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Target test prep > Quant > Flashcards

Quant Flashcards

1
Q

In data sufficiency questions, what are we being asked to calculate?

A

NOT the numerical answer e.g., x=5, but rather, could you get the value of x? so only analyse up until the point where you can say yes or no!

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2
Q

what are the 5 strategic numbers to evaluate statements?

A
  1. positvie integer
  2. positive fraction (0-1)
  3. 0
  4. negative integer
  5. negative fraction (-1 -0)
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3
Q

simple fractions. what is a proper and improper fraction?

A

proper fraction: numerator is less than the denomenator (5/7)
improper fraction: numerator is greater than the denomenator around (3/2)

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4
Q

what is mixed number?

A

number + proper fraction (7/2 = 3 1/2, 2 is called quotient)

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5
Q

Least Common Denominator (LCD) is… ?

LCD of 1/2, 1/3, and 1/8 be..?

A

smallest non-zero whole number that is divisible by each of the denominators
24

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6
Q

what is Equivalent fraction?

A

Same value but appear different a/b = c/d but also ad=bc

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7
Q

Rational number, integer, whole number, natural number?

A

Rational: any numbers incl. fraction
integer: incl. 0 and negatives
whole number: 0, 1,2,3,4…
Natural number: 1,2,3,4,…

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8
Q

What is reciprocal of 5? what is the only number that doesn’t have reciprocal?

A

1/5, 0

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9
Q

complex fraction

A

fractions that numerator, denominator or both are also fractions

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10
Q

compare the size of 4/17, 8/49 and 12/75?

A

24/102, 24/147 and 24/150. So compare using numerator.

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11
Q

what is the units digit?

A

same as ones, units digit for 675 is 5

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12
Q

whats the tenth and hundredth of 7.54952?

A

tenth: 5, hundredth: 4

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13
Q

What is principal square root?

A

The unique nonnegative square root of a nonnegative real number. principal square root of 121 is 11 although root of 121 is +/- 11.

  • real number includes rational and irrational number like root 2.
  • we only consider principal square root when √ is used.
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14
Q

x^2 < x < √x under what condition of x?

A

0

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15
Q

what is a perfect square?

A

A number made by squaring a whole number.

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16
Q

What is the opposite of the number 7?

A

-7

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17
Q

Whats the order of math calculations?

A

P: Parentheses or absolute value bars or radicals
E: exponets
M and D: multiple and division from the left
A and S: addition and subtraction form the left

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18
Q

what is 0!

A

1

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19
Q

List 2 properties of 0 involving multiples and factors.

A

0 is a multiple of all numbers.

0 is the only factor of itself.

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20
Q

List 3 properties of 1 involving multiples, factors, and prime numbers.

A

every number is a multiple of 1.
1 is a factor of all numbers.
1 is not a prime number.

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21
Q

Rules of addition, multiplication and division between odd and even numbers?

A

Addition: only combination of odd and even leads to odd numbers.

Multiplication: only odd times odd will be odd.

Division: even divided by odd will be even.
odd divided by odd will be odd.
even divided by even can be either.

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22
Q

What is the definition of prime number?

A

Any integer greater than 1 and has no factors other than 1 and itself

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23
Q

What are composite numbers?

A

Number that is not a prime number

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24
Q

How do you calculate the number of factors does the value 12,000 has?

A
  1. prime factorize 12,000 = 5^3 * 3 * 2^5
  2. add 1 to each of the exponents
  3. multiply all of the the (exponent + 1)s
    (3+1)2(5+1)=48 factors.
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25
Q

How many prime factors and unique prime factors do 45 have?

A

3^2* 5 so you have 3 prime factors and 2 unique prime factors.

26
Q

How many unique prime factors do the prime numbers have?

A

One. Prime numbers have 2 factors, 1 and the number itself. Since 1 is not the prime number, the number itself is the only unique prime factor.

27
Q

What is the range of numbers when I say numbers between 1 and 10?

A

2-9

28
Q

Does a number of unique prime factors of x change when you squared the x?

A

No.
6 = 23 –> 2 UPFs
36 = 2^23^3 –> 2 UPFs

29
Q

What is LCM?

A

The smallest positive multiple of all integers in the set.

Careful with the 3 or more variables in the set!

30
Q

What is the GCF?

A

The positive integer that the largest number that divides into all of the numbers in the set

31
Q

If we know LCM(x,y) and GCF(x,y), what can we calculate?

A

xy

32
Q

What does x is divisible by y mean?

A

x/y has no remainder

and x is not divisible if (5√x)/5 = √x as x could be integer or not

33
Q

If integer x is divisible by 15 and 20, does x also be divisible by LCM(15,20)?

A

Yes

34
Q

Divisibility rule: How do you know if the number is divisible by 4?

A

Last 2 digits are divisible by 4.
For 244, 44/4=11 so its divisible.

00s are divisible by 4

35
Q

Divisibility rule: How do you know if the number is divisible by 6?

A

Even number + sum of all digits is divisible by 3

36
Q

Divisibility rule: How do you know if the number is divisible by 8 ?

A

even + last 3 digits is divisible by 8

000s are divisible by 8.

37
Q

Divisibility rule: How do you know if the number is divisible by 9?

A

Sum of all digits is divisible by 9

38
Q

Divisibility rule: How do you know if the number is divisible by 11?

