Modules 1&2: Essential GMAT Quant Skills Flashcards
Types of DS Questions (2)
- Value questions
- Yes/No questions
Be careful not to re-state one type of DS question as another.
Six Test Cases
- 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
Tips for improving accuracy (6)
- 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
Measuring accuracy (2 methods)
- Hit rate
- Streak length: underrated way to self-evaluate. The GMAT rewards long streaks of correct answers very handsomely.
How to quickly convert an improper fraction to a mixed number
Divide the numerator by the denominator:
7/2
3 1/2 (3 with remainder 1.)
How to quickly convert a mixed number to an improper fraction
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
Equivalent fractions; how to check if fractions are equivalent
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.
The distributive property of division over addition/subtraction
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)
Finding Common Denominator: Algebra shortcut
a/b, c/d
Common Denominator:
a/b + c/d = (ad + bc) / bd
a/b - c/d = (ad - bc) / bd
Re-write: A + b/c
(c x A + b) / c
Re-write: A - b/c
(c x A - b) / c
Subtracting a proper fraction from a whole number: shortcut
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
Dividing fractions
Invert (reciprocal) the second fraction and multiply
Simplify: A x (b/c)
(A x b) / c
Cancelling fractions (2 methods w/ rules and limitations.)
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
Simplifying Complex Fractions (3 methods)
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
When I get stuck on a complex fraction, I will
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.)
Comparing the Size of Fractions (4 methods)
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
Fractions: Adding/Subtracting Same Constant to Numerator & Denominator
0 - 1: Positive constant add = bigger, subtract = smaller
1 + : Positive constant add = smaller, subtract = bigger (if still positive)
Multiplying Decimals
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.
Multiplying Decimals: Estimation + 1 catch
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
How to Convert a Fraction to a Decimal
Long division. Denominator outside
1/8
0.125
3/8
0.375
5/8
0.625
7/8
0.875
1/9
0.111…
1/6
0.1666…
1/7
0.143
2/7
0.286
3/7
0.429
4/7
0.571
5/7
0.714
6/7
0.857
5/6
0.8333
Zero is: (positive / negative / neither)
Neither
Parity of Square Roots vs. Squares/Exponents
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
Square/Square Root of Fractions
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
Square & Square Root of Proper Fractions
(0 < x < 1)
Square root is greater
Square is lesser
Perfect squares will never end in the digits ________; they will always end in one of _________
Never: 2, 3, 7, 8
Always: 0, 1, 4, 5, 6, 9
PEMDAS things to remember (4)
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)
Time-saving elements of addition & multiplication
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.
Distributive Property & factoring use
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)
Simplifying Factorials Strategy
Expand greater factorials to include up to the smaller factorial by which you are cancelling them, and then cancel the equal factorials to simplify
Factoring Out Factorials - example
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)
2!
2
3!
6
4!
24
5!
120
6!
720
7!
5040
Fractional exponents
Can be rewritten as roots
1.4^2
~2
1.7^2
~3
Sqrt of 2
1.4
Sqrt of 3
1.7
Sqrt of 121
11
Sqrt of 144
12
Sqrt of 169
13
Sqrt of 196
14
Sqrt of 225
15
Sqrt of 256
16
Sqrt of 400
20
Sqrt of 625
25
Sqrt of 900
30
11^2
121
12^2
144
13^2
169
14^2
196
15^2
225
16^2
256
17^2
289
20^2
400
25^2
625
30^2
900
2^3
8
3^3
27
4^3
64
5^3
125
10^3
1000
6^3
216
Cube root of 216
6
Cube root of 125
5
Cube root of 64
4
Cube root of 27
3
Cube root of 8
2
Cube root of 1000
10
When I am about to cancel a fraction, I will
Ensure that I am ONLY cancelling pieces of multiplication or division, NOT addition or subtraction
