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Tommy spent six lucky days in Las Vegas. On his first day he won a net

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Tommy spent six lucky days in Las Vegas. On his first day he won a net [#permalink]

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New post 24 May 2015, 04:58
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Question Stats:

80% (01:25) correct 20% (08:34) wrong based on 150 sessions

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Tommy spent six lucky days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommy won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?

A. 330
B. 500
C. 520
D. 540
E. 620

What if the question asked for d?


[Reveal] Spoiler:
Given that

Sum = Average x Number of days

1620 = [(x + 20) / 2] x 6

Where x is the amount won on last day.

1620 = [(x + 20) / 2] x 6

--> 1620 = [(x + 20) / 2] x 6

--> 1620 / 6 = [(x + 20) / 2]

--> 2 x 1620 /6 = (x + 20)

--> 540 = (x + 20)

--> 540 - 20 = x

--> 520 = x

Hence, this is the correct answer.
[Reveal] Spoiler: OA

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Re: Tommy spent six lucky days in Las Vegas. On his first day he won a net [#permalink]

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New post 24 May 2015, 08:10
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You could just write down his daily earnings:

20
20+d
20+2d
20+3d
20+4d
20+5d

Adding these, we get 120 + 15d. So 120+15d = 1620, and 15d = 1500, so d = 100. With the value of d, you can answer any question - we can see above he won 20+5d on the last day, so he won 520 on the last day.

I prefer a different approach. He won an average of 1620/6 = 270 per day. Our set is equally spaced (increasing by a constant d each day); in an equally spaced set, the average of the smallest and largest things is always the same as the average of the entire set. The smallest value is 20, and the largest is what we want to find. If we call the largest value x, we then know that the average of 20 and x is equal to 270:

(20+x)/2 = 270
20 + x = 540
x = 520.
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Re: Tommy spent six lucky days in Las Vegas. On his first day he won a net [#permalink]

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New post 24 May 2015, 12:33
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I drew a diagram:

1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620

Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, he earned $520. Answer choice C.
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Tommy spent six lucky days in Las Vegas. On his first day he won a net [#permalink]

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New post 27 Jul 2015, 00:18
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mjvoss wrote:
I drew a diagram:

1 - $20
2 -
3 -
4 - $320
5 -
6 -
Total: $1,620

Between 1 and 6 are 5 days where he won $1,600. This means he averaged $320 per day (1600/5). You can put $320 by 4 because it's the middle number. Now you just find the two points betwenn $20 and $320 (320-20 = 300 / 3 = 100). So each day, he earned $100 more. This means on day 6, he earned $520. Answer choice C.


how come 4 become the middle number of 6, when 6 is an even number? It worked for you but its more easy and to the point if you pick formula.
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GMAT PS Question [#permalink]

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New post 31 Aug 2015, 11:13
Tommy spent six days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommy won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?

Can anyone please help me in solving this questions?
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Re: Tommy spent six lucky days in Las Vegas. On his first day he won a net [#permalink]

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traceroute wrote:
Tommy spent six days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommy won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?

Can anyone please help me in solving this questions?


Merging topics. Please refer to the discussion above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Thank you.
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Re: Tommy spent six lucky days in Las Vegas. On his first day he won a net [#permalink]

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New post 21 Sep 2015, 12:33
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traceroute wrote:
Tommy spent six days in Las Vegas. On his first day he won a net amount of only $20, but on each of the following days, the daily net amount he won grew by d dollars. If Tommy won a total net amount of $1620 during his stay in Las Vegas, how much did he win on the last day?

Can anyone please help me in solving this questions?


This question can be solved by using Arithmetic Progression series.
1st day : 20
2nd day: 20+d
3rd day : 20+2d
...
...
...
add the earning for all days, and then equate the total earning to total winning amount of 1620. Find d and hence you can find the winning on any day.
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Re: Tommy spent six lucky days in Las Vegas. On his first day he won a net [#permalink]

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Re: Tommy spent six lucky days in Las Vegas. On his first day he won a net   [#permalink] 15 Feb 2017, 06:16
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