What was Johns age on 1st January, 1992? (1) The average age of John

Question

What was John’s age on 1st January, 1992?

(1) The average age of John and the five members of his family on 1st January, 1982, was equal to the average age of the five members of John’s family and a child on 1st January, 1992.

(2) The child was born on 1st January, 1992.

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prantorboni · Answer

What was John’s age on 1st January, 1992?

(1) The average age of John and the five members of his family on 1st January, 1982, was equal to the average age of the five members of John’s family and a child on 1st January, 1992. 
 Based on this information, we are unable to conclude the age of John. Insufficient.

(2) The child was born on 1st January, 1992. 
 Based on this information, we are unable to conclude the age of John. Insufficient.

Now, assume, The average age of John and the five members of his family on 1st January, 1982, was 100 and the average age of the five members of John’s family and a child on 1st January, 1992 was 100. Since, the child was born on 1st January, 1992 means 0, we can say the average age of the five members of John’s family was 100. So, to keep the average same, we have not considerd the age of John while calculation the average age of the five members of John’s family. But, from 1st January, 1982, to 1st January, 1992 every family members including John has gained a total 10+10+10+10+10+10=60 years of age. Clearly, John's age on 1st January, 1982 was 50 and on 1st January, 1992 was 60. Sufficient.

Answer: C.

Githinji · Answer

i find this question hard to understand. How is it possible that average of age of a group of people at one time can be equal to avaerage of age of the same group at a later date. 
Regards.

Bunuel · Answer

John’s aga in 1982 = x
 The combined age of  the five members of his family in 1982 = y

The combined age of the five members of his family and a child in 1992 = y + 50 + 0

We are told that (x + y)/6 = (y + 50 + 0)/6, which gives x = 50.

Hope it helps.

Ertucinar · Answer

From statement (1), we have the equation:

\frac{J (1982) + F}{6} = \frac{F + C + 5 	imes 10}{6}

Where:
 J(1982) = John's age on 1st January, 1982
 J = John's age on 1st January, 1992
 F = The sum of the ages of the five members of John's family 1982
 C = The age of the child on 1st January, 1992

Simplifying the equation:
 J (1982) + F = F + C + 50 
 J (1982) = C + 50 
Not Sufficent

From statement (2), we know:
 C = 0 
Not Sufficent

From statement (1+2):
 J (1982) = 0 + 50 = 50 
 J = 60 
Option C - Together Sufficent

What was Johns age on 1st January, 1992? (1) The average age of John

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GMAT Data Sufficiency (DS) Questions

What was Johns age on 1st January, 1992? (1) The average age of John

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards