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GMAT: TTP Quant > Modules 1&2: Essential GMAT Quant Skills > Flashcards

Modules 1&2: Essential GMAT Quant Skills Flashcards

1
Q

Types of DS Questions (2)

A
  • Value questions
  • Yes/No questions

Be careful not to re-state one type of DS question as another.

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2
Q

Six Test Cases

A
  • positive integers greater than 1
  • one
  • positive proper fractions (btwn 0 & 1)
  • zero
  • negative proper fractions (btwn -1 & 0)
  • negative integers

Develop a strategy to choose which ones to try first

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3
Q

Tips for improving accuracy (6)

A
  • Eliminate/ignore distractions (compartmentalize your brain)
  • Focus intensely on the current step. One step at a time.
  • Understand the concept of problems - this will help me to notice careless errors as I make them.
  • Positive self-talk (Fake it till you make it!)
  • Throw away your fear of failure (Life Plan B is a perfectly fine option!)
  • Practice writing confidently and in an organized fashion
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4
Q

Measuring accuracy (2 methods)

A
  • Hit rate

- Streak length: underrated way to self-evaluate. The GMAT rewards long streaks of correct answers very handsomely.

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5
Q

How to quickly convert an improper fraction to a mixed number

A

Divide the numerator by the denominator:

7/2

3 1/2 (3 with remainder 1.)

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6
Q

How to quickly convert a mixed number to an improper fraction

A

Multiply the whole number by the denominator, and add the numerator. Take the result and put it over the original denominator.

3 1/2
3*2 + 1 = 7
7/2

A b/c = (c x A + b) / c

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7
Q

Equivalent fractions; how to check if fractions are equivalent

A

Two fractions that represent the same part of a whole. Would be the same if simplified.

In a/b & c/d:

If a x d = b x c

THEN fractions are equivalent.

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8
Q

The distributive property of division over addition/subtraction

A

Addition: (a + c)/b = a/b + c/b.

Subtraction: (a - c)/b = a/b - c/b

Works only when DENOMINATORS are the same. The following statement is not correct:

b/a + b/c = b/(a+c)

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9
Q

Finding Common Denominator: Algebra shortcut

A

a/b, c/d

Common Denominator:

a/b + c/d = (ad + bc) / bd

a/b - c/d = (ad - bc) / bd

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10
Q

Re-write: A + b/c

A

(c x A + b) / c

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11
Q

Re-write: A - b/c

A

(c x A - b) / c

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12
Q

Subtracting a proper fraction from a whole number: shortcut

A

Convert whole number A to a pseudo-mixed number.

A = (A - 1) c/c

Subtract 2/3 from 6?

6 = (6 - 1) 3/3

5 3/3 - 2/3 = 5 1/3

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13
Q

Dividing fractions

A

Invert (reciprocal) the second fraction and multiply

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14
Q

Simplify: A x (b/c)

A

(A x b) / c

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15
Q

Cancelling fractions (2 methods w/ rules and limitations.)

A

Top-and-bottom: simplifying fractions in a calculation before performing the operation

56/64 x 3/1 –> 7/8 x 3/1

Cross Cancel: Cancel numerator of one fraction with the denominator of another.

  • Can be applied to fractions that are not next to each other: ANY numerator, ANY denominator.
  • ONLY works for multiplication

35/64 x 1/2 x 56/45

35/45 -> 7/9

64/56 -> 8/7

7/8 x 1/2 x 7/9

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16
Q

Simplifying Complex Fractions (3 methods)

A

3 example:

1) Multiply the ENTIRE numerator and ENTIRE denominator by the Lowest Common Denominator. (Find the LCD by calculating the smallest number that is divisible by all denominators in the complex fraction.)
2) Simplify numerator & denominator into single fractions and then divide (take reciprocal)
3) (If single fraction) Product of “extremes” (outside numbers) divided by “means” (inside numbers). Remember E / M

(a/b) / (c/d) = ad / bc

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17
Q

When I get stuck on a complex fraction, I will

A

think: does this get simpler if I put a component of the fraction over 1? (then, division can become reciprocal by inverting the second/bottom fraction - easier.)

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18
Q

Comparing the Size of Fractions (4 methods)

A

1) Use a reference point to compare each fraction (are they each close to 50%? Greater than or less than?)
2) Bow Tie Method - cross multiply two fractions. The larger fraction is the one in which the NUMERATOR is part of the larger product.
3) Find Common Denominator using LCM calculation - good for set of 3+ fractions
4) Find Common Numerator - same idea, flipped

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19
Q

Fractions: Adding/Subtracting Same Constant to Numerator & Denominator

A

0 - 1: Positive constant add = bigger, subtract = smaller

1 + : Positive constant add = smaller, subtract = bigger (if still positive)

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20
Q

Multiplying Decimals

A

Ignore the decimal point until the answer. Count the number of Decimal places in both factors. Use that number of decimal places to write the answer.

