Arithmetic - PSAT Math

Let the original price = p.

After the first reduction, the price is (7/8)p

After the second reduction, the price is (5/6)(7/8)p = (35/48)p

30 miles / 1 hour * 5280 ft / 1 mile * 3600 seconds / 1 hour = 44 ft/sec

The expression must first be factored in order to be solvable. Both the numerator and the denominator can be factored, which would give

.

can be divided from both the numerator and the denominator to give

The expression can be rewritten as

The first bounce reaches a height of 175. The second bounce will equal 175 multiplied by 2/5 or 70. Repeat this process. You will get the data below. 4.48 is rounded to 4.5.

Let us assume that the original purse is $100. The price after the first reduction is $80. After the second reduction the price is now $56. The difference between 100 and 56 is 44, giving 44% off.

The original price was $50. First you take 30% off (50 * (100 - 30)/100 = $35). Then you take an additional 50% off the new price (35 * 50/100 = 17.50)

Remember, when you multiply fractions, you can directly multiply their denominators and their numerators; therefore, you can begin this problem by making it into one large fraction:

Now, you could multiply all of this out and then divide. However, you can cancel things immediately. The goes into the and the into the . Thus, you have:

If Charlie is 2 years old now; in 10 years he will be 12 years old. At that point, Alan will be twice as old as Charlie. Twice 12 is 24. This means that Alan is currently 10 years younger than 24, or 14. Since Alan is currently twice as old as Betty, she must be half of 14, or 7.

Another way to express ratios is through division. 10 divided by 14 is approximate 0.71.

Since this a combination problem and we want to know how many different ways the cookies can be created we can solve this using the Fundamental counting principle. 4 x 3 x 8 = 96

Multiplying each of the possible choices together.

Since we are only told that "at least" one of the numbers is even, we could have one even and one odd integer OR we could have two even integers.

Even plus odd is odd, but even plus even is even, so x + y could be either even or odd.

Even times odd is even, and even times even is even, so xy must be even.

Consider the possible values for (x, y):

(1, 100)

(2, 50)

(4, 25)

(5, 20)

Note that (10, 10) is not possible since the two variables are to be distinct. The sums of the above pairs, respectively, are:

1 + 100 = 101

2 + 50 = 52

4 + 25 = 29

5 + 20 = 25, the smallest possible value.

A rational number is a number that can be written in the form of a/b, where a and b are integers, aka a real number that can be written as a simple fraction or ratio. 4 of the 5 answer choices can be written as fractions and are thus rational.

5 = 5/1, 1.75 = 7/4, .001 = 1/1000, 0.111... = 1/9

√2 cannot be written as a fraction because it is irrational. The two most famous irrational numbers are √2 and pi.

Four consecutive integers could be represented as n, n+1, n+2, n+3

Therefore, by saying that they have a mean of 9.5, we mean to say:

(n + n+1 + n+2 + n+ 3)/4 = 9.5

(4n + 6)/4 = 9.5 → 4n + 6 = 38 → 4n = 32 → n = 8

Therefore, the largest value is n + 3, or 11.

First, begin by remembering that is the same as :

Next, recall that you multiply fractions by multiplying the numerators and denominators by each other. It is very simple. This would give you:

Now, you can cancel the and the :

Next, you can reduce the and the :

You can also reduce the resulting and the :

All of the values in the sequence must be a multiple of 3. All answers are multiples of 3 except 461 so 461 cannot be part of the sequence.

Profit = Revenue – Expense

% Profit = $ Profit ÷ $ Total Revenue

% Profit = ($150,000 – $75,000) ÷ $150,000 = 50%

The answer is 23. 23*$4.50 = $103.50, which is more than what Nicki earned.