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On the first even day of the month, Steve Roggers saves $5

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On the first even day of the month, Steve Roggers saves $5  [#permalink]

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New post 11 Oct 2018, 11:39
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A
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On the first even day of the month, Steve Roggers saves $5, and on each following even day he saves $5 more than he saved the previous even day of the month. If there were 30 days in the certain month, how much money did Steve Roggers save by the end of the month?
A) $680
B) $640
C) $600
D) $580
E) $360

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Re: On the first even day of the month, Steve Roggers saves $5  [#permalink]

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New post 11 Oct 2018, 14:40
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Abhi077 wrote:
On the first even day of the month, Steve Roggers saves $5, and on each following even day he saves $5 more than he saved the previous even day of the month. If there were 30 days in the certain month, how much money did Steve Roggers save by the end of the month?
A) $680
B) $640
C) $600
D) $580
E) $360


Let's use a table to look for a pattern.

Day 2: $5 = 1($5)
Day 4: $5 + $5 = 2($5)
Day 6: $5 + $5 + $5 = 3($5)
Day 8: $5 + $5 + $5 + $5 = 4($5)
.
.
.
Day 28: 14($5)
Day 30: 15($5)

So, TOTAL savings = (1)($5) + (2)($5) + (3)($5) + (4)($5) + . . . . + (14)($5) + (15)($5)
= ($5)(1 + 2 + 3 + 4 + . . . + 14 + 15) [I factored out the $5 from each term]

ASIDE: Here's a useful formula: 1 + 2 + 3 + . . . + n = (n)(n + 1)/2
Now apply this formula to the sum above to get:
= ($5)[(15)(16)/2]
= ($5)(15)(8)
= 600

Answer: C
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Re: On the first even day of the month, Steve Roggers saves $5  [#permalink]

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New post 11 Oct 2018, 16:03
1
Abhi077 wrote:
On the first even day of the month, Steve Roggers saves $5, and on each following even day he saves $5 more than he saved the previous even day of the month. If there were 30 days in the certain month, how much money did Steve Roggers save by the end of the month?
A) $680
B) $640
C) $600
D) $580
E) $360


Day 2 = 5
Day 4 = 5 + 5 = 10

This is in the form of 5 + 5(n-1)

Where n is the even day.

30-2 = 28/2 = 14 + 1 = 15 even days.

D30 = 5 + 5(14) = 5 + 70 = 75.

Avg of D2 to D30 = (75+5)/2 = 40 this is possible because it is evenly spaced.

The sum would be = 40*15 = 600

Answer choice C

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On the first even day of the month, Steve Roggers saves $5  [#permalink]

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New post 12 Oct 2018, 00:39
2
Abhi077 wrote:
On the first even day of the month, Steve Roggers saves $5, and on each following even day he saves $5 more than he saved the previous even day of the month. If there were 30 days in the certain month, how much money did Steve Roggers save by the end of the month?
A) $680
B) $640
C) $600
D) $580
E) $360


You can think about it in terms of an arithmetic progression. There are 15 even days (half of the 30 days) so n = 15
First term of AP (first amount) = $5
Common difference of AP (increase in amount each time) = $5

Sum of all amounts = (n/2)*(2a + (n-1)*d) = (15/2)*(2*5 + (15 - 1)*5) = 600

Answer (C)

For more on AP, check: https://www.veritasprep.com/blog/2012/0 ... gressions/
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On the first even day of the month, Steve Roggers saves $5   [#permalink] 12 Oct 2018, 00:39
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