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operations on integers

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by minuit7 » Mon Aug 15, 2016 3:14 pm
Looking for quick ways to approach the following question:

A certain drive-in movie theater has a total of 17 rows of parking spaces. There are 20 parking spaces in the first row and 21 parking spaces in the second row. In each subsequent row there are 2 more parking spaces than in the previous row. What is the total number of parking spaces in the movie theater?

A 412
B 544
C 596
D 632
E 692

Thank you!
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by [email protected] » Mon Aug 15, 2016 6:00 pm
Hi minuit7,

This question can be solved with a bit of Arithmetic and 'bunching.'

We're told that the first two rows of parking spaces contain 20 and 21 spaces respective, then the following 15 rows increase by 2 each (re: 23, 25, 27, etc.). We're asked for the TOTAL number of parking spaces.

The first two rows total 20+21 = 41 spaces. The remaining 15 rows are the odd numbers from 23 through 51, inclusive. By adding the smallest and largest of those numbers, we get:

23 + 51 = 74

By adding the next smallest and next biggest, we get:

25 + 49 = 74

This pattern is consistent, so we'll end up with 7 "pairs" of numbers that add up to 74 and one number "in the middle" that doesn't 'pair up': 37.

Thus, the total number of spaces is... 41 + 7(74) + 37 = 596

Final Answer: C

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by Matt@VeritasPrep » Fri Aug 19, 2016 1:49 am
We've got

20 + 21 + (21 + 1*2) + (21 + 2*2) + ... + (21 + 15*2)

or

20 + 21*16 + 1*2 + 2*2 + ... + 15*2

or

20 + 21*16 + 2*(1 + 2 + ... + 15)

or

20 + 336 + 240
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