GRE Cumulative addition problem.

Question

The following problem is quoted from Manhattan 5lb Book of GRE Practice Problems, 2016ed.

Question: Molly worked at an amusement park over the summer. Every two weeks she was paid according to the following schedule: at the end of 1st $2$ weeks, she received \$$160$. At the end of each subsequent 2-week period, she received \$$1$, plus an additional amount equal to the sum of all payments she had received in the previous weeks. How much money was Molly paid during the full $10$ weeks of summer?

Solution: \$$2575$

I am not sure why Molly received \$ $2575$ at the end of 10 week. To my understanding, she should receive \$ $1288$.

My understanding is the following

Weeks        Paid
  2          160
  4          1+160 = 161
  6          1+161+160 = 322
  8          1+322+161+160 = 644
  10         1+644+322+161+160 = 1288

Why was additional \$$1287$ paid?

Can anyone explain?

Also, the question "How much money was Molly paid during the full 10 weeks of summer?" is different from "How much money was Molly paid in week 10?" — Matti P., May 08 '18 at 08:05
The third term in the last row should read 322, not 422. — CiaPan, May 08 '18 at 08:27

score 1 · Answer 1 · answered May 08 '18 at 08:31

1

The question is how much did Molly earn in total, not in the last two-week period. The mysterious 'additional $\$1287$' is simply the sum of all earlier earnings: $$1287 = 160+161+322+644$$ hence her total earning is $$160+161+322+644 + 1288 = 2575$$

answered May 08 '18 at 08:31

CiaPan

13,049

@yahoo.com Probably that was paid, because the agreement between Molly and the amusement park stated so. She worked for them, they paid her for the work. – CiaPan May 08 '18 at 09:17

score 0 · Answer 2 · answered May 08 '18 at 08:10

0

Weeks Paid

2 160

4 1+160 = 161

6 1+161+160 = 322

8 1+322+161+160 = 644

10 1+644+322+161+160 = 1288

Now 160 + 161 + 322 + 644 + 1288 = ...

answered May 08 '18 at 08:10

why was additional 1287 paid? – user366312 May 08 '18 at 08:12
1

She earned 1288 in week 10 only, in order to get the total salaries you need to sum up the weekly ones. – May 08 '18 at 08:21
I still don't understand. – user366312 May 08 '18 at 08:24
2

Imagine you work one week and you earn 1 a day. Although you get 1 on sunday you get 7 in total. – May 08 '18 at 08:30

score 0 · Answer 3 · answered May 30 '18 at 23:20

I will give a brief explanation

In $2$ weeks she earned $=160$

In the next two weeks she earned $=1+160=161$

In the next two weeks she earned $=1+161+160=322$

In the next two weeks she earned $=1+161+160+322=644$

In the final two weeks she earned $=1+322+161+160+644=1288=>$ Note that $1288$ is the amount she earned in last $2$ weeks

Now we need to add the total amount $=160+161+322++644+1288=2575$

GRE Cumulative addition problem.

3 Answers3