Math Olympiad 4

Math Olympiad 4( Week 31 Quiz 6)

9 × 9 + 7	=	88
98 × 9 + 6	=	888
987 × 9 + 5	=	8888
9876 × 9 + 4	=	88888

Fill the following blank by observing the above pattern:

98765 × 9 +

888888

2. If the 1st day of a month is Sunday, which of the following could be the last day of the month?

A) Friday

B) Wednesday

C) Thursday

D) Sunday

3. The last day of a month is Tuesday. Which of the following could it be the 1st day of the month?

A) Monday

B) Friday

C) Thursday

D) Saturday

1 × 9 + 2	=	11
12 × 9 + 3	=	111
123 × 9 + 4	=	1111
1234 × 9 + 5	=	11111

Fill the following blank by observing the above pattern:

× 9 + 8

11111111

5. 4ⁿ is n 4s multiplied together. What are the last digits of 4², 4³, 4⁴ respectively ?

6. What is the next term in the following sequence? 0.5, 1.3, 2.1, 2.9, 3.7, 4.5,

7. Find the pattern, and fill the blanks for the next two numbers.
45, 45, 37, 41, 29, 37, 21, 33, , .

10. Figure out how the first two sets of numbers are related and then select the number from the choices to fill the question mark so that the third set of numbers have the same relationship as the first two sets.

11. Is the result of (283 − 132) × 192 an odd number?

Yes No

12. The last Saturday of a month was on the 28th day of the month. What day of the week was the first day of the month?

A) Wednesday

B) Sunday

C) Saturday

D) Monday

13. Below is a calendar of a certain month in a certain year. Each cell on the calendar is a 1x1 square. There are 15 possible 3x3 grids (Do not count the title row of the grid). What is the largest sum of the numbers in a 3x3 grid (If a cell has no number, assume it will be a 0)?

14. Find the 60th term in the following sequence: 1,4,9,16,25,36...

15. In the arithmetic sequence below, 103, 101, 99, 97, 95, ... What is the 48th term?