GRE arithmetic
Terms
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using the average to find the missing number:
ave of 4 numbers is 7. if 3 of the numbers are 3,5, and 8, what is the 4th number?
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To find the missing number when there is an average, use the sum:
- sum=(ave)x(# of terms)
- sum=4x7=28
- add the known numbers, subtract from sum, giving you the 4th number
- 3+5+8=16
- 28-16=12 (the 4th number)
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- average
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ave=(sum of terms)/(# of terms)
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average of consective numbers
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ave of evenly spaced numbers:
- ave the smallest and largest
- (a+z)/2
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average rate
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ave A per B=(total A)/(totaol B)
ave speed= (total dist)/(total time)
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comparing fractions
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- reexpress fractions with a common denominator
- or convert both to decimals
3/4=21/28 and 5/7=20/28 (21/28 is greater)3/4=0.75 and 5/7=0.714 (0.75 is greater)
- converting eighths
- 1/8= 0.125= 12 1/2%
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converting fifths
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1/5 = 0.2 = 20%
- converting fourths
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1/4 = 0.25 = 25%
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converting fractions to decimals
- divide the bottom into the top
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converting tenths
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1/10 = 0.1 = 10%
- converting thirds
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1/3 = 0.333... =33 1/3%
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counting consecutive integers
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to count consectutive integers:
- subtract the smallest from the largest
- add 1
31-13=18
18+1=19
- subtract the smallest from the largest
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distance, rate, time
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distance= rate x time
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dividing fractions
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invert the second one and multiply
- factors
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Factors: + integers that ÷ into n w/no remainder
Multiples: integers that n ÷ into w/ no remainder
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Greatest common factor (GCF)
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- break down numbers into their prime factorizations
- take all the prime factors they have in common
- multiply together for GCF
36=2x2x3x3
48=2x2x2x2x3
GCF=2x2x3=12
- integer
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- a multiple of 1
- include negetive whole #'s
- includes 0
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Least Common Multiple (LCM)
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the smallest number that can be divided into a number:
LCM of 12 and 15?
60 (12 and 15 can both divide into it)
- median
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- the middle value
- if there is an even # of values, the median is halfway b/t the 2 middle values
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multiples of 2 and 4
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an integer is:
- divisible by 2 if the last digit is even
- divisible by 4 if the last 2 digits make a multiple of 4
- multiples of 3 and 9
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divisible by 3
- sum of digits is divisible by 3
divisible by 9
- sum of is digits is divisible by 9
- sum of digits is divisible by 3
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multiplying fractions
- mult. numerators and multiply the denominators
- percent
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Percent: a fraction w/an implied denominator of 100.
32% = 32/100 = 8/25
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percent increase
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To increase a number by a percent:
- add the percent to 100%
- convert to a decimal
- multiply by the number
25%>40?
- 25%+100%=125%
- 125%=1.25
- 1.25 x 40=50
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Prime numbers
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Positive integer that is divisible only by 1 and itself.
Smallest and only even prime # is 2
- probability
- probability= (# of desired outcomes)/(total # of possible &
- reciprocal
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reciprocal of a fraction:
- switch the numerator and the denominator
- the product of reciprocals is 1
- remainder
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487 is 2 more than 485, which is a multiple of 5.
when 487 is divided by 5, the remainder is 2
- using a ratio to find a number
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If the parts add up to the whole, a part-to-part ratio can be turned into 2 part-to-whole ratios by putting easch number in the original ratio over the sum of the numbers.
1:2 men:women in a group of 18 people. how many women are there?
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using the ave to find the sum
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sum=(ave)x(#of terms)