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

[hazelnut01]

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. 322

OFFICIAL ANSWER : D

[Brent@GMATPrepNow]

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. 322

OFFICIAL ANSWER : A

The correct answer is not A.

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

Since the last two values ($644 and $1288) add to more than $1900, we know the correct answer is greater than $1900, which means the correct answer must be D, since that's the only answer choice that's greater than $1900

Cheers,
Brent

[Brent@GMATPrepNow]

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. 322

OFFICIAL ANSWER : A

ASIDE: Once we know that the TOTAL of all payments = $160 + $161 + $322 + $644 + $1288, we can avoid adding these values together if we first recognize that the UNITS DIGITS in the 5 answer choices are all DIFFERENT.

So, let's just add the UNITS digits in the sum $160 + $161 + $322 + $644 + $1288

We get: 0 + 1 + 2 + 4 + 8 = 15

So, the correct answer must have 5 as its units digit.

Answer: D

Cheers,
Brent

[[email protected]]

Hi ziyuenlau,

Since the answers to this question are fairly 'spread out', we can use estimation and avoid doing every exact calculation.

The first payment received is $160, and each subsequent payment equals the SUM of the payments that Molly previously received. If we call the first payment "X" (and ignore the "+ $1" that is added in each time , we can organize the information this way:

1st payment = X
2nd payment = X
3rd payment = X + X = 2X
4th payment = X + X + 2X = 4X
5th payment = X + X + 2X + 4X = 8X

Total = X + X + 2X + 4X + 8X = 16X

Since X = $160.... 16X = 16(160) = about $2560

There's only one answer that's close to that...

Final Answer: D

GMAT assassins aren't born, they're made,
Rich

[ms.ts]

Can this problem be solved using Arithmetic progression?

[indranilc]

IMO ans is D.

There are 5 2-week periods here.

1: 160
2: 1 + (what she has received till now) = 1 + 160 = 161
3: 1 + (what she has received till now) = 1 + (160 + 161) = 322 [notice this is double of last]
4: 1 + (what she has received till now) = 1 + (160 + 161 + 322) = 644 [notice this is double of last]
5: 644*2 = 1288

Total amount received is 1288 + 644 + 322 + + 161 + 160 ~= 1300 + 600 + 300 + 300 ~= 2500

@ ms.ts

This is in fact a Geometric Progression rather than an Arithmetic Progression

[ms.ts]

@indranilc Yes, I did get 2560 upon using GP formula. Thanks!

[Matt@VeritasPrep]

Can this problem be solved using Arithmetic progression?

You can use progressions, but you don't need to - GMAT problems are designed not to benefit from higher math. (Not that an arithmetic series is particularly difficult; it's just higher than the math on the GMAT.)

[Matt@VeritasPrep]

This is in fact a Geometric Progression rather than an Arithmetic Progression

For those who aren't familiar with the lingo here, geometric series are generated by multiplying by a constant, while arithmetic series are generated by adding a constant.

A geometric series would be something like: 1, 2, 4, 8, 16, ... (multiplying by two every time)

An arithmetic series would be something like: 1, 3, 5, 7, 9, ... (adding two every time)

[Matt@VeritasPrep]

This is in fact a Geometric Progression rather than an Arithmetic Progression

So with my last point in mind, this is not exactly a geometric series. For it be geometric, the ratio between each pair of consecutive terms would be constant (2/1 = 4/2 = 8/4 = ...), and here that's not the case: 161/160 ≠ 322/161. (I get the idea, but it doesn't apply perfectly here.)

All this progression/series talk is tangential to the GMAT, though, and can be safely ignored.

[ms.ts]

@Matt I actually tried GP to see if I get an exact answer as mentioned in the options and was wondering why I did not get an exact match if the problem was actually a GP. Thanks for clarifying!

[Scott@TargetTestPrep]

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. 322

OFFICIAL ANSWER : D

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