Miscellaneous

Question 1

Use listing if

Answer 1

Full list is very short (<10)

Question 2

Rounding

Answer 2

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

Question 3

if bˣ = bʸ

Answer 3

then x=y (if b is NOT 0/1/-1)

Question 4

Comparing numbers (in prime factorised format)

Answer 4

Get them to same base or same exponent (If different bases -> same exponent => convert all to SMALLEST power)

Question 5

mⁿ, if m>1 & n<0

Answer 5

then 0 < mⁿ < 1

Question 6

x & 1-x

Answer 6

x < 1-x (x<0.5); x=1-x (x=0.5); x > 1-x (x>0.5)

Question 7

The mean/median/both, Standard deviation?

Answer 7

Cannot be determined

Question 8

Mixing 2 entities with concentrations x% & y%

Answer 8

x% < concentration of resultant entity < y%

Question 9

Inequality - check for

Answer 9

Big -ve no, -ve b/w -1 & 0, Big +ve no, +ve b/w 0 & 1

Question 10

0

Answer 10

even, neither +ve nor -ve

Question 11

1

Answer 11

Not prime/composite

Question 12

Every higher factorial is divisible by

Answer 12

a lower factorial

Question 13

Arranging in a random order with constraint/relation b/w 2 items

Answer 13

Use symmetry / mirroring (for each possibility has a mirror), 1-1 correspondence, Probability = 50%

Question 14

Adding the same number to terms in a list

Answer 14

DOESN’T change the standard deviation

Question 15

√ (P x Q)

Answer 15

√ P x √ Q

Question 16

√ (P / Q) given P>0, Q>0

Answer 16

√ P / √ Q

Question 17

Do NOT assume numbers are integers unless

Answer 17

EXPLICITLY stated

Question 18

Order DOESN’T matter

Answer 18

choice of individual elements DOESN’T make any meaningful difference in final set

Question 19

A divided by B, quotient Q, remainder R

Answer 19

A = Q(B) + R => A/B = Q (integer) + R/B (fraction/decimal part) & 0<=R<B

Question 20

If x²>0

Answer 20

x<0 / x>0 [for both +ve & -ve numbers, square is +ve]

Question 21

Changing one unit to another

Answer 21

x unit-conversion factor => (_ desired unit / _ given unit)

Question 22

Difference of squares

Answer 22

a²-b² = (a+b)(a-b)

Question 23

Tautological statements

Answer 23

Insufficient in themselves & canNOT combine with other insufficient statements to make a sufficient combination [C]

Question 24

Be aware of the CATEGORY of numbers involved

Answer 24

positive, 0, negative, whole no, fractions, decimals

Question 25

It is IMPOSSIBLE to produce an algebraic formula that will always produce

Answer 25

primenumbers

Question 26

Guessing Strategy for Probability

Answer 26

Use instincts, problems with complement rule (look for complement pairs in the options), think about overlap

Question 27

For Data Sufficiency

Answer 27

Using 0 or 1 can be quick

Question 28

Order matters

Answer 28

If counting the no of physical arragements, roles are specified for each choice, choosing elements in different orders produces meaningful different outcomes

Question 29

Use counting techniques if

Answer 29

problem involves selection of several elements from a set (with a certain restrictions)

Question 30

Solutions/Mixtures Questions

Answer 30

(1) VOLUME EQ: Total amount of liquid eq (2) SOLUTE EQ: Total amount of solute dissolved

Question 31

%s in succession comparison (P%-> Q% Vs. R%)

Answer 31

P+Q+PQ/100 Vs. R

Question 32

If 0 < b < 1

Answer 32

0 < b² < b < √b < 1

Question 33

Estimate when

Answer 33

lengthy or complex calculation / answer choices are spaced far apart

Question 34

Cubing Inequalities

Answer 34

Cubing retains +ve/-ve sign; x<0 => x³<0; x>0 => x³>0

Question 35

Age Questions

Answer 35

Rows: person A, person B, ...; Columns: cur-x year, cur year, cur+x year

Question 36

Multiple Traveller Problems

Answer 36

Each traveller & trip gets its own D=RT

Question 37

Shortcut: N/5

Answer 37

Nx2 / 10

Question 38

Square of a number ending in 5 => (x5)²

Answer 38

(x)(x+1)25

Question 39

Multiplication of 2 numbers => xy

Answer 39

(x)(2) * (y/2)

Question 40

Growth & Decay

Answer 40

Use the multiplier, step-by-step, one change interval at a time

Question 41

Principal Square Root Sign

Answer 41

Only returns +ve square roots, If we take square roots ourselves we consider +ve & -ve roots

Question 42

Use formal algebraic probability rules if

Answer 42

Problem gives you algebraic expressions, items are coins/cards/dice/etc, language of problem uses mutually exclusive/independent

Question 43

If j, k, and N are positive integers such that (jN)/k is an integer, and j/k is fully reduced, then N

Answer 43

Must be divisible by k