Quant Strategies

Question 1

DS: ID the question

Answer 1

Value or Yes/No

Question 2

x^-1, (x^a)^b, x^(1/2)

Answer 2

1/x, x^(a*b), sqrt(x)

Question 3

DS process

Answer 3

1. ID the question - Value or Yes-No - What are we looking for?
2. Simplify the question stem as much as possible! (i.e. Factor, distribute, split fractions, etc - we’ll see a ton more of this throughout the course)
3. Attack one of the statements to try to prove it insufficient (get multiple values if a value Q or get both a Yes and a No if Y/N question)
4. Eliminate! If you started with the 1st Statement, we’re down to AD or BCE; If you started with the 2nd Statement, we’re down to BD or ACE.
5. Attack the other statement ALONE and try to prove it insufficient as well (be sure to avoid statement carryover from the first statement)
6. ONLY if EACH Statement 1 alone and Statement 2 alone were insufficient do we need to attack both statements together. In this case you’d be down to C or E.

Question 4

Problem Solving Process

Answer 4

1. Understand: Glance/Read/Jot [5-10 sec]
2. Plan: Reflect/Organize [20-30 sec]
3. Solve: Work [~1.5 min]

Question 5

Answer 5

Question 6

Ratios - Two ways to solve ratio problems

Answer 6

1) Line up ratios and multiply them to find least common multiples in order to combine them, or 2) Use the labeled fractions “factor label method,” starting with your target unit and multiplying by ratios until you get the unit you need.

Question 7

unknown multiplier questions

Answer 7

put each ratio in terms of x (like 2x: 3x: 5x); often times we’ll need to add these all together to more quickly find the sum (i.e. those equal 10x)

Question 8

“story problem,”

Answer 8

you’ll either need to translate the words into equations and solve algebraically, or Work Backwards (see below). You can also occasionally use estimation (this strategy is great when you very pressed for time).

Question 9

Working Backwards -

Answer 9

Start at the answer choice and ask yourself, “What else can I find based on information in the question?” Keep going through the scenario until you find that that answer choice FITS or DOESN’T FIT the situation described. Remember - start with B or D then check the other in order to establish a trend.
When can I work backwards? In general, you can Work Backwards any time the answer choices are giving a single discrete value (i.e. NOT “the difference” between two values), and answer choices are all “nice” numbers that are relatively easy to work backwards from

Question 10

Smart Numbers

Answer 10

Choose small numbers whenever possible, unless working with percents (then use 100) - we’re just trying to find ONE working solution.
When can I use Smart numbers? Whenever there are variables in the answer choices, or whenever there’s a quantity in the question stem that would be super nice to know but they aren’t telling you - just make one up! You can also use them whenever we are dealing with ONLY FDPRs. If there are two variables, we can pick for either one!

Question 11

Look for COMBOS!

Answer 11

Is the problem asking for just x, or the “combo” x + y? Oftentimes, especially in DS, it’s possible to answer the question about the combo even though we won’t know the value of either x or y individually.

Question 12

Simplifying the question stem is CRUCIAL! You can split a fraction with multiple terms in its numerator: (3x + x – 5)/(x – 5)

Answer 12

3x/(x-5) + (x-5)/(x-5)

Question 13

solve a system of two equations if

Answer 13

You can solve a system of two equations if the equations are both linear (no square roots or exponents) and of the form ax + by = c and unique (i.e. one is NOT just the multiple of another).

Question 14

Estimation

Answer 14

For FDPs, try to figure out if the answer is < or > 50%

Question 15

simplify radicals

Answer 15

break down each number into a product involving a perfect square.

Question 15

simplify radicals

Answer 15

break down each number into a product involving a perfect square.

Question 16

exponential terms being added or subtracted

Answer 16

look to FACTOR out the smallest common exponential term.
Rewrite terms in the SAME base in order to create equations. Like for the equation 4^x = 8^(x - 2), rewrite both the 4 and 8 in base 2 and then write an equation (Try it! x = 6).

Question 17

Algebra II: Special Experessions

Answer 17

(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2
(a +b)(a - b) = a^2 - b^2

Question 18

To solve inequalities

Answer 18

just treat it as if it were an equation and solve for the critical value(s). Then figure out where to shade by testing a case or two to see if those values are in the solution set; checking x = 0 will often help.

Question 19

Dealing with Lists:

Answer 19

If there are fewer than 10 items or combinations, just write the whole list out. If there are more than 10 items, write the beginning and end terms and look for patterns or pairs you might be able to make.

