Question 1

What is 5/12?

Accepted Answer

Key Takeaway: Things frequently come in dozens, so dividing by 12 in case interviews can be quite common.
1/12 = .083333
5/12 = .41666
7/12 = .58333
11/12 = .916666
There is a bit of a pattern in there, but we don't think it's helpful to try to use a pattern. Rather, just take the time to memorize these 4 decimals. The rest can be reduced.

Question 2

A car that regularly sells for $29,600 has been marked down to $22,100. What is the approximate percentage of the discount?

Accepted Answer

Key takeaway: When working with markdowns, markups, and percentages in general, be aware of the quickest ways to calculate.
Also, remember that to change a decimal to a percent, move the decimal 2 places to the right, and add a percent sign. To change a percent to a decimal, move the decimal 2 places to the left, and remove the percent sign. If there is no decimal point, it is understood to be at the end of the number.

Question 3

Olivia has $5,000 to invest. She invests in a fund at 4% interest. How long will it take for her money to double?

Accepted Answer

Key Takeaway: The rule of 72 is a quick mental calculation tool that provides an estimate of how long it would take an investment to grow. To determine how long it would take for an investment to triple in value, divide 114 by the interest rate (or expected rate of return).
To determine how long it would take for an investment to quadruple in value, divide 144 by the interest rate. Remember, these are not absolute, they are estimates. However, they provide a general guideline for planning purposes.

Question 4

Kathleen projects her expenditures for purchasing office supplies to be $85/week. How much will she spend on office supplies over a 4-week time span?

Accepted Answer

$340. It is very easy to mentally multiply a number by 4. Simply double the number, then double that resulting number. In this case, 85 doubled is 170, and 170 doubled is 340.
Key Takeaway: This trick of doubling numbers twice in order to multiply by four comes in handy when you are doing calculations related to quarters, for example. This isn't a tough question, but speed is what matters here.

Question 5

In initial production of a new video game, it is discovered that the ratio of functional games to defective games is 20 to 1. If 360 games are produced, how many could be expected to be defective?

Accepted Answer

Set this problem up as a ratio: 1 out of every 20 (1/20) equal to x out of 360 (x/360). Cross-multiply to find that 18 games would be defective.
Key Takeaway: Become proficient at visualizing ratios, and setting up the cross-multiplication in Solving these relationships is singularly dependent upon setting the fractions up correctly, then doing the calculation accurately.

Question 6

What is 1/7?

Accepted Answer

Key Takeaway: If you memorize the sequence 1-4-2-8-5-7 you can calculate any number divided by 7 quickly.
1/7 = .142857
2/7 = .285714
3/7 = .428571
4/7 = .571428
5/7 = .714285
6/7 = .857142
Editor's Note: In one of my case interviews, I was asked to calculate how many $70 devices I would need to reach $2 million in revenue. Since someone had taught me this trick, I dispensed with estimating, and told the interview the answer was 28,571.428571. I got the job.

Question 7

The wholesale price of a fountain pen is $2.80. What will the new price be if a 5% increase is instituted?

Accepted Answer

Key Takeaway: Logical reasoning is critical with percent problems. Knowing how to manipulate numbers in relation to "friendly" numbers is important. For example, to find 5%, halve 10%. To find 20%, double 10%.

Question 8

An 8-year-old boy named Albert has a 10-year-old brother named Benny. Benny joins the service at 20 leaving Albert feeling bitter that he no longer has a brother to look up to. After 7 years, Albert is finally ready to make up with Benny who has been out of the service for 5 years. How old is Albert now?

Accepted Answer

There's a 2-year difference between the boys. Benny leaves to join the service at 20 and 7 years pass, making him 27. That means Albert is 25. Note that it's irrelevant that he's been out of the service for 5 years.
Key Takeaway: Not all of us love brain teasers. If this is you - don't panic! Carefully sift through what information you have, throw out the useless information and keep what you can use.

Question 9

How long will it take for Ron's $37,353 investment to double if he expects 9% returns?

Accepted Answer

Divide 72 by the rate of growth. In this example, Ron's money would double in 8 years (72/9). The rule of 72 is a quick mental calculation tool that provides an estimate of how long it would take an investment to grow double.
Key Takeaway: For a few days, practice this every time you see a growth rate in the news paper or at work.

Question 10

If the speed of a car is 200 km per hour, how may minutes does it take to travel 60 km?

Accepted Answer

You can quickly reduce that to 3/10. Then multiply 3/10 by 60 to get 18 minutes.
Key Takeaway: Again, we can't emphasize the value of being really comfortable with the time units. 60 breaks down nicely with fractions as it is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30.

