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Mark

by greenwich » Mon Sep 30, 2013 1:25 pm
If Mark saved an average (arithmetic mean) of $80 per week for 3 consecutive weeks, how much did he save the second week?
(1) The average amount that Mark saved per week for the first 2 weeks was $60.
(2) The amount that Mark saved the first week was 1/2 the amount he saved the second week and 1/3 the amount he saved the third week.
Source: — Data Sufficiency |

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by theCodeToGMAT » Mon Sep 30, 2013 7:51 pm
( a + b + c ) = 240
b?

Statement 1:
a + b = 120
INSUFFICIENT

Statement 2:

a = 1/2 * b ==> b = 2a
a = 1/3 * c ==> c = 3a


6a = 240 ==> a = 40 So, b = 80
SUFFICIENT

Answer {B}
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by [email protected] » Mon Sep 30, 2013 11:53 pm
Hi greenwich,

This DS question hides a "system math" shortcut. If you can spot the system "pattern" then you can avoid almost all of the math in this question.

To start, we're told that the average for 3 weeks = $80. This means that the sum for the 3 weeks = $240. If we call the three weeks A, B and C, then we know that A + B + C = 240. We're asked for the second week (so we're asked for the value of B). Notice how we have 1 equation and 3 variables? This will come in handy later.

Fact 1: Average for the first 2 weeks = $60.
This means A + B = 120. There's no way to figure out the value of B...
Fact 1 is INSUFFICIENT

Fact 2: First week = 1/2 of Second Week. First week = 1/3 of Third Week.
This means A = B/2 and A = C/3
Combining this with what we knew at the beginning, we have 3 variables and 3 unique equations. That is a "system" of equations. You COULD solve it, but you don't have to. This is enough information to know that Fact 2 is SUFFICIENT.

Final Answer: B

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by GMATGuruNY » Tue Oct 01, 2013 3:10 am
greenwich wrote:If Mark saved an average (arithmetic mean) of $80 per week for 3 consecutive weeks, how much did he save the second week?
(1) The average amount that Mark saved per week for the first 2 weeks was $60.
(2) The amount that Mark saved the first week was 1/2 the amount he saved the second week and 1/3 the amount he saved the third week.
Sum = (number of weeks)(average per week).

Sum for the entire 3 weeks = 3*80 = 240.

Statement 1: The average amount that Mark saved per week for the first 2 weeks was $60.
Sum for the first 2 weeks = 2*60 = 120.
Thus, the amount saved in the 3rd week = (sum for the entire 3 weeks) - (sum for the first 2 weeks) = 240-120 = 120.
No way to determine the amount saved in the 2nd week.
INSUFFICIENT.

Statement 2: The amount that Mark saved the first week was 1/2 the amount he saved the second week and 1/3 the amount he saved the third week.
Thus, for every $1 saved in the 1st week, $2 is saved in the 2nd week, and $3 is saved in the 3rd week.
In other words:
1st week : 2nd week : 3rd week = 1:2:3.
Since we know the RATIO of the 3 weeks (1:2:3) and the SUM of the 3 weeks (240), we can determine the amount saved in each week.
SUFFICIENT.

The correct answer is B.
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