What's the fastest way to do these math problems?

jamesford
Tue, 04 Aug 2009 00:37:57 +0000

In an art class, there were just enough staplers, rulers, and glue bottles so that every 2 students had to share a stapler, every 3 had to share a ruler, and every 4 had to share a glue bottle. If the sum of the number of staplers, rulers, and glue bottles used by the class was 65, how many students were in the class?

The LCM of 3, 4, and 2 is 12, so the number of students is a multiple of 12. Seeing as 12 is too small, starting off with 36 students yields 18 staplers + 12 rulers + 9 glue bottles = 39. 48 students yields 24 + 16 + 12 = 52. 60 yields 30 + 20 + 15 = 65, so the answer is 60 students.

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If a and b are integers such that a + b < 1000 and a/b = .625, what is the greatest possible value of b?

a = .625b, so .625b + b < 1000 —> b < 615

.625 = 5/8, a = 5/8 b, so b must be divisible by 8. We test down from 615: 614, 612, 610, 608 and find that 608 is the answer.

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How many positive integers less than 1,000 are multiples of 5 and are equal to 3 times an even integer?

Let’s look at this problem with numbers less than 100. We find 30, 60, 90 are the only solutions. All three are multiples of 30, which would indicate that every answer is a multiple of 30. 1000/30 = 33.33333, so we round down and get 33.