Question 11

What is 2/9?

Accepted Answer

Key Takeaway: The 9s are easy if you know the trick.
1/9 = .11111…
2/9 = .22222
3/9 = 1/3 = .333333
And so on.

Question 12

What is 3/8s?

Accepted Answer

Key Takeaway: 1/8 is equal to .125.
0.125 is a pretty easy number to work with. Just multiply by your numerator. So 7/8 is .125 times 7, or .875. Dividing by 8 is pretty common, so we recommend you save yourself precious seconds by remembering this.

Question 13

What is 5/6?

Accepted Answer

Key Takeaway: Memorize 1/6 and 5/6 to speed your calculations up (trust me, it's worth it).
1/6 = .166666
5/6 = .833333

Question 14

What is 1/11?

Accepted Answer

Key Takeaway: Dividing by 11 is far less common, but if you bought this app, you're not taking any chances. To master fractions with 11 as the denominator, just multiply your numerator by 9 to figure out the repeating digits.
1/11 = .090909
2/11 = .181818
3/11 = .272727
4/11 = .363636
5/11 = .454545
6/11 = .545454
7/11 = .636363
8/11 = .727272
9/11 = .818181
10/11 =.90909

Question 15

Which type of chart or graph would be the best graphic organizer to demonstrate the relationship between foreign aid to a nation and the decrease in child mortality rates among its citizens?

Accepted Answer

Line graphs are the best graphic organizer to demonstrate a relationship between two factors over a period of time, such as the effect of foreign aid on the child mortality rate of an impoverished nation. Histograms are best suited for displaying the distribution of probability. Pie charts are best for displaying how a whole unit is divided into parts. Bar graphs are best for displaying discrete information in a comparative manner.

Question 16

What is the mean for the following expenditures? $79.84, $278.99, $342.16, $466.25, $111.39, $502.47, $98.12

Accepted Answer

The mean for the data set above is $268.46. The median or middle number when the numbers are in ascending order ($79.84, $98.12, $111.39, $278.99, $342.16, $466.25, $502.47) is $278.99.

Question 17

People who score in the 95th percentile on an exam:

Accepted Answer

A test taker who scores in the 95th percentile scored as well or better than 95% of the people who took the exam. It is a comparative measure of success that has nothing to do with the number of questions on the exam, the number of correct responses given or the "score" of the exam in a 1 to 100 grading scheme. Early education exams are typically evaluated solely on this measure. Secondary school, higher education and professional exams vary in their emphasis on this method, but most report comparative percentile scores as a frame of reference.

Question 18

On a trip to the Netherlands you spend €275 per night in a hotel, €37.58 per day on meals and €50 per day on transportation. If you were there for four days and three nights, and the exchange rate from U.S. dollars to euros was $1.00 : €0.7515, about how much did you spend altogether, in U.S. dollars?

Accepted Answer

An expense of €1175, at an exchange rate of $1.00 : €0.7515, would total $1564. The total expenses were (€275 x 3) + (€37.58 x 4) + (€50 x 4), with the final sum being €1175.32. If the exchange rate was $1.00 : €0.7515, then €1175.32 is 75.15% of the total expense in U.S. dollars. Cross-multiply €1175.32 to find the dollar value of the expense. (€1175.32 x 100) ÷ 75.15 = $1563.97.

Question 19

Jacqueline and Lee are meeting for the weekend somewhere between their cities, which are 420 miles apart. Jacqueline drives 80 mph for the duration of her trip. If they both left home at 10 a.m. and met at 1 p.m., what speed did Lee drive to reach their meeting spot?

Accepted Answer

Lee drove 180 miles at 60 mph to reach the meeting place where Jacqueline arrived after driving 240 miles at 80 mph. Jacqueline drove 80 mph for three hours, which is 240 miles altogether. If she drove 240 miles, then Lee drove what remained of their 420-mile distance, which is 180 miles. She had three hours to complete that distance which means she traveled 60 miles each hour.

Question 20

The division of your company that you oversee contains 18 employees whose total salary last year was $855,000. The average salary of all company employees with the same level of responsibility and qualifications is $50,000. Is your department above or below the company average?

Accepted Answer

The average salary of a worker in your department is $47,500, which is 5% below the company average. Divide your workers' total salary by the number of workers. There is a $2,500 difference between the average salary in your division and the company's average. $2,500 is 5% of $50,000.

Quiz 8: Mathematics