Quant Notes

# of Integers in Interval

• sum = 1 + Last - First

  • ie: “How many integers from 13 to 92?” → 92 - 13 + 1 = 80

Sum of Integers in Interval

• sum = (n(a+l)) / 2

  • n = # of integers; a = first term; l = last term

  • ie: “sum of all integers from 50 to 300” → 251(50 + 300) / 2 = 43,925

Even and Odd (±)

• even ± even = even

• odd ± odd = even

• odd ± even = odd

Even and Odd (*)

• even * even = even

• odd * odd = odd

• odd * even = even

# of Multiples in Interval

• sum = 1 + ((Last Multiple - First Multiple) / Multiple in Question)

  • ie: “How many multiples of 3 from 29 to 112?” → 1 + ((111-30)/3) = 28

Product (Sum) of Multiples in Interval

• product = (sum of pairs)(total # of pairs)

  • total # of pairs = # of Multiples in Interval / 2

  • sum of pairs = Last multiple + First multiple

• ie: sum of all multiples of 6 from 75 to 286

  • total # of pairs = 1 + ((282-78)/6) = 35/2 = 17.5

  • sum of pairs = 282 + 78 = 360

  • product = (360)(17.5) = 6,300

Percent Change (Increase ONLY)

• Big - Small / Small

Percent Change (Decrease ONLY)

• Big - Small / Big

Ratio

• part over part, NOT part over whole (fraction)

  • ie: ratio of 3 girls to 2 boys = 3:2 = 3/2

$$\left(\sqrt{x}\right)^2$$

$$x$$

$$\sqrt{x^2}$$

$$x$$

$$\sqrt{x}\sqrt{y}$$

$$\sqrt{xy}$$

$$\frac{\sqrt{x}}{\sqrt{y}}$$

$$\sqrt{\frac{x}{y}}$$

Factorial

$$10!=10\cdot9\cdot8\cdot7\cdot6\cdot5\cdot4\cdot3\cdot2\cdot1$$

PEMDAS Trickiness

• multiplication/division

• addition subtraction

  • ALWAYS go left to right, NOT PEMDAS

  • ie: 6 / 2 × 3 = 9

Even and Odd Integers

• Even = whole numbers divisible by 2

• Odd = whole numbers NOT divisible by 2