Theory from GMAT OG

Question 1

how to solve simultaneous equation quickly? x+y+z=180, x+y=80

Answer 1

treat x+y as one variable (if you have one expression in terms of two variables instead of in terms of one)

Question 2

1. what is ratio
2. examples of ratio
3. what is important in ratio
4. when is this not important? (exception!)

Answer 2

1.
ratio is how much of something you have per unit of something else, expressed in smallest integers (so that neither number is a decimal!) = how much you have for (every time you have) y units of something else.

2.

• x:y
• x/y
• x to y

3.
order of numbers is important, because ratio of something given a number of y must be expressed as something:y !!! (not the opposite way around, otherwise for every given unit of y you get a different (smaller than one instead of larger than one or viceversa) decimal number)!!!

4.
order of fraction is unimportant when x and y have same ABSOLUTE value (might have different signs), because ratio will always = 1 or -1.

Question 3

what is a proportion and how can you solve?

Answer 3

• proportion is an equality of ratios (two things have different magnitude (they are not expressed as x:1 (number given one unit of y) or as number given a specific units of y), but different units of y, so that units of x will also differ, but differ in the same proportion. A proportion is saying that two ratios are the same but just elongated / shrunk
• you can solve by cross multiplying!!

Question 4

what is a fraction?

Question 5

• compound interest (p.46)
• how to find if some percentages add up to a certain numerical value (p.47)
• how to solve questions that tell you cross percentages? (p.48)

Answer 5

• formula is principal*(1+i)^n, BUT WATCH OUT:
  i = interest for the period (if quarterly, n = interest accrued in 3 months!!! = interest / 4)
  n = number of periods (NOT of years, if quarterly, n = number of QUARTERS)!!!
  but interest stated as ANNUAL INTEREST in question, divide by number of times the specified period happens in a year to get the period’s interest i !!!
• construct table!!! with sum of rows and column’s percentages, and solve to find cell percentages by knowing that each cel must add up to the rows / columns sum
• either multiply total by percentage or find out a numerical value (e.g., 70) and know how much 70/TOT is in n% !!! If a certain percentage = n% then the number it corresponds to is 70, otherwise number is lower if percentage is lower than n% or number is higher if percentage of it is higher than n% !!!

Question 6

1. how to find percentage increase or decrease?
2. what is a negative decrease???
3. properties of percentage increases and decreases?

Answer 6

1.
find number value of increase / decrease, then divide it by the original value

2.
increase

3.

• can be larger than 100%!!!
• vary depending on size of starting value (if larger starting value, same change corresponds to lower percentage. If larger starting value, same percentage change amounts to a larger number change compared to same percentage change in a smaller starting value).

Question 7

1. double discount formula

2. how to solve exercise

Answer 7

1.
double discount exercises are when a discount is applied to a value, which is then further discounted

2.
to solve double discounts, be aware that new value = middle value * (100%-discount2%) = value * (100%-discount1%) * middle value * (100%-discount2%)

Question 8

sometimes percentages are applied to these formulas, so write formulas:

• gross profit
• simple annual interest
• compound interest

Answer 8

• gross profit = selling price - cost
• principal * simple interest * time (as a fraction of a year)
• principal * (1+i)^n (i and n converted correctly depending on period)

Question 9

what is the relation of productivity, time, and units produced?

Answer 9

• productivity = units/1unit of time
• so, time needed = units/productivity !!!
• and, units produced = time * productivity

Question 10

standard formula to complete WORK problems

Answer 10

1/r + 1/s = 1/h
where 1 is a task to be completed (e.g. 1000 bolts)
and r and s are the times it takes for person A and person B to complete the task (which can be completing 7 glasses)
1/h is the joint productivity = time it takes for the two people together to complete the given task (because productivity is higher, so time it takes (for 1 task) =1/prod. is lower)

Question 11

when is 1/productivity = time to complete a task?

Answer 11

when you need time to complete 1 task, because productivity = 1 !!! task / time for 1 !!! task.