Question 20

Over-Under method

Answer 20

great if we have the weighted average and both weights but are missing one of the end point values OR if we have both end point values and are missing one of the weights. Find the distance between each of the end points and the given weighted average, and use the formula (under dist)(under weight) = (over dist)(over weight)

Question 21

Tug of War Method

Answer 21

allows us to find the weighted average if we have both weights and both end point values. Find out the difference between the two values we’re averaging, then break that distance up into the number of parts involved in the ratio. Finally, think about which number “wins” the tug of war, and use the reverse of the ratio to figure out your weighted average. Ex: I scored 5 90’s and 2 45’s on some exams. 90 – 55 = 35 and 35/(5+2) = 5. So break the distance up by 5s and see that we must be 2 of these tick marks away from 90, giving us the weighted average of 80. Alternatively we can do (905 + 552)/7= 80

Question 22

For any evenly spaced set

Answer 22

the average value is the average of the endpoints.

Question 23

For any set of consecutive integers, the number of terms is

Answer 23

Max - Min + 1.

Question 24

The sum of the numbers in the set (1 + 2 + 3 +…+ n)

Answer 24

is given by n(n+1)/2

Question 25

PS approaches

Answer 25

Working Backwards, Smart Numbers, Estimation, and Algebra

Question 26

DS

Answer 26

Testing Cases to Prove Insufficient after you’ve simplified each stem. Remember to test weird numbers taht are allowed (fractions, negatives, radicals, pi, etc.)

Question 27

Large numbers being multiplied or divided in a problem?

Answer 27

Make a factor tree!

Question 28

Perfect squares have prime factors coming in pairs.

Answer 28

Know all prime numbers less than 30 (remember, prime numbers have exactly two factors: 1 and themselves. Composites have 3 or more factors. 1 is neither prime nor composite). 2, 3, 5, 7, 11, 13, 17, 19, 23, 29

Question 29

Know your even and odd rules for x/+.

Answer 29

Even + Even = Even
Odd + Odd = Even
Even - Even = Even
Odd - Odd = Even
Even + Odd = Odd
Even - Odd = Odd
Even * Even = Even
Even * Odd = Even
Odd * Odd = Odd

Question 30

KNOW THE CODE! Make flash cards as you learn new “codes.” Codes discussed below:

Answer 30

“xy is even” means at least one of x or y is even.
“xy is odd” means BOTH x and y are odd.
“x + y is even” means x and y are both even or both odd
“x + y is odd” means one of them is even and one of them is odd.
-“x/y > 0” means x and y are the same sign.
-“x/y < 0” means x and y are different signs.
-“x + y > 0” means at least one of them is positive.
-“x + y < 0” means at least one of them is negative.
-“y^x < 0” means y must be negative and x must be odd.
-“y^x > 0” means either y is positive and x is anything, OR y is negative and x is even.
-If k is an integer, k(k+1) must be divisible by 2
-If k is an integer, k(k+1)(k+2) must be divisible by 2, 3, and 6.

Question 31

DS diagrams are NOT drawn to scale

Answer 31

but PS problems ARE.

Question 32

Steps for Geometry problems

Answer 32

1) Draw/redraw and Label. 2) Identify what you’re looking for. 3) Infer from the givens and solve the puzzle

Question 33

Opposite sides of a parallelogram are congruent and parallel. Diagonals of a parallelogram bisect each other. Rhombus, Rectangle, and Square are all special types of parallelograms.

Answer 33

Rhombuses have 4 congruent sides; Rectangles have 4 right angles; squares have BOTH.
Diagonals of a rhombus are perpendicular; diagonals of a rectangle are congruent; diagonals of a square are BOTH.

Question 34

Perimeters/Areas/Volumes

Answer 34

Triangle: A=1/2*b*h
Rectangle: P = 2w+2l, A=l*w
Rectangular prism: V: l*w*h
square: P = 4s, A = s^2
cube: V = s^3
circle: P = 2*pi*r = pi*d, A = pi*r^2
sphere: SA = 4/3*pi*r^2, V= 4*pi*r^3
cylinder: SA= 2*pi*r*h+2*pi*r^2, V= pi*r^2*h

Question 35

Special Triangles

Answer 35

30-60-90 triangles follow a x - xroot(3) - 2x pattern, and 45-45-90 triangles follow an x - x - xroot(2) pattern
recognize 3,4,5 (6,8,10) triangles

Question 36

arc length

Answer 36

Arc length = 2pir*(angle/360)

Question 37

Slope = Rise/Run. On the coordinate plane, parallel lines….perpendicular lines…

Answer 37

parallel lines have the same slope; perpendicular lines have opposite reciprocal slopes.