MGMAT

Question 1

Unknown Digits Problems

Answer 1

1. Be ready to create variables to represent unknown digits.
2. Recognize that each unknown is restricted to at most ten possible values (0-9).
3. Apply any given constraints, may involve number properties like divisibility or odds & evens.

Question 2

Powers of 10 & Decimals

Answer 2

1. When you multiply by a power of 10, move the decimal right the number of specified places.
2. When you divide by a power of 10, move the decimal left.
3. Negative powers of 10 reverse the process.

“trading decimal places for powers of ten”

Question 3

How to find the Last Digit Shortcut

Answer 3

1. Drop any digits but the ones unit from all numbers.
2. Multiply/add all the ones digits.
3. Take the ones digit of the final product.

Question 4

Why use Heavy Division Shortcut

Answer 4

To solve division problems with complex decimals:

Question 5

How to use Heavy Division Shortcut

Answer 5

1. Set up the division problem in fraction form.
2. Rewrite the problem, eliminating powers of 10.
3. Get a single digit to the left of the decimal in the denominator.
4. Focus on the whole number parts of the numerator and denominator and solve.
   - if not precise enough, keep one more decimal place and do long division.

Question 6

What do you do with the decimal in Addition Subraction

Answer 6

• make sure to line up the decimal points and make decimals the same length.

Question 7

What do you do with the decimal in Multiplication:

Answer 7

• ignore the decimal until the end.
• multiply and count the total number of digits to the right of the decimal in both factors. Put that many digits in the product.
• if multiplying a very small and large number, move decimals in the opposite direction to make the same number of places.

Question 8

What do you do with the decimal in Division

Answer 8

• if a decimal In the dividend (inner #), bring the decimal point straight up to the answer and divide.
• if a decimal in the divisor (outer #), shift the decimal point in both the divisor and dividend to make the divisor a whole number. Then divide.
• simplify division by moving decimals in the same direction.

Question 9

How do you take a power or a root of a decimal

Answer 9

By splitting the decimal into 2 parts: an integer and a power of ten.

Question 10

the number of decimal places in a cube is HOW MANY TIMES the number of decimals in the original number.

Answer 10

the number of decimal places in a cube is 3x the number of decimals in the original number.

Question 11

• the number of decimals in a cube root is WHAT FRACTION of the number in the original.

Answer 11

• the number of decimals in a cube root is 1/3 the number in the original.

Question 12

What are proper fractions

Answer 12

are those that fall between 0 and 1, numerator always smaller than denominator.

Question 13

What are improper fractions

Answer 13

greater than 1, numerator greater than denominator.

Question 14

What are mixed numbers

Answer 14

Mixed numbers: written as integer and proper fraction.

Question 15

What are Complex Fractions

Answer 15

sum or difference in numerator/denominator

Question 16

For positive fractions,

1. As the numerator increases,

Answer 16

the fraction increases.

Question 17

For positive fractions,2. As the denominator increases,

Answer 17

the fraction decreases.

Question 18

For positive fractions,Adding the same number to both the numerator and denominator brings the fraction

Answer 18

closer to 1.

Question 19

What is The Multiplication Shortcut

Answer 19

Before multiplying fractions, cancel out factors to reduce to simpler numbers.

Question 20

Adding, subtracting, multiplying, and dividing each fraction each respectively does what

Answer 20

Adding - increases the value
Subtracting - decreases the value
Multiplying - decreases the value
Dividing - increases the value

Question 21

How to compare fractions

Answer 21

1. Set the fractions next to each other.
2. Cross multiply the fractions and put each answer by the corresponding numerator.
3. Compare the answers.

Question 22

What is the shortcut for addition and subracton of fractions

Answer 22

There is no shortcut

Question 23

What must you do to add or subtract fractions

Answer 23

1) Find a common denominator
2) Change each fractioon so that it is expressed using this common denominator
3) add up the numerators only

Question 24

What must you do to divide fractions

Answer 24

Flip the second fraction and multiply

Question 25

What do do with DOUBLE DECKER fractions ie (1/2) / (3/4)

Answer 25

= 1/2 * 4/3

Question 26

When simplifying fractions, that incorporate fractions, what must you remember about the numerator and denominator

Answer 26

You may may split the numerator but you may NEVER split the denominator

Question 27

100% = what number

Answer 27

1

Question 28

Percents can be converted into decimals by

Answer 28

moving the decimal point 2 spaces to the left

Question 29

Remember, the percentage is always WHAT than the decimal

Answer 29

BIGGER

Question 30

How to write A PART is some PERCENT of a WHOLE

Answer 30

A PART is some PERCENT of a WHOLE

Question 31

How to find 10% of any number

Answer 31

Just move the decimal point to the left one place

Question 32

Increasing - percent of original

Answer 32

If a quantity is increasing by x%, the the new quantity is (100+x)% OF the original.

Question 33

decreasing -percent of original

Answer 33

If a quantity is decreasing by x%, then the new quantity is (100-x)% OF the original.

Question 34

ORIGINAL x (1 + [percent increase/100] ORIGINAL x (1 + [percent increase/100] = WHAT

Answer 34

NEW

Question 35

Original + Change = WHAT

Answer 35

Percent Change

Question 36

What is so tricky about Successive percents

Answer 36

They cannot simply be added or subtracted together. | They cannot simply be added or subtracted together.

Question 37

How to solve successive percents

Answer 37

# Choose real numbers and see what happens: 100 is the easiest number to choose. ORIGINAL x (1+x%) x (1+y%) = FINAL

Question 38

Simple interest

Answer 38

principal x rate x time

Question 39

Compound Interest

Answer 39

P = C (1 + r/n) nt where P = future value C = initial deposit r = interest rate (expressed as a fraction: eg. 0.06) n = # of times per year interest is compounded t = number of years invested

Question 40

What should be set up with chemical mixture problems

Answer 40

set up a mixture chart with the substance labels in rows and "original" "change" and "new" in the colums. This way, you can keep careful track of the vatious components and their changes.

Question 41

``` 1/100 0.01 1% 1/50 0.02 2% 1/25 0.04 4% 1/20 0.05 5% 1/10 0.10 10% 1/9 0.11(repeat) 11.1% 1/8 0.125 12.5% 1/6 0.16(6 repeat) 16.7% 1/5 0.2 20% 1/4 0.25 25% 3/10 0.3 30% 1/3 0.3(repeat) 33% 3/8 0.375 37.5% 2/5 0.4 40% 1/2 0.5 50% 3/5 0.6 60% 5/8 0.625 62.5% 2/3 0.6(repeat) 66.6% 7/10 0.7 70% 3/4 0.75 75% 4/5 0.8 80% 5/6 0.83(3 repeat) 83.3% 7/8 0.875 87.5% 9/10 0.9 90% 1/1 1 or 100% 5/4 1.25 125% 4/3 1.3(3 repeat) 133% 3/2 1.5 150% 7/4 1.75 175% ```

Answer 41

MEMORIZE

Question 42

When to use? | Fractions:

Answer 42

- canceling factors in multiplication | - best way to exactly express proportions

Question 43

When to use?

Answer 43

- estimate results or compare sizes

Question 44

Prefer fractions for doing what 2 things

Answer 44

multiplication or division;

Question 45

prefer decimals and Percents for what 4 things

Answer 45

doing addition and subtraction, for estimating numbers, or for comparing numbers.