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