You might not be familiar with the phrase “quantitative aptitude questions,” but you have surely been subjected to these types of questions on standardized and specialized testing. Quantitative aptitude is a measurement of a person’s numerical ability and accuracy in mathematical calculations. These are what the average person knows as “math and reasoning” problems.

You will find these kinds of questions on exams such as the Common Aptitude Test (CAT), the Miller Analogies Test (MAT), the GRE, GMAT, CSAT, CLAT, ICET, UPSC, SSC, SNAP, KPSC, XAT and many, many others. Almost any high-level testing will contain quantitative aptitude questions. There are a number of examples below, and you can learn more concepts and tips from this quantitative aptitude course for examinations and interviews.

## Averages

Let’s start with a question that challenges your ability to calculate averages.

**Question #1**

The average weight of the first 8 men on a basketball team is 60.5 kg. The average weight of the other 6 team members is 66.75 kg. What is the average weight of all the men on the basketball team?

A. 64.55 kg

B. 63.18 kg

C. 66.25 kg

D. 62.34 kg

To find an average, we need find the total weight of all the men and then divide it by the total number of men. The total number of men is easy: 8 + 6 = 14. The total weight is slightly more difficult.

First we need to find the weight of each group of men: (8 x 60.5) = 484 ; (6 x 66.75) = 400.5.

Now all that’s left to do is divide the total weight by the total number of men:

(484 + 400.5) / (8 + 6) =

884.5 / 14 = **63.18 kg**

The correct answer is B: 63.18 kg.

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## Clocks

Questions about clocks and clock faces are very common because they easily confuse the test taker. Let’s look at a question and how to avoid getting turned around.

**Question #2**

An accurate clock shows that it is exactly 9 o’clock in the morning. How many degrees will the hour hand rotate when it is exactly 3 o’clock in the afternoon?

A. 165

B. 171

C. 180

D. 183

There are two important things to keep in mind: 1) the question is asking about the **hour** hand and, 2) going from 9 o’clock in the morning to 3 o’clock in the afternoon is equal to 6 hours of passed time.

Now we need to wrap our heads around angles. We know that a clock is a circle: this means it contains 360 degrees. These 360 degrees are broken down into the 12 hours of the day. This means there are (360 / 12) degrees in an hour; or, 30 degrees in one hour. Since 6 hours pass in the question, we simple multiply (30 x 6), which gives us our answer, 180 degrees.

The correct answer is C: 180 degrees.

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## Percentages

Percentage questions are almost guaranteed to show up on aptitude tests. Here is a common example of a format you are likely to encounter.

**Question #3**

A grocer sells mangos Monday through Thursday. She sells 65% of her mangos and still has 280 mangos left. How many mangos did the grocer have originally?

A. 650

B. 700

C. 800

D. 850

There is a very simple way to arrive at the answer. You should also note that the detail “Monday through Thursday” is irrelevant information and included in the question to confuse you. It is vital to your success that you are able to recognize information that has no bearing on the answer.

The first thing we need to do is determine what percentage of the mangos equals 280. This is easy: if 65% are gone, then the remainder (100% – 65%) must equal 280. That means 280 represents 35% of the original mangos. We then set up a simple equation to find the total number of original mangos:

**35% of Mangos = 280 Mangos**

**(35 x Total Mangos) / (100) = 280 ** Note: we know that if we multiply 35% by the total, it will equal 280. We then divide by 100 because it is a percentage.

**(Total Mangos / 100) = 8 **Note: this is a simple matter of simplifying equations. I divided both sides by 35. This negates the 35 on the left side of the equation, and (280 / 35) = 8. Now we just need to do this one more time, but now we are going to multiply by 100 to balance the equation completely.

**Total Mangos = 800**

The correct answer is C: 800.

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## Probability

Probability questions are just as popular as percentages; in a way they are similar, and for this very reason they tend to be trickier. You must distinguish between probability and percentages; probability is almost always expressed as a fraction or decimal.

**Question #4**

One card is drawn at random from a pack of 52 cards. What is the probability that the card drawn is either a 2 or a face card?

A. 4/13

B. 3/13

C. 5/13

D. 6/13

We need to turn the original question into a matter of fractions, since that is how all of the answers are presented.

We know there are 52 cards in the deck. 52, then, is going to be the denominator in our fraction. But what is the numerator? All we have to figure out is how many cards the 2s plus the face cards account for: there will be four of every type of card, so: four 2s, four Jacks, four Queens, and four Kings. That gives us a total of 16 cards, which will be our denominator.

Now our equation looks like this: 16/52. If we divide by the highest common multiple (4), we get our answer: the correct answer is A: 4/13.

Get some extra free practice and advice from this blog post on probability equations and determining odds.

## Distances

Distance questions are difficult because they always include other factors: time, speed, direction, etc. We’re going to look at a question that considers speed and time.

**Question #5**

The speed of a train is 54 kmph when it is carrying passengers and not stopping. When it is carrying passengers and stopping at stations, the speed is 45 kmph. Over the course of an hour, how many minutes does the train lose to stopping at stations?

A. 8 min

B. 14 min

C. 12 min

D. 10 min

Let’s look at the facts: the total loss of speed is easy calculate: 54 kmph – 45 kmph = 9 kmph. We know the question is concerned with how many minutes are lost over the course of an hour, so we know that in one hour the train covers 9 less km (since speeds are in kilometers per *hour*).

We will use the distance/speed equation. The distance is 9 km and the speed is the original speed: 54 kmph.

**So: 9 km / 54 kmph = 1 / 6 **Note: because we are dividing numbers *and* units, the two “km” cancel out. This leaves us with just the “ph” or “per hour” designation, which means we are now dealing with *only* time (instead of time *and* speed).

However, 1/6 of an hour is not an acceptable answer. We can multiply the equation by 60 because there are 60 minutes in an hour. This gives us: **60/6 = 10**. The correct answer is D: 10 min.

## Real World Practice

While many people are interested in quantitative aptitude because of how it affects their performance in exams, some people, especially those in finance and business, need it for real world applications (and especially in interviews). Those wanting to learn how quantitative methods factor into ethics, financial reporting and analysis, fixed income and equity, corporate finance, economics, portfolio management or alternative investments should check out this five-star CFA Level 1 Workshop for Quantitative Methods and Ethics.