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21
Q

Multiplying Decimals: Estimation + 1 catch

A

For a PS question, count the number of decimals in each answer and choose the one that matches the correct number of decimal places.

CATCH: Be careful if the product of the two numbers (after the decimal point is ignored) ends in 0. The solution will be one less digit than expected

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22
Q

How to Convert a Fraction to a Decimal

A

Long division. Denominator outside

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23
Q

1/8

A

0.125

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24
Q

3/8

A

0.375

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25
Q

5/8

A

0.625

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26
Q

7/8

A

0.875

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27
Q

1/9

A

0.111…

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28
Q

1/6

A

0.1666…

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29
Q

1/7

A

0.143

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30
Q

2/7

A

0.286

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31
Q

3/7

A

0.429

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32
Q

4/7

A

0.571

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33
Q

5/7

A

0.714

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34
Q

6/7

A

0.857

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35
Q

5/6

A

0.8333

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36
Q

Zero is: (positive / negative / neither)

A

Neither

37
Q

Parity of Square Roots vs. Squares/Exponents

A

Exponents: Evens are always positive, Odds keep the original sign of the base

Square roots: Always positive. A negative number under a square root sign is impossible

38
Q

Square/Square Root of Fractions

A

If the fraction is inside parentheses or under the square root sign, you can perform the operation to both the numerator and the denominator.

If not, then the operation is only performed to the numerator & the answer will be different

39
Q

Square & Square Root of Proper Fractions

A

(0 < x < 1)

Square root is greater

Square is lesser

40
Q

Perfect squares will never end in the digits ________; they will always end in one of _________

A

Never: 2, 3, 7, 8

Always: 0, 1, 4, 5, 6, 9

41
Q

PEMDAS things to remember (4)

A

Absolute value bars take top priority, along with parentheses

If no parentheses, remember to apply same-priority operations from left to right

Simplifying one “term” should not affect another “term” (terms are separated by a plus or minus sign that is outside of parentheses.)

In fractions that are not combined, then the combination operation takes top priority (before dividing numerator by denominator)

42
Q

Time-saving elements of addition & multiplication

A

Commutative & associative properties indicate that the order of addition/multiplication can be changed with the same end result. Re-order addition/multiplication to make easier calculations.

43
Q

Distributive Property & factoring use

A

44 x 87 + 56 x 87

a(b + c) = ab + ac

Use this to simplify expressions by factoring out common factors:

(44 + 56) x 87 (easier math)

44
Q

Simplifying Factorials Strategy

A

Expand greater factorials to include up to the smaller factorial by which you are cancelling them, and then cancel the equal factorials to simplify

45
Q

Factoring Out Factorials - example

A

20! + 19! + 18!

20 x 19 x 18!) + (19 x 18!) + (1 x 18!
18!(20 x 19 + 19 + 1)
18!([20 x 19] + 20)
18!(400)

46
Q

2!

A

2

47
Q

3!

A

6

48
Q

4!

A

24

49
Q

5!

A

120

50
Q

6!

A

720

51
Q

7!

A

5040

52
Q

Fractional exponents

A

Can be rewritten as roots

53
Q

1.4^2

A

~2

54
Q

1.7^2

A

~3

55
Q

Sqrt of 2

A

1.4

56
Q

Sqrt of 3

A

1.7

57
Q

Sqrt of 121

A

11

58
Q

Sqrt of 144

A

12

59
Q

Sqrt of 169

A

13

60
Q

Sqrt of 196

A

14

61
Q

Sqrt of 225

A

15

62
Q

Sqrt of 256

A

16

63
Q

Sqrt of 400

A

20

64
Q

Sqrt of 625

A

25

65
Q

Sqrt of 900

A

30

66
Q

11^2

A

121

67
Q

12^2

A

144

68
Q

13^2

A

169

69
Q

14^2

A

196

70
Q

15^2

A

225

71
Q

16^2

A

256

72
Q

17^2

A

289

73
Q

20^2

A

400

74
Q

25^2

A

625

75
Q

30^2

A

900

76
Q

2^3

A

8

77
Q

3^3

A

27

78
Q

4^3

A

64

79
Q

5^3

A

125

80
Q

10^3

A

1000

81
Q

6^3

A

216

82
Q

Cube root of 216

A

6

83
Q

Cube root of 125

A

5

84
Q

Cube root of 64

A

4

85
Q

Cube root of 27

A

3

86
Q

Cube root of 8

A

2

87
Q

Cube root of 1000

A

10

88
Q

When I am about to cancel a fraction, I will

A

Ensure that I am ONLY cancelling pieces of multiplication or division, NOT addition or subtraction

GMAT: TTP Quant (18 decks)

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