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If Mark saved an average (arithmetic mean) of $80 per week for 3 conse

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If Mark saved an average (arithmetic mean) of $80 per week for 3 conse  [#permalink]

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New post 23 Dec 2014, 07:20
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Tough and Tricky questions: Word Problems.



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.

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Re: If Mark saved an average (arithmetic mean) of $80 per week for 3 conse  [#permalink]

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New post 23 Dec 2014, 07:30
Solution: Say savings of three weeks be a, b & c respectively.
(a+b+c)/3 = 80 --- eq 1

Statement 1: The average amount that Mark saved per week for the first 2 weeks was $60
(a+b)/2 = 60 --- eq 2
Solving Eq 1 & 2, we can determine c but not b -- 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
a:b:c = 1:2:3 -- substituting this ration in eq 1, we can solve for b -- Sufficient

Answer B
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Re: If Mark saved an average (arithmetic mean) of $80 per week for 3 conse  [#permalink]

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New post 23 Dec 2014, 09:03
Bunuel wrote:

Tough and Tricky questions: Word Problems.



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.

Kudos for a correct solution.


Savings on week 1, 2 and 3 are A B C
we need to find B where A+B+C / 3 = 80

stmt1: A+B/2 = 60 from this we can find A+B but not B - Not sufficient
stmt2: A=B/2; A=C/3=> B = 2C/3 or C=3/2B substitute it in first equation => B/2+B+3B/2 / 3 = 80 => 3b = 240 - Sufficient

Ans : B
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Re: If Mark saved an average (arithmetic mean) of $80 per week for 3 conse  [#permalink]

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New post 23 Dec 2014, 09:25
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The question calls for whether the answer is C or B.
Now, there is a one on one relationship between A,B & C. If we know the function of any one of them in terms of the others, the actual quantity of each can be found out.
Hence stat 2 is sufficient. Answer B.
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Re: If Mark saved an average (arithmetic mean) of $80 per week for 3 conse  [#permalink]

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New post 24 Dec 2014, 07:14
1
Bunuel wrote:

Tough and Tricky questions: Word Problems.



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.

Kudos for a correct solution.


St-1: Using the information of average of first two weeks and average of three weeks one can find only third week savings. Not sufficient
St-2: Relation between wk-1 and wk-2,wk-3 are available. So one can find savings of each week. Sufficient.

Ans-B
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Re: If Mark saved an average (arithmetic mean) of $80 per week for 3 conse  [#permalink]

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New post 24 Dec 2014, 13:41
Question Stem
a + b + c = 240
b = ?
You have 1 equation and 3 variables. If you get 2 more distinct, linear equations you can solve this stuff by the Equation Rule of Sufficiency.


Statement 1
a + b = 120
This statement provides you with 1 more equation.
Insufficient

Statement 2
a = (1/2) b
a = (1/3) c
This statement provides you with 2 more equations.
Sufficient

Correct Answer = B
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Re: If Mark saved an average (arithmetic mean) of $80 per week for 3 conse  [#permalink]

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New post 07 Dec 2017, 17:48
1
Bunuel 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.


We are given that Mark saved an average (arithmetic mean) of $80 per week for 3 consecutive weeks. Thus, we can say:

The sum of money saved for 3 weeks = 80 x 3 = 240

We need to determine how much he saved in the second week.

Statement One Alone:

The average amount that Mark saved per week for the first 2 weeks was $60.

Statement one tells us that Mark saved a total of $60 x 2 = $120 in the first two weeks. This means that he saved $120 in the third week. However, we cannot determine the amount of money he saved in the second week. We can eliminate answer choices A and D.

Statement Two Alone:

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.

We can let the amount saved in the 1st week = w. Since this was 1/2 the amount he saved in the 2nd week, the amount he saved in the 2nd week was twice that in the 1st week. Therefore, the amount saved in the 2nd week = 2w. Likewise, since the amount saved in the 1st week is 1/3 the amount he saved in the 3rd week, the amount he saved in the 3rd week was three times that in the 1st week, therefore, the amount saved in the 3rd week = 3w. So we can create the following equation:

w + 2x + 3w = 240

6w = 240

w = 40

Since the amount he saved in the 2nd week is 2w, the amount saved is 2(40) = $80. Statement two alone is sufficient to answer the question.

Answer: B
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Re: If Mark saved an average (arithmetic mean) of $80 per week for 3 conse &nbs [#permalink] 07 Dec 2017, 17:48
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