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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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24 May 2015, 05:58
2
2
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Difficulty:

25% (medium)

Question Stats:

78% (02:06) correct 22% (02:31) wrong based on 170 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?

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.

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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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24 May 2015, 09:10
6
1
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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##### General Discussion
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Joined: 07 Jul 2015
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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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27 Jul 2015, 01:18
2
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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Re: Tommy spent six lucky days in Las Vegas. On his first day he won a net  [#permalink]

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21 Sep 2015, 13:33
2
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?

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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24 May 2015, 13:33
1
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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Joined: 02 Sep 2009
Posts: 58094
Re: Tommy spent six lucky days in Las Vegas. On his first day he won a net  [#permalink]

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31 Aug 2015, 12:21
1
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?

Merging topics. Please refer to the discussion above.

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GMAT PS Question  [#permalink]

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31 Aug 2015, 12:13
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?

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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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05 Jan 2019, 14:27
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Re: Tommy spent six lucky days in Las Vegas. On his first day he won a net   [#permalink] 05 Jan 2019, 14:27
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