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12 Cards in this Set

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What is the procedure for finding the last digit in a multiplication?
1. Multiply the unit digits together.

Example:

5^2*9^2*4^3

5^2=25
9^2=81
4^3=64

Therefore 5*1*4=20, thus the last digit is 0.
What happens when the numerator and denominator both increase by the same value?
When the numerator and denominator increase by the same value the fraction gets closer to 1.
What is a quick way to compare two fractions?
Cross multiply.

Example.

Which fraction is greater 7/9 or 4/5?

Cross multiply:

7*5 4*9
35 < 36

Thus 4/5 is greater.
What is benchmarking and when do you use it?
When you find seemingly complicated fractions on the GMAT, use Benchmark Values to make sense of them.

Example:

Which is greater: 127/355 or 162/320.

If yu recongize that 127 is less than half of 255 and 162 is more than half of 320 you will save yourself a lot of cumbersome computation.
What is the simple interest formula?
principal * rate * time.

Example:

$5000 invested for 6 months at an annual rate of 7% will earn $175 in a simple interest. Principal = $5000, Rate = 7%, or 0.07, Time = 6 months or 0.5 years.

PRT = 5000*0.07*0.5=175
What is the compound interest formula?
P*(1+r/n)^nt

P is principal
r is rate
n is number of times per year
t is number of years.

5000 invested for 1 year at a rate of 8% compounded quarterly will earn approximately 412.

5000*(1+0.08/4)^4*1=5412.
Chemical Mixture problem.
Example.

500 ml solution is 20% alcohol by volume. If 100 ml of water is added what is the new concentration of alcohol.

Original solution
Substance Amount Percentage
Alcochol 100ml 20%
Water 400ml 80%
Total 500ml 100%

New solution
Substance Amount Percentage
Alcochol 100ml
Water 500ml
Total 600ml

100ml/600ml=16.6%
Express as a decimal:

1/8?
0.125
Express as a decimal:

1/6?
0.166
Express as a decimal:

5/4?
1.25
Express as a decimal:

4/3?
1.33
1/16
0.0625