Question 1

When formulating answers to market-sizing questions, what's one of the best strategies to keep in mind?
A)Be sure to use exact numbers at all times.
B)Go slow and be as methodical as possible.
C)Estimate and round numbers whenever possible.
D)Pick odd numbers that aren't related to each other in any way.

Accepted Answer

Estimating and rounding numbers is a key skill in getting through questions as quickly as possible.
Key Takeaway: Before formulating your answer, take a moment to choose your numbers carefully
be sure to pick rounded numbers that work easily together, making your arithmetic much less of a headache.

Question 2

What is the ratio of 8 feet to 28 inches?
A)2:7
B)7:24
C)24:7
D)7:2
E)5:3

Accepted Answer

24:7. When comparing distances, we have to "speak the same language", so we first have to get both distances in a common unit. In this case, convert 8 feet to inches by multiplying by 12, therefore 96 inches. Then, the ratio in inches is 96:28. Reduce the two numbers by 4, which results in a ratio of 24:7.
Key Takeaway: When comparing two quantities, it is important to work in the same unit. It is much easier to compare inches with inches, rather than feet with inches, or minutes to minutes, rather than minutes to days.

Question 3

What is 1/7?
A) .142857
B) .153
C) .12
D) .125
E) .144

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 4

Seven/Twelve has $4 million in sales over the past week. What were the approximate sales per day?
A) $589,000
B) $571,000
C) $518,200
D) $552,000
E) $578,750

Accepted Answer

$571,000 4 million divided by 7 days is an average of $571,429 per day.
Key Takeaway: Dividing by seven is an important skill because of the week unit is frequently used. If you remembered the repeating decimal we gave you earlier, all you have to do is move it over in this question.
1/7 = .142857
2/7 = .285714
3/7 = .428571
4/7 = .571428
5/7 = .714285
6/7 = .857142

Question 5

What is 2/9?
A) .17
B) .19
C) .1818
D) .2222
E) .235

Accepted Answer

2/9 is .22222… The 2s repeat forever.
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 6

What is 3/8?
A) .36
B) .38
C) .375
D) .3833
E) .365

Accepted Answer

3/8 is .375.
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 7

What is 5/6?
A) .8
B) .8444
C) .8333
D) .825
E) .875

Accepted Answer

5/6 is equal to .8333. The 3s repeat forever.
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 8

It is sunny on 83% of the 120 days Silver Slides Waterpark is open on average. How many days will Silver Slides be open this summer?
A)100
B)102
C)98
D)99
E)92

Accepted Answer

100. 83% is equal to approximately 5/6. 5/6 times 120 is equal to 100.
Key Takeaway: Covert tricky percentages into fractions that are easy to work with.

Question 9

What is 1/11?
A) .095
B) .0909
C) .0888
D) .9414
E) .142857

Accepted Answer

1/11 is .090909. The zero and nine repeat indefinitely.
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 10

What is 5/12?
A) .41666
B) .42
C) .4333
D) .41333
E) .415

Accepted Answer

5/12 is .41666. The 6s repeat forever.
Key Takeaway: Things frequently come in dozens, so dividing by 12 in case interviews can be quite common.
1/12 = .83333
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 11

Every five minutes a baby is born in the Nigindia. How many babies are born in a year?
A)150,120
B)105,120
C)100,510
D)300,450
E)103,555

Accepted Answer

There are 60 minutes in an hour, thus 60/5 minutes is 12. Multiply that by 24 hours in a day which is 288 per day. 288 x 365 days is 105,120 babies per year.
FYI, close to 4 million babies are born a day in the United States. That's one nearly every 14 seconds!
Key Takeaway: Get good working with 7, 12, 24, 30 and 60. Units of time are frequently used. Days, months, hours and minutes are frequently calculations you will have to make.

Question 12

A man buys a piece of land at auction which is 256 feet by 10 yards. How many acres did he buy? There are 43,560 feet in an acre.
A) .059 acres
B) .59 acres
C) 1.76 acres
D) .0176 acres
E) .176 acres

Accepted Answer

.176 acres
To find the area of the piece of land multiply 256 x 30 feet (10 yards x 3 feet)
which is 7,680 square feet. Then divide by the number of square feet in an acre (43,560) and you'll get .176 acres rounded off to the nearest hundredth.
Key Takeaway: Dividing small numbers by big ones is common. Practice getting your decimal places right. Also, notice in this question that you were given one unit in feet, and one in yards. That is testing whether you are listening/reading carefully.

