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Retired Moderator P
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8 people in a room: A, B, C, D, E, F, G, H, have an average age of 36  [#permalink]

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Difficulty:   85% (hard)

Question Stats: 38% (01:54) correct 62% (01:40) wrong based on 77 sessions

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8 people in a room: A, B, C, D, E, F, G, H, have an average age of 36 years. G leaves the room, and immediately another one J comes from outside. What is the average age of these 8 people now?

(1) Difference between ages of G and J is 9 years.

(2) If G does not leave and still J joins, then the average age of these 9 people will be 37 years.
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Re: 8 people in a room: A, B, C, D, E, F, G, H, have an average age of 36  [#permalink]

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amanvermagmat wrote:
8 people in a room: A, B, C, D, E, F, G, H, have an average age of 36 years. G leaves the room, and immediately another one J comes from outside. What is the average age of these 8 people now?

(1) Difference between ages of G and J is 9 years.

(2) If G does not leave and still J joins, then the average age of these 9 people will be 37 years.

Since we know the number of people, to calculate the average we need to know the sum of their ages.
We'll look for statements that give us this information, a Logical approach

(1) Knowing that the difference in ages is 9 years does not tell us if G is older or J is older.
So we can't know if the sum of the ages increased or decreased by 9 years and cannot calculate the average.
Insufficient!

(2) This lets us calculate the age of J (as we can subtract A+B+...+G+H = 36*8 from A+B+...+H+j=37*9).
But, without knowing the age of G we cannot calculate the sum of ages in the group.
Insufficient!

Combined: We still cannot calculate the age of G because we don't know if it is 9 more or 9 less than J.
Insufficient!

(E) is our answer.
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Re: 8 people in a room: A, B, C, D, E, F, G, H, have an average age of 36  [#permalink]

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amanvermagmat wrote:
8 people in a room: A, B, C, D, E, F, G, H, have an average age of 36 years. G leaves the room, and immediately another one J comes from outside. What is the average age of these 8 people now?

(1) Difference between ages of G and J is 9 years.

(2) If G does not leave and still J joins, then the average age of these 9 people will be 37 years.

Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 9 variables and 1 equation, E is most likely to be the answer. So, we should consider conditions 1) & 2) together first. After comparing the number of variables and the number of equations, we can save time by considering conditions 1) & 2) together first.

The equation from the original condition is ( A + B + C + D + E + F + G + H ) / 8 = 36 or A + B + C + D + E + F + G + H = 288.
The question asks for the value of ( A + B + C + D + E + F + H + J ) / 8 or ( 288 - G + J ) / 8.

Conditions 1) & 2):
G - J = 9 or J - G = 9 from the condition 1)

We have ( A + B + C + D + E + F + G + H + J ) / 9 = 37 or 288 + J = 333 from the condition 2).
Thus J = 45.

Then G = 36 or G = 54.
Since we don't obtain a unique solution, both conditions together are not sufficient.

Therefore, E is the answer.

In cases where 3 or more additional equations are required, such as for original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, conditions 1) and 2) usually supply only one additional equation. Therefore, there is an 80% chance that E is the answer, a 15% chance that C is the answer, and a 5% chance that the answer is A, B or D. Since E (i.e. conditions 1) & 2) are NOT sufficient, when taken together) is most likely to be the answer, it is generally most efficient to begin by checking the sufficiency of conditions 1) and 2), when taken together. Obviously, there may be occasions on which the answer is A, B, C or D.
_________________ Re: 8 people in a room: A, B, C, D, E, F, G, H, have an average age of 36   [#permalink] 03 Mar 2018, 13:24
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