Miscellaneous Flashcards
Use listing if
Full list is very short (<10)
Rounding
When we round to any place, we look at the single digit in the next smallest place; if digit is <=4, round DOWN, if digit is >=5, round UP
if bˣ = bʸ
then x=y (if b is NOT 0/1/-1)
Comparing numbers (in prime factorised format)
Get them to same base or same exponent (If different bases -> same exponent => convert all to SMALLEST power)
mⁿ, if m>1 & n<0
then 0 < mⁿ < 1
x & 1-x
x < 1-x (x<0.5); x=1-x (x=0.5); x > 1-x (x>0.5)
The mean/median/both, Standard deviation?
Cannot be determined
Mixing 2 entities with concentrations x% & y%
x% < concentration of resultant entity < y%
Inequality - check for
Big -ve no, -ve b/w -1 & 0, Big +ve no, +ve b/w 0 & 1
0
even, neither +ve nor -ve
1
Not prime/composite
Every higher factorial is divisible by
a lower factorial
Arranging in a random order with constraint/relation b/w 2 items
Use symmetry / mirroring (for each possibility has a mirror), 1-1 correspondence, Probability = 50%
Adding the same number to terms in a list
DOESN’T change the standard deviation
√ (P x Q)
√ P x √ Q
√ (P / Q) given P>0, Q>0
√ P / √ Q
Do NOT assume numbers are integers unless
EXPLICITLY stated
Order DOESN’T matter
choice of individual elements DOESN’T make any meaningful difference in final set
A divided by B, quotient Q, remainder R
A = Q(B) + R => A/B = Q (integer) + R/B (fraction/decimal part) & 0<=R<B
If x²>0
x<0 / x>0 [for both +ve & -ve numbers, square is +ve]
Changing one unit to another
x unit-conversion factor => (_ desired unit / _ given unit)
Difference of squares
a²-b² = (a+b)(a-b)
Tautological statements
Insufficient in themselves & canNOT combine with other insufficient statements to make a sufficient combination [C]
Be aware of the CATEGORY of numbers involved
positive, 0, negative, whole no, fractions, decimals
It is IMPOSSIBLE to produce an algebraic formula that will always produce
primenumbers
Guessing Strategy for Probability
Use instincts, problems with complement rule (look for complement pairs in the options), think about overlap
For Data Sufficiency
Using 0 or 1 can be quick
Order matters
If counting the no of physical arragements, roles are specified for each choice, choosing elements in different orders produces meaningful different outcomes
Use counting techniques if
problem involves selection of several elements from a set (with a certain restrictions)
Solutions/Mixtures Questions
(1) VOLUME EQ: Total amount of liquid eq (2) SOLUTE EQ: Total amount of solute dissolved
%s in succession comparison (P%-> Q% Vs. R%)
P+Q+PQ/100 Vs. R
If 0 < b < 1
0 < b² < b < √b < 1
Estimate when
lengthy or complex calculation / answer choices are spaced far apart
Cubing Inequalities
Cubing retains +ve/-ve sign; x<0 => x³<0; x>0 => x³>0
Age Questions
Rows: person A, person B, …; Columns: cur-x year, cur year, cur+x year
Multiple Traveller Problems
Each traveller & trip gets its own D=RT
Shortcut: N/5
Nx2 / 10
Square of a number ending in 5 => (x5)²
(x)(x+1)25
Multiplication of 2 numbers => xy
(x)(2) * (y/2)
Growth & Decay
Use the multiplier, step-by-step, one change interval at a time
Principal Square Root Sign
Only returns +ve square roots, If we take square roots ourselves we consider +ve & -ve roots
Use formal algebraic probability rules if
Problem gives you algebraic expressions, items are coins/cards/dice/etc, language of problem uses mutually exclusive/independent
If j, k, and N are positive integers such that (jN)/k is an integer, and j/k is fully reduced, then N
Must be divisible by k