Question 13

A car that regularly sells for $29,600 has been marked down to $22,100. What is the approximate percentage of the discount?
A)20%
B)22%
C)25%
D)30%
E)33%

Accepted Answer

First, determine the amount of the markdown in dollars (29,600
22,100 = 7,500). Then, divide the total markdown of $7,500 by the original price of $29,600, which results in 0.2533. Move the decimal point two places to the right, to determine that the markdown is a little over 25%.
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 14

The population of the town of Homeville increased by approximately 0.5% last year. If the population at the beginning of the year was 2,460, what was the approximate population by the end of the year?
A)2,472
B)2,960
C)2,465.
D)2,465
E)2,510

Accepted Answer

This problem is asking you to find ½ of 1 percent change of 2,460. To do this mentally, first determine what 1 percent of the original number is, then half that. In this case, 1% of 2,460 is 24.6, and half of that is 12.3. Since you can't have 3/10 of a person, we can approximate the population increase as 12 people. Add that to the initial 2,460 to find that the new population is 2,472.
Key takeaway: There are many types of percent problems you may encounter. It will be helpful to you if you know that you find 10% of a number by moving the decimal one place to the left and 1% of a number by moving the decimal point two places to the left.

Question 15

Last year, Smith's Auto Shop made gross revenue of $460,000. This year, their gross revenue increased significantly - by an amazing 25%. What was the gross revenue this year?
A)$525,000
B)$550,000
C)$560,000
D)$575,000
E)$585,000

Accepted Answer

To find 25% of a given number, simply halve the number, then halve it again. In this example, half of 460,000 is 230,000, then half of 230,000 is 115,000. Therefore, 25% of $460,000 is $115,000. Add $115,000 to the original $460,000 to find the gross revenue for the year
$575,000.
Key takeaway: It is helpful to know shortcuts for mentally calculating certain percentages. To find 10% of a number, drop the last digit. To find 20% of a number, drop the last digit, and double the resulting number. To find 25% of a number, halve the number twice.

Question 16

Olivia has $5,000 to invest. She invests in a fund at 4% interest. How long will it take for her money to double?
A)10 years
B)12 years
C)15 years
D)18 years
E)20 years

Accepted Answer

To calculate this answer mentally, use the Rule of 72. To determine how long it takes for something that grows to double (in this case, an investment; other examples
GDP, population), divide 72 by the rate of growth. In this example, Olivia's money would double in 18 years (72/4).
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 17

A small firm allocates 28% of its gross profits into an account for insurance. Last year, the firm's gross profit was $400,000. What amount was deposited into the insurance account?
A)$100,000
B)$108,000
C)$109,500
D)$112,000
E)$128,000

Accepted Answer

To calculate this mentally, use this idea: x% of y = y% of x. Therefore, 28% of 400,000 is the same as 400,000% of 28. Multiply 4 x 28 to get 112, then add the zeroes back at the end ($112,000). You know that this is a reasonable answer because 28% is a little over ¼, and ¼ of 400,000 is 100,000.
Key Takeaway: When you are calculating percentages of round numbers, it is helpful to know that x% of y is the same as y% of x.
Using this, you are often doubling, tripling, or multiplying by a single number, then adding the zeroes back at the end.
This takes some practice, but it works well for some people.

Question 18

Brian is opening a small sporting goods store. After considering her market, she sets her initial sales goal at $32,000 a month. He knows that the rent for his store should be about 8% of sales. Approximately what should he plan to pay for rent, based on the sales figure given?
A)$2,400
B)$2,560
C)$3,200
D)$3,260
E)$3,305

Accepted Answer

8% of $32,000 is $2,560.
A mental shortcut for multiplying by 8 is to multiply the number by 10, then subtract the original number twice. In this example, multiply 32,000 by 10, which equals 320,000. Then subtract 32,000 twice (320,000
32,000 = 288,000; 288,000
32,000 = 256,000).
Remember, that you are considering 8 percent, so move the decimal point two places to the left, to reach an answer of $2,560. We know this is a reasonable answer because 10% of $32,000 would be $3,200, so the answer is only slightly less than that.
Key Takeaway: It is easy to calculate percentages that are near 10%. To multiply by seven
(to find 7% of a number), for example, you would multiply by 10, then subtract the original number three times. To multiply by twelve (to find 120%), you would multiply by 10, then add the original number twice.

