2013 8:01 am

Combined:
A + B + C = 21 * 3
25 + 24 + C = 63
C = 63 - 49 = 14 (COMBINED ABSOLUTE ANSWER)

D + E + F = 63
I) So if F = 12, (D + E) = 51 = 25 + 26 (26 is too old)
So if F = 13, (D + E) = 50 = 25 + 25 (OK)
So if F = 14, (D + E) = 49 = 25 + 24
Therefore the youngest is 13 or older. (sufficient)

II) D + E = 63 - 21 = 42
If D = 24, E = 18 (SUFFICIENT)

Correct Answer: A

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Tue Nov 26, 2013 8:02 am

Uva@90 wrote: I have doubt with Answer A,
This question is of type Yes/No

Coming to statement 1:
We know that, A+B = 38
We also know that Oldest age is 25.

So, We can split into 13+25 =38
(In Question No-where it is mentioned that all the three people have different ages. Even two could have same age right.)
Now answer is NO. Youngest age is not greater than 13

Or

14+24
Here answer is Yes. Youngest age is greater than 13

Hence Statement 1 is Insufficient na ?

Could you please explain me where I went wrong.

Thanks in advance.
Regards,
Uva.

Hi Uva,

I had my doubts about this question as well.

You're right in that the question doesn't state that the 3 ages are different. However, if we say that the oldest is 25 years old, then the singular word "is" suggests that there is only one oldest person, which means the other 2 people must be younger than 25.

For example, if the ages were 13, 25 and 25, would we say "the oldest IS 25?"

Cheers,
Brent

Brent Hanneson - Creator of GMATPrepNow.com

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Uva@90: Master | Next Rank: 500 Posts; Posts: 490; Joined: Thu Jul 04, 2013 7:30 amFollowed by: 5 members; Location: Chennai, India; Thanked: 83 times

by Uva@90 » Tue Nov 26, 2013 8:13 am

Brent@GMATPrepNow wrote:
Uva@90 wrote: I have doubt with Answer A,
This question is of type Yes/No

Coming to statement 1:
We know that, A+B = 38
We also know that Oldest age is 25.

So, We can split into 13+25 =38
(In Question No-where it is mentioned that all the three people have different ages. Even two could have same age right.)
Now answer is NO. Youngest age is not greater than 13

Or

14+24
Here answer is Yes. Youngest age is greater than 13

Hence Statement 1 is Insufficient na ?

Could you please explain me where I went wrong.

Thanks in advance.
Regards,
Uva.
Hi Uva,

I had my doubts about this question as well.

You're right in that the question doesn't state that the 3 ages are different. However, if we say that the oldest is 25 years old, then the singular word "is" suggests that there is only one oldest person, which means the other 2 people must be younger than 25.

For example, if the ages were 13, 25 and 25, would we say "the oldest IS 25?"

Cheers,
Brent

Hi Brent
Thanks a bundle.
You cleared my doubt.

My bad. Question Maker played with words

Regards,
Uva.

Known is a drop Unknown is an Ocean

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theCodeToGMAT: Legendary Member; Posts: 1556; Joined: Tue Aug 14, 2012 11:18 pmFollowed by: 34 members; Thanked: 448 times; GMAT Score:650

by theCodeToGMAT » Tue Nov 26, 2013 10:28 am

_ + _ + _ = 21*3

To find : Youngest > 13

Statement 1:
Oldest = 25
_ + _ + 25 = 63
_ + _ = 38
Let second largest be 24 == then youngest will be 38 - 24 = 14
SUFFICIENT

Statement 2:
One person is 24
We don't know whether 24 is the oldest or not.
INSUFFICIENT

Answer [spoiler]{A}[/spoiler]

R A H U L

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