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Bunuel
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GMAT 1: 760 Q51 V41
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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.

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

Answer : Option D
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Is there any other method except straightforward math?
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Bunuel
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.

Answer: D
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ArnoldPushkin
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 :)
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I did something similar:

Let 160 be x

Therefore after 2 weeks x
After 4 weeks 2x+1
After 6 weeks 3x+2
After 8 weeks 4x+3
After 10 weeks 5x+4

Total = x+2x+3x+4x+5x+ 15 (only answer with 15 is D)

Total = 16x+15, now substitute x =160 = 16*16 =256 i.e. 2560 +15 = 2575

georgos8888


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 :)
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