Modules 1&2: Essential GMAT Quant Skills

Question 1

Types of DS Questions (2)

Answer 1

• Value questions
• Yes/No questions

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

Question 2

Six Test Cases

Answer 2

• 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

Question 3

Tips for improving accuracy (6)

Answer 3

• 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

Question 4

Measuring accuracy (2 methods)

Answer 4

• Hit rate

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

Question 5

How to quickly convert an improper fraction to a mixed number

Answer 5

Divide the numerator by the denominator:

7/2

3 1/2 (3 with remainder 1.)

Question 6

How to quickly convert a mixed number to an improper fraction

Answer 6

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

Question 7

Equivalent fractions; how to check if fractions are equivalent

Answer 7

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.

Question 8

The distributive property of division over addition/subtraction

Answer 8

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)

Question 9

Finding Common Denominator: Algebra shortcut

Answer 9

a/b, c/d

Common Denominator:

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

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

Question 10

Re-write: A + b/c

Answer 10

(c x A + b) / c

Question 11

Re-write: A - b/c

Answer 11

(c x A - b) / c

Question 12

Subtracting a proper fraction from a whole number: shortcut

Answer 12

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

Question 13

Dividing fractions

Answer 13

Invert (reciprocal) the second fraction and multiply

Question 14

Simplify: A x (b/c)

Answer 14

(A x b) / c

Question 15

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

Answer 15

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

Question 16

Simplifying Complex Fractions (3 methods)

Answer 16

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

Question 17

When I get stuck on a complex fraction, I will

Answer 17

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.)

Question 18

Comparing the Size of Fractions (4 methods)

Answer 18

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

Question 19

Fractions: Adding/Subtracting Same Constant to Numerator & Denominator

Answer 19

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

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

Question 20

Multiplying Decimals

Answer 20

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.

Question 21

Multiplying Decimals: Estimation + 1 catch

Answer 21

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

Question 22

How to Convert a Fraction to a Decimal

Answer 22

Long division. Denominator outside

Question 23

1/8

Answer 23

0.125

Question 24

3/8

Answer 24

0.375

Question 25

5/8

Answer 25

0.625

Question 26

7/8

Answer 26

0.875

Question 27

1/9

Answer 27

0.111...

Question 28

1/6

Answer 28

0.1666...

Question 29

1/7

Answer 29

0.143

Question 30

2/7

Answer 30

0.286

Question 31

3/7

Answer 31

0.429

Question 32

4/7

Answer 32

0.571

Question 33

5/7

Answer 33

0.714

Question 34

6/7

Answer 34

0.857

Question 35

5/6

Answer 35

0.8333

Question 36

Zero is: (positive / negative / neither)

Answer 36

Neither

Question 37

Parity of Square Roots vs. Squares/Exponents

Answer 37

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*

Question 38

Square/Square Root of Fractions

Answer 38

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

Question 39

Square & Square Root of Proper Fractions

Answer 39

(0 < x < 1) Square root is greater Square is lesser

Question 40

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

Answer 40

Never: 2, 3, 7, 8 Always: 0, 1, 4, 5, 6, 9

Question 41

PEMDAS things to remember (4)

Answer 41

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)

Question 42

Time-saving elements of addition & multiplication

Answer 42

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.

Question 43

Distributive Property & factoring use

Answer 43

a(b + c) = ab + ac Use this to simplify expressions by factoring out common factors: 44 x 87 + 56 x 87 = (44 + 56) x 87 (easier math)

Question 44

Simplifying Factorials Strategy

Answer 44

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

Question 45

Factoring Out Factorials - example

Answer 45

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)

Question 46

2!

Answer 46

2

Question 47

3!

Answer 47

6

Question 48

4!

Answer 48

24

Question 49

5!

Answer 49

120

Question 50

6!

Answer 50

720

Question 51

7!

Answer 51

5040

Question 52

Fractional exponents

Answer 52

Can be rewritten as roots

Question 53

1.4^2

Answer 53

~2

Question 54

1.7^2

Answer 54

~3

Question 55

Sqrt of 2

Answer 55

1.4

Question 56

Sqrt of 3

Answer 56

1.7

Question 57

Sqrt of 121

Answer 57

11

Question 58

Sqrt of 144

Answer 58

12

Question 59

Sqrt of 169

Answer 59

13

Question 60

Sqrt of 196

Answer 60

14

Question 61

Sqrt of 225

Answer 61

15

Question 62

Sqrt of 256

Answer 62

16

Question 63

Sqrt of 400

Answer 63

20

Question 64

Sqrt of 625

Answer 64

25

Question 65

Sqrt of 900

Answer 65

30

Question 66

11^2

Answer 66

121

Question 67

12^2

Answer 67

144

Question 68

13^2

Answer 68

169

Question 69

14^2

Answer 69

196

Question 70

15^2

Answer 70

225

Question 71

16^2

Answer 71

256

Question 72

17^2

Answer 72

289

Question 73

20^2

Answer 73

400

Question 74

25^2

Answer 74

625

Question 75

30^2

Answer 75

900

Question 76

2^3

Answer 76

8

Question 77

3^3

Answer 77

27

Question 78

4^3

Answer 78

64

Question 79

5^3

Answer 79

125

Question 80

10^3

Answer 80

1000

Question 81

6^3

Answer 81

216

Question 82

Cube root of 216

Answer 82

6

Question 83

Cube root of 125

Answer 83

5

Question 84

Cube root of 64

Answer 84

4

Question 85

Cube root of 27

Answer 85

3

Question 86

Cube root of 8

Answer 86

2

Question 87

Cube root of 1000

Answer 87

10

Question 88

When I am about to cancel a fraction, I will

Answer 88

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