GMATQ 1-6
Even * Even =
Even
Even * Odd =
Even
Even +/- Even =
Even
Odd * Even =
Even
Odd +/- Odd =
Even
Absolute value
Its distance on the number line from the origin *Ignore the sign*
Even +/- Odd =
Odd
Odd * Odd =
Odd
Proportion What does this mean 2:3::8:12 in words? whats answer to this?
Proportion: mathematical equivalent of a verbal analogy May be written as ratios or fractions i.e. 2:3::8:12 is equivalent to "two is to three as eight is to twelve" - The product of the extremes always equals the product of the means --> Extremes - outsides, 2 *12 = 24 --> Means - insides, 3 * 8 = 24 For a fraction, we can cross multiply 2/3 = 8/12 --> 2 x 12 = 3 x 8 = 24
Ratio What are 3 different ways to express the ratio of a classroom made up of 5 boys and 8 girls
Ratio: a comparison of two or more quantities Order is very important when stating a ratio - It must reflect the order of the categories - When comparing more than 2, pay close attention to the inside figures --> *Ratios can be manipulated in the same way as fractions* --> Think common denominators - Ratios can also express weighted values --> 2:3 can be 40% and 60% of a whole Many ways to express the ratio of a classroom made up of 5 boys and 8 girls - The ratio of boys to girls is: 5 to 8 5:8 5/8
12 is what percent of 6? (how do you set this up)
Setting up the is/of = %/100 --> 12/6 = X/100 X = (12x100)/6 --> 2 x 100 = 200%
Standard deviation
Steps for calculating S.D. of n observations 1. Calculate the arithmetic mean of the n numbers 2. Calculate the differences between the mean and each of the n numbers 3. Square each of the differences 4. Calculate the average of the squared differences 5. Take the nonnegative square root of the average from step 4. This is the standard deviation
Mode
The mode is the value that appears most frequently in a set of data - There may be no mode - There may be more than one mode 1, 2, 2, 4, 5, 6, 6, 8, 8, 9 --> Mode is 2, 6, and 8 1, 2, 3, 4, 5, 6, 7, 8, 9 --> No Mode
Range
The range of a set of numbers is the simplest measure of the spread of the data *The difference between the highest and lowest numbers in the set* ex) 1, 2, 2, 4, 5, 6, 6, 8, 8, 9 --> Range is 8 ex) 1, 5, 6, 9 --> Range is 8
Median
When arranged in ascending or descending order... - Of an odd number of data values, the median is the middle value ex) 2, 2, 4, 5, 6, 6, 8, 8, 9 --> Median is 6 - Of an even number of data values, the median is the average of the two middle values ex) 1, 2, 2, 4, 5, 6, 6, 8, 8, 9 --> Median is (5+6)/2 = 5.5
How to divide decimals when divisor is a decimal
When the divisor is a decimal - First "clear" the number of the fractional part by moving the decimal point to the right 8.57 --> 857 - You must move the decimal point in the dividend by the same number of places 50/8.57 --> 5000/857 - Set up the problem as long division - Place the decimal point in the quotient immediately above the decimal point and calculate - Doesn't matter if the dividend number is whole or not
How to divide decimals when divisor is a whole number
When the divisor is a whole number - Set up the problem as long division - Place the decimal point in the quotient immediately above the decimal point and calculate - Doesn't matter if the dividend number is whole or not
If Mike's test average is 92 for the 5 tests this semester, what was his score for the missing test? 88, 91, 96, X, 95
Work backwards 5*92 = 460 --> 460-88-91-96-95 = 90 Double check your work 90+95+96+91+88 = 460 --> 460/5 = 92
Common Denominator
a number that is a multiple of the denominators of two or more fractions 1/3 + 3/4 --> common denominator 12 (3*4)
Irrational numbers
cannot convert into a fraction/ratio ie. pi
Percentages less than 100%
decimals
Is 0 considered even or odd?
