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Flashcards in Quant Revisit List Deck (53)
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1
Q

sqrt(3)

A

1.7

2
Q

sqrt(2)

A

1.4

3
Q

Put this into an equation:

A
4
Q

Draw 2 variable + total matrix for this problem:

A
5
Q

What are the steps to solve:

A

EASY

Process: 1) split 10 into factors (5*2)^n => (5^n * 2^n) so we have common base 2) solve for n

6
Q

What’s the median and mean for consecutive integers?

A

2,4,6,8 = MEDIAN=5, MEAN=5; for 1,2,3,4,5,6,7 then MEDIAN=4 and MEAN=4. Middle number is both mean and median.

7
Q
A

U got this bro!

8
Q

Count number of multiples of 3

A

(Last - First)/(multiple) + 1

9
Q

How many different ways can you draw an isocolies triangle 40 degree angle?

A

40,40,100; 40,70,70; etc.

10
Q

Imagine you’re given a triangle inside a square, if that triangle’s base is the diameter of the circle, and the triangle touches the outside of a circle. What do you know about this triangle?

A

I know that the triangle has a 90 degree angle at the point that touches the circle.

11
Q

(x+y)^2

A

x^2 + 2xy + y^2

12
Q

(x-y)^2

A

x^2 -2xy + y^2

13
Q

How to solve?

A

SUBTRACT AREAS! will need to create equation using each triangle

14
Q

((x^5)^4) =

A

x^20

15
Q

y^4 * y^9 =

A

y^13

16
Q

Sqrt(p*q) =

A

Sqrt(p)*Sqrt(q)

17
Q

Even * Odd * Even = ?

A

Even

18
Q

Odd * Even * Odd = ?

A

Even

19
Q

Factor 147

A

Methodology: go from smallest to biggest when prime factoring. Clearly not divisible by 2, because 147 is odd.

Next, check for divisibility by 3 – 1+4+7 = 12, so it’s divisible by 3. (or, better, notice that it’s 3 less than the round number 150, which is 3x50, so 147 is 3x49)

20
Q

How do we tell if something is divisible by 3?

A

If each digit summed up sums to something that is divisible by three, then the answer is YES.

Example: 147 divisible by 3? Is 3 a factor of 147? 1+4+7 = 12, therefore YES.

21
Q

Is 0 an integer?
Is 0 even?

A

YES

and

YES

Zero is both EVEN and an integer.

22
Q

Is 1 a prime number?

A

NO!

23
Q

Are any prime numbers even?

A

YES! 2 is the ONLY even prime number.

24
Q

What are the factors of 6?

A

1,2,3,6

25
Q

What are the multiples of 6?

A

6,12,18,24…

26
Q

How do we tell if a fraction will be finite or repeating?

A

If denominator as 2 and 5 as prime factors => NOT REPEATING

What is a prime factor?

The prime factors of 15 are 3 and 5 (because 3×5=15, and 3 and 5 are prime numbers).

27
Q

When X and Y are both positive integers and the remainder is 2:

A

x/y = integer + remainder / y

This can help solve modulo or remainder questions.

28
Q

if 0 < x < 1 then rank:

sqrt(x), x^2, and x from least to greatest order

A

x^2 < x < sqrt(x)

29
Q

x^2 * y^2 - 16 = ?

A

(xy - 4)(xy + 4)

30
Q

x^2 - 9 = ?

A

(x-3)(x+3)

31
Q

5/4 = 1 + 1/4

A

1 is the REMAINDER, the MODULO. Use example to memorize this equation from my intuition.

32
Q

|2x + 4| = 12, x=?

A

Solution: Solve the equation TWICE. once for when absolute value is positive, a second time for when it is negative:

POSITIVE:

2x + 4 = 12 therefore x = 4

NEGATIVE

-(2x+4) = 12 therefore x = -8

33
Q

sqrt(10,000) = ?

A

100

34
Q

If two absolute values are equal, what must be true of the expressions?

A

It must be true that the expressions with the absolute value bars are either equals or opposites.

So:

|expression1 | = |expression2|

becomes in the equals case:

( expression1 ) = ( expression2)

and in the opposite case:

( expression1 ) = -( expression2)

Similar to solving an absolute value, you must solve twice for the unknown

35
Q

Equation for compound interest:

A

A = P(1 + r/n)^nt

36
Q
A

Remember 5^(x-3) = 5^x / 5^3

37
Q
A
38
Q
A

this one will be hard to solve w/o paper due to math. But main point is to translate from question to equation DIRECTLY:

A = 0.36*C

39
Q
A

Note: translate equations directly from the question.

“mixture weights more than 20 ounces” => m > 20

40
Q
A

Property of parallelogram: opposite triangles are the same area. This helps us solve for the isosceles triangle.

41
Q
A

Note: it is important to rephrase (a) the information that is given, and (b) the question:

42
Q
A

Any scalar => can solve.

43
Q
A

GMAT Hack: turn the two digits into variables. Tens digit = 10*A, one’s digit = 1*B.

Note: Translate equations from text!

44
Q

If y is the smallest positive integer such that 3,150 multiplied by y is the square of an integer, then y must be

(A) 2
(B) 5
(C) 6
(D) 7
(E) 14

A
45
Q

True of False: In a perfect square, the prime factors come in pairs

A

TRUE.

46
Q

How to tell if divisible by 11?

ex: is 143 divisible by 11?

A

Units digit and Hundreds digit sum to middle digit:

ex: is 143 divisible by 11?

1+3 = 4, therefore divisible by 11 !

47
Q

If n=12, how many positive and even divisors does n have, including n?

A

divisors of 12 = {1,2,3,4,6,12}

even divisors of 12 = {2,4,6,12}

therefore, 4.

48
Q
A
49
Q
A

the diagram is wrong. answer should read:

2^2 + 2(2) + 1 = (2+1)(2+1) = 3*3* = 9

50
Q

How do we know the area of an obtuse triangle?

A

still (1/2)*b*h, however the height is from the triangle that forms a right angle (see photo–blue triangle)

51
Q
A
52
Q

If a given triangle has two sides taht are the same length, is it isocolies?

A

YES. and the two opposite angles are both the SAME angle as well.

This problem, for example, can’t be solved without knowing this:

53
Q

How many 2 person teams can be formed with persons 1,2,3,4,5,6,7, and 8?

A

8 choose 2 =

n! / ((n-k)! k!)

8! / ((8-2)! * 2! )

8*7 / 2

56 /2

28.

NOTE: team “1,2,3” is same as “3,1,2” and “2,1,3” therefore order doesn’t matter. This is why we use COMBINATIONS equation.