General Words Problems Flashcards
is
=
was
=
has been
=
years older
+
years younger
-
less
-
times
*
fewer
-
as many
*
factor
*
Age problems
In nearly all the age problems, we are presented with ages at a different point, so
1st: Define the present day using a variable
2nd: If we need to represent the age in the present-day then add that variable
3rd: If we need to represent the age in the past, we subtract from that variables
Length Problems
-> typically ask us to that something has been cut into segments and we need to determine the lengths of one or more pieces
To determine it:
1st: Let each piece represent different variable
2nd: The sum of all the variables will be equal to the whole rope
Total cost of item purchased
price per item * number of items
Price per item
numbers of identical items purchased
Profit
Total Revenue - Total Cost
-> Profit = Total Revenue - [ Total Fixed Cost + Total Variable Cost]
Splitting the Cost
i.e:
if 10 poeple were to split the cost of a bill that was d dollars, the cost per person would be d/10 dollars. If only 8 people actually split the bill, those 8 people would each pay d/8 dollars, a difference of d/8- d/10= d/40
Which salary should I choose?/ How much will I make
Two alternative ways to compensate for the job/ when the person would be indifferent
–> you can equal them to each others and by doing that we will yield a variable that will yield a same pay
Which Price Structure makes the most sense/how much will I pay
you can make the two prices equal to each other
Fraction Word Problems
i.e:
If the first friend serves himself 1/3 of the pizza and the second friend serves himself 2/3 of what remains, what fractions of the pizza will be left?
-> It would be mistake to assume that since 1/3 of the pizza was removed initially and another 2/3 was removed after that, the pizza must be gone.
-> You fail to notice that the second friend did not serve himself 2/3 of the pizza -> he served himself 2/3 of what was remained after the first amount was taken
The fractional parts of the whole numbers must sum to the whole
when the whole number or whole value is broken up into fractional parts, the sum of the fractions, as well as any remaining parts, must equal the (original) whole
Simple Interest
= Principalratetime
- > units for the rate must match the units of time (if the rate were expressed as 2 percent per month, the units for the time would have to be expressed in months)
- > GMAT will commonly present an annual interest rate for a loan or investment whose duration is less than a year
When interest rate is expressed as a variable such as z percent, use
x/100 rather than using simple x
Compound interest
A=
A= P(1+(r/n))^nt
A= future value if the investment P= initial value (principal) r= interest rate per year (expressed in decimal form) t= time (number of years) n= number of compounding periods per year
In compounding periods when interest is paid more than once
we need to match the number of compounding periods
-> we do it by making adjustment to the r/n
Linear Growth model formula
Fn= Kn+p where:
Fn = final value after the growth has occurred k = growth constant n = number of growth periods and p = original value prior to the growth
In exponential Growth
initial growth value is multiplied by a constant factor in each growth period. When exponential growth occurs the amount by which the initial value increases in each growth period is not constant
Equation: (initial value) * ( growth factor) ^growth period
In order to determine growth rate
- we need a growth driver
- > if we see a pattern, just don’t go a ahead and make assumption -> you need to know the growth driver
- > they need to explicitly tell you that something doubles, triples in certain time
Exponent decay
When exponential decay occurs, the amount of decay decreases with each successive decay period. The greatest decay occurs during the first period of the decay
One digit is often referred to as
unit digit
Whole digit term
- billion
- hundred millions
- ten millions
- one millions
- hundred thousands
- ten thousand
- one thousand
- hundreds
- tens
- ones
Decimal
- tenths
- hundredths
- thousandths
The value of two digit will follow this equation
10(Tens digit)+unit digit = the value of any two-digit number
i.e: 48 -> 40+8
Consecutive word problems
It’s helpful to let the first integer be x and add/ multiply from there
Consecutive odd and even integer can be written as
x, x+2, x+4..
Consecutive multiple can be written as
for multiple of 5: x, x+5, x+10, x+15
for multiple of 8: x, x+8, x+16….
Mixture problems can be solved using a
matrix
i.e
Price per coin * Number of coins = values
Gold Coins
Silver Coins
-------------------
MixtureMixture of problem for drinks
% of apple juice Volume of drink Total apple juice
.present
10% apple juice
17% apple drink
————————
Dry Mixture formula
rate*time = amount formula
Examples of drying mixture
1) Price per pound * number of pounds = total price
2) Fractions of class wearing shoes * number of students in the class = total number wearing shoes
3) Interest rate on bonds * value of bonds= Total interest
In general if you (or anyone) are the mth person counted from the beginning of the line and the nth person counted from the end of the line, then the number of people waiting in the line is
m+n-1
i. e:
- If you are the 10th person, counting from the beginning of the line, there are 9 people in front of you
- If you are the 15th person, counting from the end of the line, there are 14 people behind you
- > 9+1+14= 24
- > 10+15-1= 24
