QUANT facts

Question 1

3 ^ k means…

Answer 1

how many 3s are there?

Question 2

“if x is a multiple of 7, and y is a multiple of 7, then x +y is a multiple of?”

Answer 2

If two numbers are both multiples of the same number, their SUM is also a multiple of that number

Question 3

The greatest POSSIBLE factor of A and B is…

Answer 3

The positive distance between them.

ex: | A - B | = x

two numbers that are X apart may both be multiples of X, but cannot be multiples of any number larger than X.

Question 4

(a + b) ^2 =

Answer 4

a^2 + 2(a)(b) + b^2

Question 5

(a - b) ^2 =

Answer 5

a^2 - 2(a)(b) + b^2

Question 6

(a^2 - b^2) =

Answer 6

(a-b) (a+b)

Question 7

when are the mean and the median always equal?

Answer 7

In a set of consecutive integers

Question 8

Divisibility fact about a set of “n” consecutive integers

Answer 8

at least one of the numbers in the set is divisible by “n”

Question 9

If “n” number of consecutive integers is even

Answer 9

Then sum is NOT a multiple of “n”

AND

The range is odd

Question 10

If “n” number of consecutive integers is odd

Answer 10

Then sum IS a multiple of “n”

AND

The range is even

Question 11

Two ways to calculate percent change

Answer 11

(New - Old) / Old

OR

(amt of change / starting amount) x100

Question 12

Trailing Zeros Formula

ex: how many zeros are in the end of 32!

Answer 12

n/5 + n/5^2

ex: 7 zeros are in the end of 32!

Question 12

xy > 0

signals?

Answer 12

x and y are either both positive or both negative

Question 13

Overlapping Sets Formulas (3 different ones)

Answer 13

A+B - Both + Neither

A+B+C - (sum of 2 groups) + (all 3) + Neither

A+B+C - (sum EXACTLY both) - 2(all 3) + Neither

Question 14

Ratio or fraction like this signals what 2 two things?

A:B = 5:2
or
A/B = 5/2

Answer 14

1- that A and B have the same sign

2- that A has a larger magnitude than B (aka, A will be further from 0 than B will be)

Question 15

xy < 0 signals?

Answer 15

z and y have different signs (one pos, one neg)

Question 16

X^2 - X < 0 signals?

Answer 16

0 < X < 1

Question 17

X^2 < X signals?

Answer 17

0 < X < 1

Question 18

Average Speed

Answer 18

total distance
= ____________
total time

Question 19

ABC /= 0 signals?

Answer 19

You can divide by an of the #s

*b/c otherwise, if any of the numbers were = 0, you can’t divide by 0.

Question 20

Exponent rules:

5^8 x 2^8 =

Answer 20

10^8

Question 21

Any # or base ^ 0 =

Answer 21

= 1

ONE exception: 0^0 = 0, not 1.

Question 22

Exponent Rules: what is the greatest prime factor of 4^20 + 4^21 + 4^22?

Answer 22

= 4^20 + 4^21 + 4^22
= 4^20 (4^0 + 4^1 + 4^2)
= 4^20 (1 + 4 + 16)
= 4^20 (21)
= (2^2)^10 (3 x 7) 

= 7 is the greatest prime factor.

Question 23

What does this signal on DS problem?

is |a| + |b| > |a + b| ?

Answer 23

signals that a and b must have opposite signs to be true.

Question 24

|x+y| = |x| + |y| WHEN?

Answer 24

when x and y have the same sign OR at least one of them = 0.

Question 25

|x+y| < |x| + |y| WHEN?

Answer 25

When x and y have OPPOSITE signs

Question 26

|x - y| = |x| - |y| WHEN?

Answer 26

1) when x and why have the same sign AND
2) when x has a greater than (or equal to) absolute value of y

OR 2) when y = 0

Question 27

|x - y| > |x| - |y| WHEN?

Answer 27

all cases that x and y have different signs OR when x has a lesser value than y

Question 28

square root of 196

Answer 28

14

Question 29

square root of 169

Answer 29

13

Question 30

square root of 225

Answer 30

15

Question 31

square root of 256

Answer 31

16

Question 32

4 different right triangle sets:

Answer 32

(3,4,5)

(5,12,13)

(7,24,25)

(8,15,17)