Factorials sometimes appear on your ASVAB Mathematics Knowledge exam and, just like exponents in the previous section, are easy marks! Factorials are mostly used in probability but this subject per se does not appear on your exam. However, solving basic factorials do appear, and we’ll look at two such examples here to cement its simplicity in your mind.,

Q. Solve 6!

To solve a factorial question such as this, you need to break 6 down. So, 6! (where ! is pronounced as ‘factorial’), you simply need to solve 6 x 5 x 4 x 3 x 2 x 1. When you multiply these numbers out, the solution is 720. Similarly, if you were ask 4!, all you would need to do is solve 4 x 3 x 2 x 1.

Q. 5! x 4!

In this question, you need to rewrite the question in the following way:

The same is true if you wanted to divide 5! by 4! as it would be presented as the following:

All in all, solving factorials is very easy, particularly when you understand what the (!) actually stands for. You should have no problem answering a factorial question if it appears on your exam – it’s some of the easiest marks you could pick up.

John has $2,000 in his bank account and receives 3% interest per year. What will John’s balance be at the end of two years?

In this type of question, you’re asked to calculate the amount of interest John will earn over a two year period. In order to tackle this question, we must first calculate how much interest John will earn after 1 year. To do this, we simply calculate 3% of $2,000.

So at the end of Year 1, John will have $2,060 in his bank account. Now, in order to calculate how much he’ll have at the end of Year 2, we must get 3% of $2,060, as evidently this will be the amount present in his account. Many candidates make the mistake of doubling $60 and assuming the interest is the same for both years. This is an error.

Even though it’s only a difference of $1.80 on the previous year, we must include it if we’re to answer the question correctly. This means that John will have accrued $60 from Year 1 and $61.80 from Year 2, giving a total interest accrual of $121.80. This means that John will have $2,121.80 in his bank account at the end of Year 2, all else being equal.

In this section, we’re going to take a look at five short questions that regularly appear on the ASVAB Mathematics Knowledge exam – all pertaining to the topic of numbers.

What is the square of five, and what is the cube of five?

The cube of five is written mathematically as 5^3 – which is the same as 5 x 5 x 5. The answer is 125.

The square of five is written mathematically as 5^2 – which is the same as 5 x 5. The answer is 25.

What is the fourth root of 81?

The fourth root of something is any number, N, to the power of 4, written as N4, where N is any regular number (a regular number, such as 1, 5, and 16, are also known as integers!).

These questions are quite easy to solve! After all, 24, or 2 x 2 x 2 x 2 = 16, while 34, or 3 x 3 x 3 x 3 = 81. You can see how the numbers get quite high quite quickly. You won’t be asked any fourth root greater than the number of 5, and such a number would be 5 x 5 x 5 x 5 = 625.

Of the following numbers, which is a prime number?

A prime number is a number that can only divide into itself or 1. For these answers, only the number 17 qualifies for this purpose. 9 for example, can divide into itself (9) or 1, but the number 3 also divides into it! The same is true for 27, while the numbers 2 and 7 can divide into 14.

Find the mean, median, mode, and range for the following numbers:

The mean is the same as the average. This means we total up all the numbers and divide this total by the number of numbers in the list.

The median is the middle value found in your list. To discover this value, we need to align the numbers in numerical order:

As we have 9 numbers, we cannot choose a central number as it isn’t even. So, to get around this, we use the following formula: (Amount of Odd Numbers) + 1 divided by 2. This means we have 9 +1, or 10, divided by 2, which is 5. This means the median is the fifth number, or 14.

To find the mode, we simply need to select the number repeated the most times. Given that 13 appears more times than any other number, 13 is the mode of the list.

To find the range, we simply find the highest value number (21) and the lowest value number (13) and find the difference between them: 21 – 13 = 8. So, the range of this list is 8.

Solve √64+ √91

In this question, we need to use square roots. You should be familiar with the word ‘square’ by now, as it was this word we used to describe anything to the power of two – such as 52, 82, or 122. The square root, as symbolized by √, is the symbol we use to reverse a squared number. For instance, five squared, or 52, is the same as 5 x 5, which is obviously 25. If we take the square root of 25, or √25, we return back to the number 5. It’s that simple. In the example here, the square root of 64 is 8 – why? – as 82, or 8 x 8, equals 64. So, the answer to this problem is 8 plus 9, which is 17.

What is the next number in the following sequence: 5, 6, 8, 11, 15, 20, ?

In sequences, you need to work out the logical pattern in a given sequence. In this particular sequence, we can see how each number is added according to the following pattern: 1 + 2 + 3 + 4 + 5. For instance, we add 1 to 5 to make 6, we add 2 to 6 to make 8, we add 3 to 8 to make 11 etc. Thus, given that the preceding difference between 15 and 20 is 5, we can confidently suggest the next number in the sequence is 26. While sequences aren’t the most prolific type of question in the ASVAB Mathematics Knowledge exam, you should nonetheless be aware of its form and how to answer it should it make an appearance.

In the final part of our numbers section, we’re going to take a quick glance at the importance of understanding reciprocals and rounding.

What is the reciprocal of 1/5?

The reciprocal value of a number is basically what the number looks like in reverse. In this case, the reciprocal of 1/5 is 5/1 or, put simply, 5. After all, 5/1 is the same as 5. We could posit many more examples: the reciprocal of 7/8 is 8/7 and the reciprocal of ¾ is 4/3. It really is that simple. However, if we were asked to find the reciprocal of:

We would need to turn this regular fraction into what’s known as an improper fraction. You can create an improper fraction by multiplying the denominator (the bottom number of a fraction) by the integer (2) to make 6, and add the numerator (the top number of a fraction) to make 7. This turns the fraction into 7/3, and the reciprocal of this is 3/7. So, if a fraction like this were ever to appear on your ASVAB Mathematics Knowledge exam, be sure to first convert it into an improper fraction before reciprocating it to find the answer.

Round the following numbers to the nearest whole number:

A whole number is something like 4, 5, and 6 – in other words, a number with no relevant decimal places. When you are asked to ‘round’ a number, you’re usually expected to eliminate the decimal places to attain a clean round number. In the case of (a), we simply need to round the number up to 2, as 1.6 is nearer to 2 than it is to 1. In the case of (b), however, you need to keep in mind that every time a .5 decimal place appears, you always round up and never round down. So, 2.5 rounds up to 3 as opposed to down to 2. In the case of the final example, given that 0.4 is nearer to 0 than it is to 1, the nearest whole number is 0. If the number were 0.5, however, we would be rounding up to 1.