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Number Sense
Algebra
Mystery
Percentages
Challenge
100

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

100

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

100

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
Apples cost $100 in January. The price of apples increase 10% in February and another 10% in March. What is the total percent increase from January through March?

100(1.1)(1.1) = 121 -> 21% increase

100

If 83 = 2x, then what is the value of x2?

Answer: 81

Solution:

(23)3 = 29 = 2x so x = 9, And 92 = 81  

200

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.

200

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

200

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

200

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

200

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

300

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

300

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

300

What is the sum of x and y in the pattern:

1, 1, 2, 3, 5, 8, 13, 21, x, y...

Answer: 89

Solution:

x = 13 + 21 = 34

y = 21 + 34 = 55

x + y = 34 + 55 = 89

300

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

300

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

400

In lowest terms, what is the product of 8/15, 5/12, and 3/4?

Answer: 1/6

Solution: 

3/4 x 5/12 x 8/15 = 1/6, simplify common factors before dividing

400

If x2 = 64, what is x?

Answer: 200 points for x = 8, 200 points for x = -8

400

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?

Answer: 95%

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

400

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


400

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

500

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

500

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

500

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

500
What is 80% of 125% of x3?
Answer: x3
Solution: 

80% = 8/10

125% = 5/4

8/10 x 5/4 = 1


500
What is the smallest prime number that can be written as the sum of three different prime numbers?

19, because 3 + 5 + 11 = 19