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FDP`s > MGMAT > Flashcards

MGMAT Flashcards

1
Q

Unknown Digits Problems

A
  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.
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2
Q

Powers of 10 & Decimals

A
  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”

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3
Q

How to find the Last Digit Shortcut

A
  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.
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4
Q

Why use Heavy Division Shortcut

A

To solve division problems with complex decimals:

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5
Q

How to use Heavy Division Shortcut

A
  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.
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6
Q

What do you do with the decimal in Addition Subraction

A
  • make sure to line up the decimal points and make decimals the same length.
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7
Q

What do you do with the decimal in Multiplication:

A
  • 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.
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8
Q

What do you do with the decimal in Division

A
  • 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.
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9
Q

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

A

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

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10
Q

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

A

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

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11
Q
  • the number of decimals in a cube root is WHAT FRACTION of the number in the original.
A
  • the number of decimals in a cube root is 1/3 the number in the original.
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12
Q

What are proper fractions

A

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

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13
Q

What are improper fractions

A

greater than 1, numerator greater than denominator.

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14
Q

What are mixed numbers

A

Mixed numbers: written as integer and proper fraction.

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15
Q

What are Complex Fractions

A

sum or difference in numerator/denominator

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16
Q

For positive fractions,

1. As the numerator increases,

A

the fraction increases.

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17
Q

For positive fractions,2. As the denominator increases,

A

the fraction decreases.

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18
Q

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

A

closer to 1.

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19
Q

What is The Multiplication Shortcut

A

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

20
Q

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

A

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

21
Q

How to compare fractions

A
  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.
22
Q

What is the shortcut for addition and subracton of fractions

A

There is no shortcut

23
Q

What must you do to add or subtract fractions

A

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

24
Q

What must you do to divide fractions

A

Flip the second fraction and multiply

25
Q

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

A

= 1/2 * 4/3

26
Q

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

A

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

27
Q

100% = what number

28
Q

Percents can be converted into decimals by

A

moving the decimal point 2 spaces to the left

29
Q

Remember, the percentage is always WHAT than the decimal

30
Q

How to write A PART is some PERCENT of a WHOLE

A

A PART is some PERCENT of a WHOLE

31
Q

How to find 10% of any number

A

Just move the decimal point to the left one place

32
Q

Increasing - percent of original

A

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

33
Q

decreasing -percent of original

A

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

34
Q

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

35
Q

Original + Change = WHAT

A

Percent Change

36
Q

What is so tricky about Successive percents

A

They cannot simply be added or subtracted together.

They cannot simply be added or subtracted together.

37
Q

How to solve successive percents

A

Choose real numbers and see what happens: 100 is the easiest number to choose.

ORIGINAL x (1+x%) x (1+y%) = FINAL

38
Q

Simple interest

A

principal x rate x time

39
Q

Compound Interest

A

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

40
Q

What should be set up with chemical mixture problems

A

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.

41
Q 
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%
42
Q

When to use?

Fractions:

A
  • canceling factors in multiplication

- best way to exactly express proportions

43
Q

When to use?

A
  • estimate results or compare sizes
44
Q

Prefer fractions for doing what 2 things

A

multiplication or division;

45
Q

prefer decimals and Percents for what 4 things

A

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

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