July's Problem

A solution to this problem

will appear along with next month’s problem.

Solution to June's Problem

ANSWER: 40

Solution:

Mathod 1: Sets
Number of Multiples of 2 in 1,2,3,...,100 is 50
Number of Multiples of 5 in 1,2,3,...,100 is 20
Number of Multiples of 10 (i.e. 2 & 5) in 1,2,3,...,100 is 10
Number of unique multiples of 2 or 5 is 50 + 20 - 10 = 60
Remaining numbers 1,2,3,...100 is 100 - 60 = 40

Mathod 2: Rules for Divisibility
multiples of 2 end in 0,2,4,6, or 8
multiples of 5 end in 0 or 5
leaving numbers ending in 1,3,7, or 9
there are 10 of each of these (e.g. ending in 1: 1, 11, 21, 31, 41, 51, 61, 71, 81, and 91)
4 x 10 = 40

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Solution to May's Problem

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ANSWER: 3 miles per hour

Solution:

( Recall: Speed = Distance / Time )

Find the distance and time for each leg of the journey.

Leg 1: "Run 6 miles at 6 mph." Distance = 6 miles and time = 1 hour.

Leg 2: "Walk 6 miles at 3 mph." Distance = 6 miles and time = 2 hours (i.e. 6/3 = 2 ).

Leg 3: "Walk 6 miles at 2 mph." Distance = 6 and time = 3 hours (i.e. 6/2 = 3 )

Total distance = 18 miles and total time = 6 hours.

Speed = 18 miles / 6 hours = 3 mph.