Surprise 1
What is 20% of 30%? (answer in percentage) (page 27)
6%
The musical Rent contains a song that starts "Five hundred and twenty five thousand six hundred minutes". Which of the following is closest to this length of time? (page 49)
A a week
B a year
C a decade
D a century
E a milennium
B year
Page 55
8 - 2pi
What is the 2019th digit after the decimal point of the decimal form of 2019/7? (page 5)
8
Page 11
36
Page 47
31 cm
A sequence satisfies a1 = 3, a2 = 5, and an+2 = an+1 - an for n >= 1. What is the value of a2013? (page 41)
2
Find all triples (x,y,z) of real numbers satisfying the equations. (page 7)
x2 + 2yz = 4
y2 + 2zx = 4
z2 + 2xy = 1
(2,0,1), (0,2,1), (-2,0,-1), and (0,-2,-1)
Find the value of the following. (page 19)
2020 * 999 - 9999 * 202 + 9999
8181
Page 25
40/13
What is the sum of the digits of (1010101)2? (page 39)
16
What time will it be 2026 minutes after 20:26 on Monday? (page 17)
6:12 on Wednesday
Page 45
C
The positive numbers x and y satisfy the equations x4 - y4 = 2009 and x2 + y2 = 49. What is the value of y? (page
2
165
How many pairs of digits (p,q) are there so that the five-digit integer "p869q" is a multiple of 15? (page 45)
6
Page 37
9
The number 987654321 is multiplied by 9. How many times does the digit 8 occur in the result? (page 51)
9
The numbers x and y satisfy the equations x + y = 6 and x3 + y3 = 198. What is the value of xy? (Page 23)
1
Page 31
1 : pi - 2
Page 13
6:35 a.m.
Ali, Bev, and Chaz never tell the truth. Each of them owns exactly one colored stone that is either red or green. Ali says, "My stone is the same color as Bev's". Bev says, "My stone is the same color as Chaz's". Chaz says, "Exactly two of us own red stones". Which of the following statements are true? (page 53)
A Ali's stone is green
B Bev's stone is green
C Chaz's stone is red
D Ali's stone and Chaz's stone are different colors
E None of the statements are true
A
Four positive integers a, b, c, and d are such that
abcd + abc + bcd + cda + dab + ab + bc + cd + da + ac + bd + a + b + c + d = 2009.
What is the value of a + b + c + d? (page 35)
73
How many digits are there in 52020 * 41008? (page 21)
2019 digits
Page 9
45 degrees