Number Sense
If the positive difference between 5.3 and 1.14 is multiplied by 0.48, the result is closest to which integer?
Answer: 2
Solution:
5.3 - 1.14 = 4.16 * 0.48, roughly 4 * 0.5 = 2
Set up an algebraic expression for the following:
The sum of three consecutive odd integers is 237. Do not solve, just write the algebraic expression.
Answer: x + (x+2) + (x+4) = 237 or 3x + 6 = 237
Solution:
Let x be the smallest of the integers. Then
x + (x + 2) + (x + 4) = 237
or
3x + 6 = 237
How many prime numbers, if any, are divisible by 2?
Answer: One prime number.
Solution: The number 2 is the only even prime number.
100(1.1)(1.1) = 121 -> 21% increase
If 83 = 2x, then what is the value of x2?
Answer: 81
Solution:
(23)3 = 29 = 2x so x = 9, And 92 = 81
What is the value of 0.5 / (0.5 / 0.125), expressed as a fraction?
Answer: 1/8
Solution: Convert to fractions and use Keep change flip which yields 1/8.
Two consecutive even integers have a product of 168. What is the larger of the two numbers?
Answer: 14
Solution:
12 x 14 = 168, so the larger number is 14
What is the product of all of the prime numbers between 0 and 10?
Answer: 210
Solution: 2 x 3 x 5 x 7 = 6 x 35 = 210
Mr. Walters sells lemonade for $1.40. He increases the price by 50% and then decreases the price by 50%. What is the final price of the lemonade?
Answer: $1.05
Solution:
1.40 -> 1.40 + 0.70 = 2.10 -> 2.10 - 1.05 = 1.05
If there are 6 basketball teams in a league, and each team plays every other team exactly once, how many total basketball games take place?
15 total games.
Call the 6 teams A, B, C, D, E and F.
AB, AC, AD, AE, AF
BC, BD, BE, BF
CD, CE, CF
DE, DF
EF
5 + 4 + 3 + 2 + 1 = 15 combinations
What is the simplified form of (12 x 81) / (9 x 144), expressed as a decimal?
Answer: 0.75
Solution:
12/144 = 1/12 and 81/9 = 9, so
9/12 = 3/4, which is 0.75
Write an algebraic expression for the following statement:
The product of two consecutive odd integers (starting with x) is fourteen more than the square of the smaller integer.
Answer: x(x+2) - 14 = x2
Solution: Also, the numbers are 7 and 9
What is the sum of x and y in the pattern:
1, 1, 2, 3, 5, 8, 13, 21, x, y...
Solution:
x = 13 + 21 = 34
y = 21 + 34 = 55
x + y = 34 + 55 = 89
What is 35% of 625?
Answer: 218.75
Solution:
10% is 62.5
x 3 = 187.50
5% is 31.25
Adding them gives 218.75
What is the 185th digit in the following pattern:
12345678910111213141516...
Answer: 7
Solution:
1-9 is 9 digits
10-19 is 20 digits, so 10-99 is 20(9) = 180 digits
In total, 189 digits
...979899, so 7 is the 185th term
In lowest terms, what is the product of 8/15, 5/12, and 3/4?
Solution:
3/4 x 5/12 x 8/15 = 1/6, simplify common factors before dividing
If x2 = 64, what is x?
Answer: 200 points for x = 8, 200 points for x = -8
The scores of Jeremiah's first four math tests are 82%, 90%, 78%, and 100%. If Jeremiah wants to have a test average of 90%, what must the average of Jeremiah's next two tests be?
Solution:
So far, 82 + 78 + 90 + 100 = 350
90 avg = x total / 6 tests
x = 540
Need to go from 350 to 540 on two tests, or 190 over two tests, or 190/2 = 95% average
Michael sold his bike to Krish for 35% more than he paid for it. Krish then sold the bike to Joseph for 20% more than he paid for it. What percent of the original price did Joseph pay for the bike?
Answer: 162% of original (not 62%)
Solution: 100 -> 135 -> 162
3a times 7b times 11c = 539, where a, b and c are all non-negative integers.What is the sum of a + b + c?
30 times 72 times 111 = 539, so a = 0, b = 2 and c = 1. Then a + b + c = 0 + 2 + 1 = 3
Which is bigger, 442% of 1232 or 1232% of 442?
Answer: Neither is bigger - they are the same!
Solution: x% of y = y% of x
If -x(4 - y) + 4x = 12, what is the twice the product of x and y?
Answer: 24
Solution:
-4x + xy + 4x = 12 so xy = 12 so the product of x and y is 12 and twice that is 24
Daily Double: 1,000 Points
Evaluate the expression
(1 + 2 + 3 + ... + 98 + 99 + 100) / 2
Answer: 2,525
Solution:
1 + 2 + 3 + ... + 98 + 99 + 100 is 50 pairs that add to 101, so 50(101) = 5,050
5,050/2 = 2,525
80% = 8/10
125% = 5/4
8/10 x 5/4 = 1
19, because 3 + 5 + 11 = 19