A

Sum of odd digits - sum of even digits is divisible by 11.

for 2915, 5+9 - (1+2)=11
for 253, 2+3-5=0 so divisible.

39
Q

Divisibility rule: How do you know if the number is divisible by 12?

A

Last 2 digits is divisible by 4 + sum of the digits divisible by 3.

40
Q

The product of n consecutive products are divisible by…?

A

n!

and if x is 3 consecutive products and y is 4 consecutive products, the xy is divisible by 3!*4!

41
Q

THe product of n consecutive even integers is divisible by…?

A

(2^n)*n!

42
Q

what is the equation for x divides into y?

and x divided by y?

A

into: y/x
by: x/y

43
Q

What is the remainder when x=131417 is divided by 5?

A
  1. divide indivisually
    13/5 = 2R3
    14/5 = 2R4
    17/5 = 3R2
  2. multiply all the reminders
    342=24
  3. Take the reminders if multiply is excessive reminders
    24/5=4R4
  4. So 4 quotients can be made from sum of remainders and what is left (remainder of the remainder) will be the overall remainder.
44
Q

What is the remainder for x= 17-13?

A
  1. divide indivisually
    17/5=3R2
    13/5=2R3
  2. subtract (add if the x is addition equation) the remainders
    2-3 = -1
  3. Remainder -1 does not make sense. If you look at the equation, 3R2 - 2R3 = 1R-1. Thus, break out the quotient of 1 and it will be 0R4. Thus remaineder is 4.

※This technique of quotient reduction idea can only be used on adding and subtracting.

45
Q

prime factorization of (5*2) creates what?

A

Trailiing 0

46
Q

How do you find how many digits in a particular number?

A
  1. prime factorize
  2. count (5*2) pairs
  3. Multiply all rests
  4. add digits of 3 and 2
47
Q

What is leading zero? and what are the 2 rules ?

A

Leading 0 is number of 0s after decimal point.

Denomenator is a perfect power of 10: K(number of denomenator digits) -2

Denomenator is NOT a perfect power of 10: K -1

48
Q

400! = (15^n)X what is the max number of n?

A

Finding number of prime numbers in the factorial

15^n = 3^n * 5^n so that since 5 appears less than 3, you only need to calculate how many 5s in the 400!.

To do that, 
1. Divide 400 by 5, 5^2, 5^3... until Quotient is 0
400/5 = 80
400/25 = 16 
400/125 = 3 (ignore the R)...
  1. add all the Quotient
    80+16+3+… = 99

Since you can divide 400! by 3 more times, there will be 99 sets of 15 in 400!

49
Q

How many times can 400! be divided by the 45?

A

400!/ 45^n = k(integer)

45^n = 3^2n * 5^n thus we dont know which comes around more.

  1. you calculate how many times you can divide 400! by 3 and find 196.
  2. since we wanna know how many 9s in 400!, there will be 196/2 = 98 9s.
  3. we know there will be 99 5s can fit in the 400! and thus, we know you can divide 400! by 45 98 times.
50
Q

What is perfet square?

A

if √x = integer, than x is perfect square

51
Q

What is the rule of the prime factorizaion of perfect square?

A

Will always contain even exponents 100 = 2^2 * 5^2

52
Q

Dicimal will terminate iff …?

A

The denomenator of the equivalent fraction calue has prime factorization that only contain 2s or 5s or both. Otherwise, it will not terminate.

53
Q

What is the remainder of 3^320 / 4?

A 
Remiander repeats! 
3^1: 3/4 = 0R3
3^2: 9/4 = 2R1
3^3: 27/4 = 6R3
3^4: 81/4 = 20R1

3,1,3,1,… sequence so that 320/4=80 so even number will have R1.

54
Q

What is a value fo units digit for 7^49?

A 
1. Find the pattern in units digit
7^1 = 7
7^2 = 49
7^3 = 343
7^4 = ~~1
7^5 = ~~7

So the sequence of units digit of 7 is 7,9,3,1.

  1. Find where the unit digit of 49th number of sequence is.
    49/4 = 12R1 thus the unit digit must be 7.
55
Q

What are the rules regarding the remainder with the positive integers with the same unit digit when divided by 5?

A 
remainder is constant. 
7/5 = 1R2
17/5 = 3R2 
57/5 = 11R2
when finished with 7, the remainder is always 2 in the specia case that same units digits and divided by 5 only!
56
Q

2 consecutive integers will never…?

A

Will never share the same prime factors.

i.e., GCF(n, n+1) = 1

57
Q

Explain the rule of the n roots when n is even and odd.

A

n is even: n√(x^n) = |x|

n is odd: n√(x^n) = x and x can be negative

58
Q

simplify 4/(a - √(b)

A

Take conjugate of the binomial (a - √(b)), which is a + √(b) and multiply to both denomenator and numerator.

4(a + √(b))/ (a^2 - b)

59
Q

What do you have to watch out for whn ou soling a equation involving the square roots?

A

Make sure after you get the x, you put them back into the equation to see if its correct.

60
Q

if n is even in n√a, a must be?

A

greater than equal to 0. As there are no number such that

x^n = negative number. (-4)^2 = 16

61
Q

x^a * y^a is ?

A

(xy)^a as long as exponents are the same, you can multiply and divide them together

Target test prep (2 decks)

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