1998 PMWC Problems

Problem I1

Calculate:

Solution

Problem I2

Solution

Problem I3

Solution

Problem I4

Suppose in each day on a certain planet, there are only 10 hours and every hour has 100 minutes. What is the measure, in degrees, of the acute angle formed by the hour hand and the minute hand at 6 o'clock 75 minutes?

Solution

Problem I5

There were many balls which were distributed into 1998 boxes and all these boxes were arranged in a row. If the second box from the left-hand contained 7 balls and any 4 consecutive boxes always had a total of 30 balls, how many balls were there in the right-hand box?

Solution

Problem I6

After a mathematics test, each of the 25 students in the class got a quick look at the teacher’s grade sheet. Each student noticed five A’s. No student saw all the grades and no student saw her or his own grade. What is the minimum number of students who scored an A on this test?

Solution

Problem I7

Solution

Problem I8

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Problem I9

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Problem I10

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Problem I11

Solution

Problem I12

Solution

Problem I13

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Problem I14

Solution

Problem I15

Solution

Problem T1

Solution

Problem T2

Solution

Problem T3

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Problem T4

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Problem T5

Solution

Problem T6

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Problem T7

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Problem T8

Solution

Problem T9

Solution

Problem T10

Solution