Halimah_O 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.

OA B

If the average for 3 weeks was 80, we know that the total for the three weeks was 3*80 = 240.

1) This tells us that the total for the first two weeks was 2*60 = 120, but we don't know how that 120 was divided between week 1 and week 2. It could have been 60 in week1 and 60 week 2 or 70 in week 1 and 50 in week 2, etc. Not sufficient.

2) We can think of this as follows. The second week was double the first week and the third week was triple the first week. Designate everything in terms in 'x'

Week 1: x
Week 2: 2x
Week 3: 3x

If the sum was 240, now we can say x + 2x + 3x = 240, 6x = 240; x = 40, so week 2 is 2*40 = 80. Sufficient. The answer is B

DavidG@VeritasPrep wrote:

Halimah_O 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.

OA B

If the average for 3 weeks was 80, we know that the total for the three weeks was 3*80 = 240.

1) This tells us that the total for the first two weeks was 2*60 = 120, but we don't know how that 120 was divided between week 1 and week 2. It could have been 60 in week1 and 60 week 2 or 70 in week 1 and 50 in week 2, etc. Not sufficient.

2) We can think of this as follows. The second week was double the first week and the third week was triple the first week. Designate everything in terms in 'x'

Week 1: x
Week 2: 2x
Week 3: 3x

If the sum was 240, now we can say x + 2x + 3x = 240, 6x = 240; x = 40, so week 2 is 2*40 = 80. Sufficient. The answer is B

Thank you David. Your solution makes it look so easy. I think I am struggling with word problems. I need to work on that.

Thanks!!

Maybe you can see it another way.
Let x,y,z be the amount save the first, second and third (respectively) week.

The question tells you (x+y+z)/3=80
And we're looking for x.

Question 1 :

(x+y)/2=60

That's two equations and 3 unknowns : we can't answer. Unsufficient.

Question 2 :

x = 1/2*y
x = 1/3*y

We get 3 equations, 3 unknowns : sufficient.

Hence B.

Halimah_O 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.

OA B

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