A bike store is having a 30%-off sale, and one of the bikes is on sale for $385. What was the original price of this bike?

0.98 + 45.102 + 32.3333 + 31 + 0.00009 = _________.

109.41539

There are two ways to solve this question. First, you can add all the given numbers and find the exact answer. This method is time-consuming and less efficient.
The second method to solve this question is by adding only the numbers on the left of the decimal and then comparing your answer with the answer choices that you are given. We add 45, 32, and 31 to get 45 + 32 + 31 = 108. Therefore, the answer must be close to, and greater than, 108. (Note that this method of approximation saves time but it is not very accurate if all the answer choices are very close to each other.)

There are 380 female students in a class. Male students make up 60% of the class. What is the total number of students in the class?

950

Let's use algebra to solve for the total number of students, denoted by "x". We know that there are 380 female students, so the number of male students can be found by subtracting 380 from the total number of students and setting it equal to 60% (or 0.6) of the total number of students:

x - 380 = 0.6x
Solving for x, we can simplify this equation as follows:

x - 0.6x = 380
0.4x = 380
x = 380 / 0.4
x = 950

Therefore, the total number of students in the class is 950.

In 18 hours, 42 trains pass near Emma’s house. How many trains pass near her house in 12 hours?

28 trains.

This is a proportion problem and the given information allows us to formulate the equation below:
42 trains/18 hours = x/12 hours
where x is the number of trains that pass near Emma’s house in 12 hours. We can solve this equation by first cross-multiplying.
18 hours × x = 42 trains × 12 hours
Carrying out the product on the right-hand side, we get:
18 hours × x = 504 trains·hours
We can solve for x by dividing both sides of the equation by 18 hours.
(18 hours × x)/18 hours = 504 trains·hours/18 hours
Carrying out the division, we get a 1 on the left-hand side and a 28 on the right-hand side.
1x= 28 trains
We can drop the 1 next to x, to get x= 28 trains. In 12 hours, 28 trains pass near Emma’s house.

Which inequality is equivalent to 3x + 2 > 5?

x > 1

3x + 2 > 5
3x > 3
x > 1

In a neighborhood, 2/5 of the houses are painted yellow. If there are 24 houses that are NOT painted yellow, how many yellow houses are in the neighborhood?

16

If 2/5 of the houses are painted yellow, then 3/5 of the houses are NOT painted yellow. Since there are 24 houses that are not yellow, divide 24 by 3/5 to find the total number of houses. Then subtract to find the number of yellow houses.
24 ÷ 3/5 = 24 × 5/3 = 40
40 – 24 = 16

David had 12 chocolates, which he decided to distribute among his friends. Alex got 2/3 of the total chocolates. How many chocolates did he get?

8

2/3 of the number of chocolates means that Alex got: 12 × 2/3 → 4 × 2 = 8 chocolates

The nursing graduates of a local college accounted for 38% of the 1322 graduates. How many of the graduates were NOT nursing graduates?

820

1322 - 502 (38% of 1322) = 820.

Which of the following shows 74,365 rounded to the nearest hundred and to the nearest thousand?

hundred: 74,400; thousand: 74,000.

The digit in the hundreds place is 3. It is rounded up to 4 because the digit in the tens place is 6, which is greater than or equal to 5. The number is thus rounded up to 74,400. The digit in the thousands place is 4 and remains 4 because the digit in the hundreds place (3) is less than 5. The number is therefore rounded to 74,000.

Which of the following is the solution set for the equation below?
|2x−5|=19

{−7,12}

Absolute value equations can be rewritten in two ways to solve:
2x−5=19 and 2x−5=−19
Solve both:
2x−5=19
2x=24
x=12
and 2x−5=−19
2x=−14
x=−7
The two solutions are: −7 and 12

In the number 743.25 which digit represents the tenth space?

2

Moving right of the decimal point one space is the tenth position.

There are 6,657 marbles in a jar. Approximately 34% are white, and the rest are black. How many black marbles are there?

4,394

If 34% of the marbles are white, then 66% must be black.
(0.66)(6,657) = 4,393.62

Patrick is coming home from vacation in Costa Rica and wants to fill one of his suitcases with bags of Costa Rican coffee. The weight limit for his suitcase is 22 kilograms, and the suitcase itself weighs 3.2 kilograms. If each bag of coffee weighs 800 grams, how many bags can he bring in his suitcase without going over the limit?

23

22 kg − 3.2 kg = 18.8 kg remaining for coffee
18.8 kg = 18,800 g
18,800 g × 1 bag of coffee/800 g =23.5 bags of coffee
Round down to 23 bags. Although 23.5 would normally round up to 24, a 24th bag of coffee would cause the suitcase to exceed the weight limit.

5 numbers have an average of 16. If the first 4 numbers have a sum of 68, what is the 5th number?

12

The average of 5 numbers is the sum of the numbers divided by 5. Multiply the average by 5 to find the sum; subtract to find the 5th number.
$sum\over5$ =16
sum = 16 × 5 = 80
80 − 68 = 12

$(3+5)^2 + 24 ÷ 16 -5 ÷ 2$
Simplify the expression. Which of the following is CORRECT?

63

First complete the operations in parentheses:
$(3+5)^2 + 24 ÷ 16 -5 ÷ 2$
$(8)^2 + 24 ÷ 16 -5 ÷ 2$
Next solve the exponents:
$(8)^2 + 24 ÷ 16 -5 ÷ 2 = 64 + 24 ÷ 16 − 5 ÷ 2$
Then complete multiplication and division operations: 64 + 24 ÷ 16 − 5 ÷ 2 = 64 + 1.5 − 2.5
Finally complete addition and subtraction operations: 64 + 1.5 − 2.5 = 63

A bike store is having a 30%-off sale, and one of the bikes is on sale for $385. What was the original price of this bike?

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