Quant Strategies Flashcards
(38 cards)
DS: ID the question
Value or Yes/No
x^-1, (x^a)^b, x^(1/2)
1/x, x^(a*b), sqrt(x)
DS process
- ID the question - Value or Yes-No - What are we looking for?
- 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)
- 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)
- 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.
- Attack the other statement ALONE and try to prove it insufficient as well (be sure to avoid statement carryover from the first statement)
- 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.
Problem Solving Process
- Understand: Glance/Read/Jot [5-10 sec]
- Plan: Reflect/Organize [20-30 sec]
- Solve: Work [~1.5 min]
Ratios - Two ways to solve ratio problems
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.
unknown multiplier questions
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)
“story problem,”
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).
Working Backwards -
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
Smart Numbers
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!
Look for COMBOS!
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.
Simplifying the question stem is CRUCIAL! You can split a fraction with multiple terms in its numerator: (3x + x – 5)/(x – 5)
3x/(x-5) + (x-5)/(x-5)
solve a system of two equations if
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).
Estimation
For FDPs, try to figure out if the answer is < or > 50%
simplify radicals
break down each number into a product involving a perfect square.
simplify radicals
break down each number into a product involving a perfect square.
exponential terms being added or subtracted
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).
Algebra II: Special Experessions
(a + b)^2 = a^2 + 2ab + b^2
(a - b)^2 = a^2 - 2ab + b^2
(a +b)(a - b) = a^2 - b^2
To solve inequalities
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.
Dealing with Lists:
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.
Over-Under method
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)
Tug of War Method
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
For any evenly spaced set
the average value is the average of the endpoints.
For any set of consecutive integers, the number of terms is
Max - Min + 1.