Question 19

Shane's Softball Production Company can produce 12 softballs in an hour. How many softballs can they produce in 14 hours?
A)154
B)160
C)168
D)172
E)188

Accepted Answer

168 softballs. Although this is not a difficult problem, and could be calculated mentally, perhaps by multiplying 14 by 10 (140), then adding 2 more 12s to the answer.
However, there is a trick that allows you to multiply numbers close to ten together within seconds.
First, consider the problem: 14 x 12
Using the 2 in 12, add it to 14: 16 (these are the first two digits of the answer).
Using the 2 in 12, multiply it by the 4 in 14: 8 (this is the last digit of the answer).
Thus, the answer to 14 x 12 is 168.
It works for larger numbers in the teens, but those involve "carrying".
Consider the problem: 17 x 14.
Using the 4 in 14, add it to 17: 21
Using the 4 in 14, multiply it by the 7 in 17 (28). The 8 is the last digit of the answer. Carry the 2 over, and add it to the 21 from the previous step to get 23. The answer to 17 x 14 is 238.
Key Takeaway: Sometimes you will find it necessary to multiply numbers in the teens together. With practice, this strategy will allow you to perform that calculation mentally, both quickly and accurately.
Again, this is a trick that requires lots of practice that works for some, and doesn't work for others.

Question 20

Greg's Golf Shop hires teenagers to collect lost golf balls from the city's golf courses. The golf balls are then packaged in boxes of a dozen for reselling. This summer, the workers collected 2,244 golf balls. After repackaging, how many golf balls will be left over?
A)2 golf balls
B)3 golf balls
C)4 golf balls
D)6 golf balls
E)No golf balls will be left over

Accepted Answer

They will all fit into the boxes, with no leftovers. This problem is asking you whether 2,244 is divisible by 12. It is, because 2,244 is divisible by both 3 and 4 (which is how you tell if a number is divisible by 12).
Key Takeaway: There are quick ways to tell if a large number is divisible by smaller ones.
A number is divisible by 2 if its last digit is even.
A number is divisible by 3 if, when you add all 3 digits together, that sum is divisible by 3.
(In the answer above, adding 2+2+4+4 = 12; 12 is divisible by 3, so 2,244 is as well.)
A number is divisible by 4 if the last 2 digits of the number is divisible by 4.
(In the answer above, 44 is divisible by 4, so 2,244 is divisible by 4.)
A number is divisible by 5 if the last digit is 5 or 0.
A number is divisible by 6 if it is even, and divisible by 3.
To determine if a number is divisible by 7, take the last digit, double it, then subtract it from the rest of the number. If the resulting number is divisible by 7, the original number is. For example, consider 132.
Take the last digit (2), double it (4), then subtract that from the rest of the number (13). 13-4 is 9. Nine is not divisible by 7, so 132 isn't either.
A number is divisible by 8 if the number formed by its last 3 digits is divisible by 8.
A number is divisible by 9 if, when you add the digits together, that sum is divisible by 9.

Quiz 2: Math: Math Tricks

When formulating answers to market-sizing questions, what's one of the best strategies to keep in mind?

What is the ratio of 8 feet to 28 inches?

What is 1/7?

Seven/Twelve has $4 million in sales over the past week. What were the approximate sales per day?

What is 2/9?

What is 3/8?

What is 5/6?

It is sunny on 83% of the 120 days Silver Slides Waterpark is open on average. How many days will Silver Slides be open this summer?

What is 1/11?

What is 5/12?

Every five minutes a baby is born in the Nigindia. How many babies are born in a year?

A man buys a piece of land at auction which is 256 feet by 10 yards. How many acres did he buy? There are 43,560 feet in an acre.

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

The population of the town of Homeville increased by approximately 0.5% last year. If the population at the beginning of the year was 2,460, what was the approximate population by the end of the year?

Last year, Smith's Auto Shop made gross revenue of $460,000. This year, their gross revenue increased significantly - by an amazing 25%. What was the gross revenue this year?

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

A small firm allocates 28% of its gross profits into an account for insurance. Last year, the firm's gross profit was $400,000. What amount was deposited into the insurance account?

Brian is opening a small sporting goods store. After considering her market, she sets her initial sales goal at $32,000 a month. He knows that the rent for his store should be about 8% of sales. Approximately what should he plan to pay for rent, based on the sales figure given?

Shane's Softball Production Company can produce 12 softballs in an hour. How many softballs can they produce in 14 hours?

Greg's Golf Shop hires teenagers to collect lost golf balls from the city's golf courses. The golf balls are then packaged in boxes of a dozen for reselling. This summer, the workers collected 2,244 golf balls. After repackaging, how many golf balls will be left over?