# Mathleague Sprint - Ritam Bhowmik

```Sprint Test
Written by Ritam Bhowmik
Name:
School:
1. Compute 2742 .
A) 69,696
B) 74,086
C) 75,076
D) 75,696
E) Other
2. What is the mean of the median and mode of the set {1, 2, 3, 3}?
A) 2.25
B) 2.5
C) 2.75
D) 3
E) Other
3. What is the remainder resulted when the number 111,111,111 is divided by 9?
A) 0
B) 2
C) 4
D) 8
E) Other
B) 337
C) 347
D) 357
E) Other
D) 55
E) Other
4. Evaluate 28 + 34 .
A) 327
5. What is the sum of the first ten positive integers?
A) 0
B) 10
C) 45
6. One mouse eats one piece of cheese in a week. How long (in days) does it take twenty mice
to eat twenty pieces of cheese?
A) 1
B) 7
C) 13
D) 20
E) Other
7. In how many ways can the letters of the word BAN AN A be arranged?
A) 60
B) 240
C) 360
D) 720
E) Other
8. Joel and Mark have 56 marbles altogether. For every 2 marbles that Joel has, Mark has 5
marbles. How many marbles does Mark have?
A) 16
B) 35
C) 37
D) 40
E) Other
9. The sum of two numbers is 24 and the positive difference of these numbers is 4. What is the
larger number?
A) 14
B) 18
C) 12
D) 10
E) Other
10. The sum of six consecutive odd numbers is 84. What is the smallest number?
A) 7
B) 9
C) 11
D) 13
E) Other
11. Joshua has a favorite number. If we multiply Joshua’s number by 2, add 6, and divide by 3,
we get the same number. What is this number?
A) 6
B) 8
C) 10
D) 9
E) Other
C) 12
D) 21
E) Other
12. Evaluate 2(4) + 2870 + 1 · 5 − 8.
A) 15
B) 18
1
Sprint Test
13. If 5 Smurfs = 6 Curfs and 3 Lurfs = 7 Curfs, then how many Lurfs is a Smurf and a Curf?
A) 57
B) 32
C) 1
D) 7
E) Other
35
14. What is the greatest prime divisor of all four-digit natural numbers in the form abba, where
a and b both represent distinct digits?
A) 7
B) 11
C) 13
D) 1001
E) Other
15. What is the sum of the first six terms of the sequence 3, 8, 13, . . .?
A) 63
B) 78
C) 93
D) 108
E) Other
16. The sum of five consecutive whole numbers can be one of these EXCEPT:
A) 100
B) 5055
C) 685
D) 87
E) Other
17. Vincent and Luis each flipped a fair two-sided coin 3 times. Vincent flipped 1 head, while
Luis flipped 3 heads, luckily. What is the probability of Vincent flipping heads if he decides
to flip the coin again?
A) 75%
B) 50%
C) 25%
D) 12.5%
E) Other
18. Jacob and Max are having a pie-eating contest. Jacob eats a pie in 18 minutes, while Max eats
a pie in 20 minutes. The contest ends if both Jacob and Max eat a pie at the same time. If it
is 7:00 PM when they both start eating pies, then what time will the pie-eating contest finish?
A) 7:38 PM
B) 8:00 PM
C) 10:00 PM
D) 11:00 PM
E) Other
1
19. Evaluate 1 +
1+
A)
4
7
1
2+1
B)
.
4
3
C)
7
4
11
7
E) Other
D) 11
E) Other
D)
20. Solve for x: 5x + 24 = 6x + 20.
A) −4
B) 4
C) −11
21. A rectangle has sides of length 7 centimeters and 24 centimeters. What is the length of the
rectangle’s diagonal, in centimeters?
√
√
A) 25
B) 5 17
C) 527
D) 30
E) Other
22. Arjun’s watch, for some reason, is not working right. His watch loses 5 minutes per hour and
it only displays the time, disregarding AM/PM. Find is the minimum number of days that
his watch will display the correct time.
A) 3
B) 4
C) 5
D) 6
E) Other
23. The proper divisors of a number are the divisors of the number besides the number itself.
Find the sum of the proper divisors of 28.
A) 28
B) 35
C) 42
2
D) 56
E) Other
Sprint Test
24. What is the greatest common divisor of the numbers 18, 20, and 47?
A) 940
B) 1880
C) 2820
D) 4230
E) Other
25. You and your friends order pizza from a delivery service. There are 8 different bases, 18
different toppings and 6 different cheeses. How many different pizzas can you have that
consist of one base, one topping, and one cheese?
A) 812
√
26. Simplify 3645.
√
A) 9 5
B) 643
C) 792
D) 839
E) Other
√
B) 9 15
√
C) 27 5
√
D) 9 35
E) Other
27. A picture with a perimeter of 120 cm is framed. One side of the picture is 40 cm, and the
distance from the edge of the picture to the edge of the frame is 1.5 cm on all sides of the
picture. What is the area of the portion of the frame not covered by the picture? Express
A) 198
B) 189
C) 203
D) 134
E) Other
28. An equilateral triangle shares the same side length as a hexagon. What is the ratio of the
area of the equilateral triangle to the area of the hexagon?
A)
1
6
B)
1
3
C)
1
2
D) 1
E) Other
29. A cube’s side length is tripled. Find the ratio of the original volume to the new volume of
the cube.
A)
1
3
B)
1
9
C)
1
81
D)
1
27
E) Other
30. Evaluate the remainder when 20172018 is divided by 5.
A) 0
B) 1
C) 2
Thank you for taking this test.
3
D) 3
E) Other
```