Percentages
A stock increases by 10% on Day 1 and decreases by 10% on Day 2. Does the overall stock price increase, decrease or remain the same?
Solution:
Start with 100.
100 -> 110 on Day 1 -> 110(.9) = 99. The overall stock price decreases.
Jackie rolls a dice and flips a coin. What is the probability that Jackie rolls a 1 or a 2, and also flips a Tails?
Solution:
Probability(1 or 2) = 1/3
Probability(Tails) =1/2
Probability(both events) = 1/6
What is the simplified form of 13(2b – 5a) + -2a?
Solution:
13(2b – 5a) + -2a = 26b – 65a + -2a = 26b – 67a
If 2^6 = 4^x, find x.
Solution:
2^6 = (2x2)x(2x2)x(2x2) = 4^3, so x = 3.
To the nearest ten, what is 5/6 x 301?
Solution:
5/6 x 300 = 5 x 50 = 250
If the price of cherries increases by 10% three days in a row, will the price change by more than, less than, or equal to 30%?
Solution:
1(1.1)(1.1)(1.1) > 1.3, so the price changes by more than 30%
Miguel flips a coin four times. All four land Heads. What is the probability that Miguel gets a Heads on his next (fifth) flip?
Solution:
Each coin flip is independent from those before it, so the probability is just 1/2
What is (0.80 – 0.35) divided by 4/9, expressed as a fraction or mixed fraction?
Solution:
(0.80 – 0.35) = 0.45 = 9/20
9/20 x 9/4 = 81/80
How many prime factors does the number 221 have?
Solution:
221 = 17 x 13, so the two prime factors are 17 and 13.
The radius of a circle is 10 centimeters. What is the area of the circle in square centimeters, to the nearest hundred?
Solution:
Area = (10^2)*pi = 100pi
Assuming pi = 3, Area is approximately 100(3) = 300 square centimeters
Suppose the variable b is multiplied by four. What is the percent increase in b?
Solution:
Suppose b goes from 1 to 4. Then the percent change is (4-1)/1 x 100% = 300% change.
Dylan rolls a dice two times. What is the probability that the product of the two dice rolls is at least 30?
Solution:
Ways to get to at least 30:
{5,6}, {6,5} or {6,6}. 3 total
Out of 36 total sets of two rolls
Probability = 3/36 = 1/12
What is the simplified form of the fraction (81x63x12)/(144x9x9) if you write it as a number with a decimal?
Solution:
63/12 = 5 1/4 = 5.25
What is the 71st term in the sequence {18, 25, 32, 39, 46, ...}?
Solution:
The 290th number is 18 + wherever we land after 70 jumps. The difference of each jump is 25 – 18 = 7, so 18 + 7 × 70 = 18 + 490 = 508
How can the decimal 0.0625 be expressed as a simplified fraction?
Solution:
0.5 = 1/2
0.25 = 1/4
0.125 = 1/8
0.0625 = 1/16
So 0.0625 can be expressed as 1/16
A soup costs $1.14. The cost increases by 20% on Monday and then by 30% on Tuesday. What is the percent increase in the cost of soup over the two days?
Solution:
The initial cost doesn’t matter! Assume it started at $100
$100(1.2)(1.3) = $100(1.56), so there is a 56% increase over the two days
Amy, Brett, and Cate each secretly write down Z, U, or T. What is the probability that Cate’s letter is different from both Amy’s letter and Brett’s letter?
Solution:
Whatever Cate picks, Amy has a 2/3 chance of being different and Brett has a 2/3 chance of being different. Then the desired probability is 2/3 x 2/3 = 4/9
Pamela, Frank and George are three siblings. Pamela’s age is twice Frank’s. Frank is six years older than George. The three combined are 34 years old. How old is George?
Solution:
Let f = Frank’s age
2f = Pamela’s age
f – 6 = George’s age
In total, 4f – 6 = 34, 4f = 40, f = 10, f – 6 = 4, So George is 4 years old.
Circle X has a radius of 2. Circle Y has a circumference of 8*pi. Circle Z has an area of 9*pi. List the circles in order from smallest to largest radius.
Solution:
Circle X, radius of 2. Circle Y has a radius of 8/2 = 4. Circle Z has a radius of = 3. Then the smallest is X with a radius of 2, then Z with a radius of approximately 3, and then Y with a radius of 4.
To two decimal places, what is 1/7 expressed as a decimal?
Solution:
Using long division, 1/7 is approximately 0.14
Over the course of the past year, Mario and Luigi combine to eat 240 slices of pizza. If Luigi eats 50% more slices of pizza than Mario, how many slices of pizza does Luigi eat?
Solution:
Mario = x; Luigi = y = 1.5x; x + 1.5x = 240; 2.5x = 240
x = 96 (Trap answer, be careful, they asked for Luigi not Mario)
1.5x = 144
Raghav rolls a 20-sided dice, which is equally likely to land on any of the twenty sides, and Bhavya rolls a 6-sided dice, which is equally likely to land on any of the six sides. What is the probability that Raghav rolls a number that is higher than Bhavya’s?
Solution:
Use the complement, which is that Raghav does not roll a number higher than Bhavya, which means that Bhavya rolls at least as high
Total ways:
Bhavya 1, Raghav 1
Bhavya 2, Raghav 1 or 2
Bhavya 3, Raghav 1, 2 or 3
Bhavya 4, Raghav 1, 2, 3 or 4
Bhavya 5, Raghav 1, 2, 3, 4 or 5
Bhavya 6, Raghav 1, 2, 3, 4, 5 or 6
Total ways: 1 + 2 + 3 + 4 + 5 + 6 = 6(7)/2 = 21
Total combinations for two dice rolls = 20(6) = 120
Raghav’s number is higher (120-21)/120 = 99/120 = 33/40
What is the value of the expression 15/16 divided by (-1.55)?
Solution:
Easiest to convert to fractions,
15/16 x -31/20 = -75/124
Suppose 6^a * 11^b * 4^c = 484. What is the sum of a + 2b + 3c?
Solution:
484 = 11(11)(4) = (6)^0 x (11)^2 x (4)^1
Then a = 0, b = 2 and c = 1, so a + 2b + 3c = 0 + 2(2) + 3(1) = 4 + 3 = 7
What is 1/6 expressed as a repeating decimal?
Solution:
1/6 = 0.1666…