Question

3 questions for 15 points

1. Randomly selecting a page in a booklet, the chance to get an even

page number is 48%. How many pages does the booklet have?


2. What is the units digit of the sum of all positive multiples of 6

smaller than 500?


3. If each dimension of a rectangle decreases by 1, its area will

decrease from 2017 to 1717. What will be the area of the rectangle if

each of its dimensions increases by 1?

Answer 1

100 pages

Unit digit = 6

Explanation:

Chance of getting an even page number = 48% = 0.48

P(Not even) = 1 - 0. 48 = 0.52

P(even) = 0.48

(0.48 + 0.52) * 100

1 * 100

= 100 pages

(Number of even pages / total pages) * 100 = 0.48

x/2 * 1/x * 100 = 0.48

200

Positive Multiples of 6 up to 500 :

6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72, 78, 84, 90, 96, 102, 108, 114, 120, 126, 132, 138, 144, 150, 156, 162, 168, 174, 180, 186, 192, 198, 204, 210, 216, 222, 228, 234, 240, 246, 252, 258, 264, 270, 276, 282, 288, 294, 300, 306, 312, 318, 324, 330, 336, 342, 348, 354, 360, 366, 372, 378, 384, 390, 396, 402, 408, 414, 420, 426, 432, 438, 444, 450, 456, 462, 468, 474, 480, 486, 492, 498.

Sum of the multiples = 20196

Unit digit of the sum = 6