Quantitative Reasoning

Question 0

If a problem says that two objects began moving at the same time, but at different speeds, and asks you to calculate the distance that one of the objects travels before crossing the path of the other object, how do you solve this problem?

Answer 0

• -Derive separate rate equations for each object each equal to time
• -You now can set each equation equal to each other because their times are equal

Question 1

If a problem says that two objects began moving at different times, and at different speeds, and asks you to calculate how long it will take the object that started later to catch up, how do you solve this problem?

Answer 1

Derive two separate rate equations and set them equal to distance
–The amount of time each object has been traveling will be different, but you can set the distances equal to each other as each object will have to travel the same distance in order to eventually be at the same place (“catching up”)

Question 2

What is formula to convert between Celsius and Fahrenheit?

Answer 2

C=(5/9)*(F-32)

Question 3

How many pounds are in 1 kg?

Answer 3

2.2 pounds

Question 4

How many questions should you use the calculator on?

Answer 4

Two maybe three tops. The calculator takes way too long to use, so practice without a calculator

Question 5

When you run into rate or distance problems, what is the best way to solve them?

Answer 5

Set up a chart with your knowns and unknowns. This way you will easily see what it is you need to solve

Question 6

What is the mode of 2,2,3,3,4,4 ?

Answer 6

None. If every number in a list occurs the same amount of times, there is no mode

Question 7

How do you always solve average rate problems when you’re only working with one individual, or one object?

Answer 7

AVG. RATE = Total Distance / Total Time

Question 8

What should you do when you come to a variance or standard deviation question?

Answer 8

If the numbers are small go for it, otherwise mark it for later cause you are really good and fast at these problems
–The math is not difficult, it just MAY take more time than other problems

Question 9

What are the four steps to solving a variance or standard deviation problem?

Answer 9

1. Find the mean of the data
2. Subtract the mean from each of the numbers in the data set
3. Square each of the results from step 2
4. Take the average of the numbers from step 3

Question 10

In layman’s terms what is probability

Answer 10

Probability=(what you want to happen) / (everything that could happen)

Question 11

How do you find a probability that one OR another of two mutually exclusive events occurs?

Answer 11

ADD the probability of the two events together

Question 12

How do you find a probability that one AND another of two independent events occurs?

Answer 12

MULTIPLY the probabilities of the two events

Question 13

What is the formula for combinations?

Answer 13

n!/ (k!*(n-k)!)

Question 14

What is the formula for permutations?

Answer 14

n!/ (n-k)!

Question 15

How do you calculate the volume of a cone or pyramid?

Answer 15

(1/3)(area of base)height

Question 16

What is the most important thing for you to remember in the quantitative reasoning section?

Answer 16

Quickly mark the questions that you will be able to solve but you know will take a little bit of time. Get to the algebra, geometry, and trick questions!!!! THESE QUESTIONS ARE A PIECE OF CAKE FOR YOU AND YOU CAN DO THEM IN SECONDS, SO DON’T LOSE THOSE POINTS BY WASTING TIME DOING QUESTIONS THAT TAKE AWHILE

Question 17

What is the volume of a cone?

Answer 17

(1/3)(pir^2)*h

Question 18

What is the lateral area of a cone?

Answer 18

(1/2)CL

where C=the circumference of the base
L=length of slanted edge (as opposed to the vertical height)

Question 19

How do you solve problems that inscribe a square or rectangle into a circle and ask you to solve for a particular shaded region?

Answer 19

Use your knowledge of angles inside of the rectangle (look for equilateral triangles) and solve for the area of the sector, then subtract out the area of the triangle left over

Question 20

What is the volume of a pyramid?

Answer 20

(1/3)BH

Question 21

What is the work formula?

Answer 21

(Product of the individual times) / (sum of the individual times)

Question 22

What is 3/5?

Answer 22

0.6

Question 23

What is 2/5?

Answer 23

0.4

Question 24

How do you take the square root of a decimal?

Answer 24

If you want to take the square root of a decimal, count the number of places after the decimal hundred square root. Your answer will have half as many places after the decimal

Question 26

How many different ways can you arrange n objects?

Answer 26

n!

Remember you only do combinations and permutations if you are trying to figure out how to order more than one thing out of a given number of options (i.e. you are planning on hanging two different pictures on your wall, and you have 10 different pictures to choose from, how many different options do you have…)

Question 27

What is one of the identities that relates sin(x) to cos(x) and vise versa?

Answer 27

sin(90-x)=cos(x)

cos(90-x)=sin(x)

Question 28

What is the decimal equivalent to 12.5%

Answer 28

1/8, or 0.125

Question 29

How do you calculate the square root of a decimal?

Answer 29

Use the “gateway technique” first, and calculator second. For example, find sqrt(0.55). Well this will be between sqrt(0.49) and sqrt(0.64). Thus the answer will be between 0.7 and 0.8.

Question 30

How can you quickly rank a list of fractions, or decide which fractions from a list is the largest?

Answer 30

First inspect the fractions and eliminate any that are clearly smaller than any other. Next, cross multiply two, the one whose numerator was used to produce the larger number will be the larger fraction. Continue this approach until you isolate the largest fraction

Question 31

How do you convert 9 and 1/2 into an improper fraction (when the numerator is larger than the denominator)?

Answer 31

Find a way to make the whole number divisible by the same number as the denominator of the mixed part of the fraction, then add the two together. (Ex, for 9 and 1/2, convert 9 into 18/2 and then add that to 1/2 to get 19/2).

Question 32

How many kilometers are in 1 mile?

Answer 32

1.61 km/mile

Question 33

What is a metric ton?

Answer 33

1000kg

Question 34

What is the interest equation?

Answer 34

F.V.=P.V.(1+i)^n
F.V.=future value
P.V.=present value
i=interest
n=number of years