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Molly worked at an amusement park over the summer.Every two weeks she

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Math Expert
Joined: 02 Sep 2009
Posts: 65765
Molly worked at an amusement park over the summer.Every two weeks she  [#permalink]

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07 Apr 2020, 06:25
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Difficulty:

55% (hard)

Question Stats:

53% (02:16) correct 47% (02:50) wrong based on 32 sessions

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

A. 644
B. 1288
C. 1770
D. 2575
E. 3229

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Re: Molly worked at an amusement park over the summer.Every two weeks she  [#permalink]

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15 Apr 2020, 08:29
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Bunuel wrote:
Molly worked at an amusement park over the summer.Every two weeks she was paid according to the following schedule:at the end of the first two weeks she received $160.At the end of each subsequent two week period she received$1, plus an additional amount equal to the sum of all the payments she had received in the previous weeks.How much money was Molly paid during full 10 weeks of summer?

A. 644
B. 1288
C. 1770
D. 2575
E. 3229

After weeks 1 and 2, she earned 160 dollars.

After weeks 3 and 4, she earned 1 + 160 = 161 dollars.

After weeks 5 and 6, she earned 1 + 160 + 161 = 322 dollars.

After weeks 7 and 8, she earned 1 + 160 + 161 + 322 = 644 dollars.

After weeks 9 and 10, she earned 1 + 160 + 161 + 322 + 644 = 1288 dollars.

Thus, the total she earned in 10 weeks is 160 + 161 + 322 + 644 + 1288 = 2575 dollars.

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Re: Molly worked at an amusement park over the summer.Every two weeks she  [#permalink]

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07 Apr 2020, 07:24
Bunuel wrote:
Molly worked at an amusement park over the summer.Every two weeks she was paid according to the following schedule:at the end of the first two weeks she received $160.At the end of each subsequent two week period she received$1, plus an additional amount equal to the sum of all the payments she had received in the previous weeks.How much money was Molly paid during full 10 weeks of summer?

A. 644
B. 1288
C. 1770
D. 2575
E. 3229

after 2 weeks : 160$after 4 weeks :1+160$=161$after 6weeks : 1+161+160$=322$after 8 weeks :1+322+161+160$=644$after 10 weeks :1+644+322+161+160$=1288$total sum= 1288+644+322+161+160=2575$
OPTION D
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Re: Molly worked at an amusement park over the summer.Every two weeks she  [#permalink]

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07 Apr 2020, 07:29
Payment after 2 weeks: $160 Payment after 4 weeks: 1 +$160 = $161 Payment after 6 weeks: 1 +$160 + $161 =$322

Payment after 8 weeks: 1 + $160 +$161 + $322 =$644

Payment after 10 weeks: 1 + $160 +$161 + $322 + 644 =$1288

So, TOTAL of all payments = $160 +$161 + $322 +$644 + $1288 so,money was Molly paid during full 10 weeks of summer =$2575

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Joined: 07 Apr 2020
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Molly worked at an amusement park over the summer.Every two weeks she  [#permalink]

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07 Apr 2020, 07:43
Solution:

• $$Money \ she \ received \ after \ every \ 2 \ weeks = sum \ of \ money \ received \ last \ weeks + 1$$

• Total money paid = money for first two week + money for third and fourth week + money for fifth and sixth week + money for seventh and eight week + money for night and tenth week.

• $$Total \ money \ paid = 160 + (160+1) + (160+161+1) + (160 + 161 +322+1 ) + (160 + 161 + 322 + 644+1) =  2575$$

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Re: Molly worked at an amusement park over the summer.Every two weeks she  [#permalink]

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08 Apr 2020, 09:39
Is there any other method except straightforward math?
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Molly worked at an amusement park over the summer.Every two weeks she  [#permalink]

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16 Apr 2020, 14:08
ArnoldPushkin wrote:
Is there any other method except straightforward math?

Yes since every answer ends in a different unit digit you can try and find the unit digit of the sum with out adding all the numbers.

you can write the amount she earns each month as

1)160
2)1+160
3)1+1+160+160
4)1+1+1+1+160+160 +160+160
5)1+1+1+1+1+1+1+1+160+160 +160+160 +160+160+160+160

Now you count all the ones

The sum of ones= 15

The only answer that ends in 5 is D

I think thats the fastest way to solve this question under 2 min. If anyone figure out an even faster way please make sure to share it
Molly worked at an amusement park over the summer.Every two weeks she   [#permalink] 16 Apr 2020, 14:08