Bad Word Problems
It's the sum of Melanie’s age and Phil’s age 6 years from now if in 10 years the product of Melanie’s age and Phil’s age will be 400 more than it is now.
What is 42?
It's how many ways four O’s can be placed in a 3×3 grid such that there are three O’s in a row either horizontally, vertically, or diagonally.
What is 48?
Azzy flips three fair coins, and removes any coins that come up heads. Lex then flips the coins that remain (if there are any). It's the probability that Lex flips exactly one head.
What is 27/64?
It's x4 + 1/x4 if x + 1/x = 3.
What is 47?
The product 20!·21!·22!···28! can be expressed in the form m · n3 , where m and n are positive integers, and m is not divisible by the cube of any prime. It's m.
What is 825?
A jeweler can get an alloy that is 40% gold for 200 dollars per ounce, an alloy that is 60% gold for 300 dollars per ounce, and an alloy that is 90% gold for 400 dollars per ounce. The jeweler will purchase some of these gold alloy products, melt them down, and combine them to get an alloy that is 50% gold. It's the minimum number of dollars the jeweler will need to spend for each ounce of the alloy she makes.
What is 240?
It's a number between 400 and 420 which occurs in both of the arithmetic sequences 17,22,27,32,... and 16,22,28,34,....
What is 412?
Suzie flips a fair coin 6 times. It's the probability that Suzie flips 3 heads in a row, but not 4 heads in a row.
What is 3/16?
It's how many distinct lines pass through the point (0,2400) and intersect the parabola y = x2 at two lattice points. (A lattice point is a point whose coordinates are integers.)
It's the smallest positive integer n such that 288n does not divide 288!.
What is 58?
On Monday, Hank drove to work at an average speed of 70 km/h and arrived 1 minute late. On Tuesday, he left at the same time and took the same route. This time he drove at an average speed of 75 km/h and arrived 1 minute early. It's how long his route is to work, in kilometers.
What is 35?
It's the number of positive integers k ≤ 2020 for which there exist integers m and n such that k = 2m +2n . For example, 64 = 25 +25 ,65 = 20 +26 , and 66 = 21 +26
What is 66?
I have a coin that comes up heads 2/5 of the time. Amanda and I play a game where we take turns flipping this coin. The first person to flip heads wins. It's the probability I win this game if I am the first person to flip the coin.
What is 5/8?
It's x if x is a positive real number such that
(x −3)(x −1)(x +1)(x +3) +16 = 1162
What is 11?
Positive integers a , b , and c satisfy
a3 +32b + 2c = 2018 and
b3 +32a + 2c = 1115 .
It's a2 + b2 + c2
What is 226?
Five lighthouses are located, in order, at points A,B,C,D, and E along the shore of a circular lake with a diameter of 10 miles. Segments AD and BE are diameters of the circle. At night, when sitting at A, the lights from B,C,D, and E appear to be equally spaced along the horizon. It's the perimeter (in miles) of pentagon ABCDE.
What is 20 + 5 root 3?
It's the number of positive integers n such that a regular polygon with n sides has internal angles with measures equal to an integer number of degrees.
What is 22?
An unfair coin is flipped 13 times. The probability it comes up heads exactly 4 times is the same as the probability it comes up heads exactly 5 times. It's the probability the coin comes up heads if it is flipped exactly once.
What is 5/14?
It's y if we let H be a convex, equilateral heptagon whose angles measure (in degrees)
168, 108, 108, 168, x, y, and z
in clockwise order.
What is 132?
It's the probability no two adjacent letters will be the same if the letters AAABBCC are arranged in random order.
What is 19/105?
It's how many different ways there are to build a regular tetrahedron with six toothpicks, each of which is red or blue. Two colorings are considered to be the same if one can be rotated in space to match the other.
What is 12?
There are digits a and b so that the 15-digit number 7a7ba7ab7ba7b77 is divisible by 99. It's 10a+b.
It's how many ways there are to tile a rectangle of height 2 and width 8 with only 1×1 square tiles and 1×2 rectangular tiles. (The rectangular tiles can be placed horizontally or vertically, and no two tiles can overlap.)
What is 3,114?
It's how many ordered pairs of positive integers (x,y) for which 1,003,003,001 is the least common multiple of x and y.
What is 343?
It's the probability that a divisor of 1024, chosen at random, is a multiple of 106.
What is 16/25?