even
Percentages more than 100%
mixed number
If x is positive and y is negative, then xy is
negative
The product/quotient of two numbers with different signs is always
negative
is 0 a real number
no
Factors
numbers that evenly divide another number - 1,2,3,4,6, and 12 are all factors of 12
If x and y are both negative, then x+y is negative and xy is
positive
If x and y are both positive, then x+y and xy are
positive
The product/quotient of two numbers with the same sign is always
positive
Multiple
when a number is evenly divisible by another number - 12 is a multiple of 1,2,3,4,6, and 12
Adding/subtracting fractions
you must first have a common denominator, then add/subtract the numerators 4/12 + 9/12 = 13/12 4/12 - 9/12 = -5/12 Check for lowest form, in this case its been obtained
What is Jenny's average if the 6th score gets 50% weight, and the remaining 5 scores get equal weight? 90, 92, 85, 100, 95, 98
90+92+85+100+95+(98*5) = 952 --> 952/10 = 95.2 (90 x 0.1) + (92 x 0.1) + (85 x 0.1) + (100 x 0.1) + (95 x 0.1) + (98 x 0.5) = 9+9.2+8.5+10+9.5+49 = 95.2
What is John's test average if his 3rd score gets 30% weight, 5th score gets 40% weight, and the rest get equal weight? 91 98 96 97 92
(91 x 0.1) + (98 x 0.1) + (96 x 0.3) + (97 x 0.1) + (92 x 0.4) = 94.2 or 91 + 98 + (96 x 3) + 97 + (92 x 4)= 942 --> 942/10 = 94.2
Sarah's test scores were, 94 97 92 84, and each gets 10% more weight than the previous test, with the first test getting 10% weight.
(94 x 0.1) + (97 x 0.2) + (92 x 0.3) + (84 x 0.4) = 90 or --> 94 + (97 x 2) + (92 x 3)+(84 x 4) = 900 --> 900/10 = 90
percent change
(new-old)/old
Dividing (and multiplying) fractions --> ex (3/8) / (5/6)
*(bottom x top) / (middle x middle)* (6 x 3) / (8 x 5) = 18/40 = 9/20 or multiply numerator by numerator (visa versa) **don't need same denominator
Steps for solving an inverse proportion
*Inverse proportion:* As one increases, the other decreases Steps for solving 1. Set up an ordinary proportion 2. Invert the right side of the proportion 3. Cross multiply and solve for the unknown
Prime number
*when a number is not evenly divisible except by 1 and itself* Prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97 - NOTE: 1 is not considered a prime number - NOTE: Even numbers are never prime (because of 2) --> exception: 2
How to convert to a decimal from a fraction with 1000 or 10000 in denominator
- Move the decimal place left the same number of 0's that are in the denominator. 365/1000 --> 365.0 --> 0.365 247/10000 --> 247.0 --> 0.0247
How to multiply decimals
- No need to find common denominator - First count the number of decimal places in the numbers to be multiplied - Drop any final 0's (right end of the number) - Ignore the decimals and multiply - Then, for the final product, place the decimal point that many places to the left, counting from the right side of the last digit 0.25 x 2.5 --> 25 x 25 = 625 --> 0.625
John's salary went from 18k to 24k, what is the percentage change?
- Quantity change over time - Is/of becomes change/original - % change = (new-old)/old --> Where (new-old) = change Change/original --> (24-18)/18 = 6/18 = 1/3 = 33%
Real numbers
- all positive or negative number's - integers/whole/natural - fractions - decimal - irrational numbers *0 is not a real number* --> only deal with real numbers + 0
1/3 as decimal
.33333333333...
1/10 as decimal
0.10
1/9 as decimal
0.111111111...
1/8 as decimal
0.125
1/7 as decimal
0.1428571428571...
1/6 as decimal
0.16666666666666...
1/5 as decimal
0.20
1/4 as decimal
0.25
1/2 as decimal
0.5
Prime numbers in teens
11, 13, 17, 19
Traveling at a constant rate of 150mph, a plane makes a trip in 4 hours. How long will the trip take if the plane flies at a constant rate of 200mph?
150/200 = 4/X --> 150/200 = X/4 --> (150/200)*4 = X X = 3
Prime numbers (less than 10)
2, 3, 5, and 7
Prime numbers in 20s
23, 29
24/6 = 4 which is dividend, quotient, and divisor
24 = dividend 6 = divisor 4 = quotient
Prime numbers in 30s
31, 37
Prime numbers in 40s
41, 43, 47
Prime numbers in 50s
53, 59
Prime numbers in 60s
61, 67
If 7 jars of jelly weighs 35 pounds, how many jars are there if the total weight is 60 pounds?
7/35 = X/60 --> (7/35)*60 = X --> X = 12
Prime numbers in 70s
71, 73, 79
Prime numbers 80s/90s
83, 89, 97
What is Jake's average test grade for the 5 tests this semester? 88, 72, 99, 96, 91
88+72+99+96+91 = 446 --> 446/5 = 89.2
Mean
Also knows as - Average - Arithmetic Mean - First add all quantities - Then divide by the number of observations
If an equation uses (a) {b} and [c] what is the order in which you should complete them
Called symbols of inclusion 1st - Parentheses ( ) 2nd - Brackets [ ] 3rd - Braces { } Help to determine the order of calculations