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TTP - Quant > Number Properties > Flashcards

Number Properties Flashcards

1
Q

what is the only number that is equal to its opposite?

A

Zero

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2
Q

What is the formula for even numbers?

A

2K where k is an int

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3
Q

What is the formula for odd numbers?

A

2k+1 or 2k-1 where k is an int

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4
Q

Multiplication rule for even numbers

A

even * any number = even

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5
Q

Multiplication rule of odd numbers

A

odd * odd = odd

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6
Q

Addition rules

A

even + even = even or odd + odd = even everything else is odd

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7
Q

Subtraction rules

A

even - even = even or odd - odd = even everything else is odd

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8
Q

X power 2 = 16; what is X?

A

X can be 4 or -4

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9
Q

X power 3 = -8; what is X?

A

X = -2

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10
Q

Factors of a prime number X?

A

itself i.e X and 1

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11
Q

Number of factors of a prime number?

A
  1. Prime factorize X 2. then add 1 to exponents and multiply
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12
Q

Rule about unique prime factors of a number

A

Number of unique prime factors doesn’t change when the number is raised to a positive integer exponent

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13
Q

What are division rules for odd and even numbers?

A

odd/odd = odd, even/odd = even, even/even = odd or even, odd/even = not possible

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14
Q

What would be the result when multiplying or dividing with numbers having same sign?

A

greater than zero

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15
Q

X^any even power. what is the sign of X?

A

can be +ve or -ve

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16
Q

X^any odd power, what is the sign of X?

A

sign of X^any odd power

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17
Q

What are the prime numbers b/w 1 and 100?

A

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 53, 59, 83, 89, 31, 37, 61, 67, 41, 43, 47, 71, 73, 79, 97

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18
Q

What is a multiple?

A

x is a multiple of y if x/y = r0

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19
Q

What is a factor?

A

y is a factor of x if x/y = r0

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20
Q

How do you calculate the LCM of X, Y?

A
  1. prime factorize both x and y 2. take the highest of repeated pf 3. identify the non repeated pf 3. multiply what you found in steps two and three.
21
Q

(x, y). x/y= r0 What is LCM and GCF?

A

LCM = x; GCF = y

22
Q

How do you calculate GCF of x, y?

A
  1. prime factorize both x and y 2. identify the lowest of repeated pfs 3. multiply what you found in step 2
23
Q

What is GCF of x, y when x, y don’t share repeated prime factors?

A

1

24
Q

What we would know about x, y if we know their LCM and GCF?

A

product of x and y

25
Q

x/y; what is divisor and dividend?

A

y is divisor, x is dividend

26
Q

when thinking about divisibility, think about what?

A

prime factorization

27
Q

z is divisible by x and y, then z must be divisible by what?

A

LCM of X and Y

28
Q

What is divisibility rule for 4?

A

last two digits of a number were divisible by 4

29
Q

What is divisibility rule for 8?

A

last three digits of a number were divisible by 8

30
Q

What is divisibility rule for 6?

A

divisible by Both 2 and 3

31
Q

Formula for division?

A

x/y = q + r/y

32
Q

How do you convert 4.33 to fraction form?

A

4 + 33/100

33
Q

How do you convert 26/6 to decimal form?

A

4 + 2/6 = 4 + 0.33 = 4.33

34
Q

Multiplying, subtracting or adding remainders rule

A

you can add or multiply remainders when you must correct the excess remainders

35
Q

the range of possible remainders of x/y

A

0 to y-1

36
Q

no of trailing zeroes in a number =

A

number of (2*5) pairs

37
Q

no of leading zeroes in a number for 1/x if x is an integer and perfect power of 10?

A

no of digits of x - 2

38
Q

no of leading zeroes in a number for 1/x if x is an integer and not a perfect power of 10?

A

no of digits of x -1

39
Q

number of primes in factorial when the base of divisor is not a prime number?

A

prime factorize the base divisor and then use the usual strategy

40
Q

prime factorization of a perfect square contains?

A

only even exponents

41
Q

prime factorization of a perfect cube contains?

A

only exponents that are multiples of 3

42
Q

How do you identify whether a fraction is terminating decimal or not?

A

if the divisor of the fraction contains either 2’s or 5s or both, then only its a terminating decimal

43
Q

When do remainders exhibit patterns?

A

when +ve ints are divided by a constant divisor or powers of certain base divided by a constant divisor

44
Q

When do unit digits exhibit patterns?

A

when a +ve int raised to a power of consecutive ints

45
Q

when integers with same units are divided by 5, what happens to remainder?

A

remainder is same

46
Q

product of n consecutive integers divisible by?

A

n!

47
Q

product of n even consecutive integers divisible by?

A

2^n(n!)

48
Q

How many numbers b/w 10 and 100 that are both perfect square and perfect cube and what they are?

A

Only 1; 64

TTP - Quant (12 decks)

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