1500 - 1500 (1/4 + 1/5 + 1/3) = 325
#212: This question is pattern recognition. The sequence looks like this: 5, 7, 1, 3, 1, 3...
After the first two terms you have 1, 3, 1, 3 ...repeating. 100 - 2 = 98
98 divided by 2 leave no remainder so the answer is "3".
#213:
#214:
#215: Use Pythagorean to get the hypotenuse:(3/2)2 + (20/3)2 = h2
9/4 + 400/9 = (81 + 1600)/36 = h2, h = 41/6
The perimeter is (3/2) + (20/3) + (41/6) = (9 + 40 + 41)/6 = 90/6 = 15 = x
The area of the triangle = (3/2)(20/3)(1/2) = 5 = y
x2 - y2 = 225 - 25 = 200
#216: To find x2y2z2 in the expansion of
(x + y + z)6, you do 6!/2!2!2! = 90
Same way as you find how many ways to arrange banana (6!/3!2!, 3 and 2 being the
repeating letters.)
Here are the explanations from Math Forum.
#217: If you count 0 as multiple of any digit, there are 9 ( from 1 to 9) numbers.
For unit digit 1, there is 1.
For unit digit 2, or other prime numbers, there are two numbers, which is 1 and itself so 4 x 2 = 8 numbers.
(2, 3, 5, 7, 4 prime numbers)
For unit digit 4, there are 1, 2, 4, three numbers.
Fro unit digit 6, there are 1, 2, 3 and 6, four numbers.
For unit digit 8, there are 1, 2, 4, and 8, four numbers.
For unit digit 9, there are 1, 3, and 9, three numbers.
Add them up and the answer is (9 + 1 + 8 + 3 + 4 + 4 + 3)/ 90 (two digit numbers from 10 - 99)
= 32/90 = 16/45
#218: Working backward, you'll see the value of each coin to the others looks like this:
1f = 4e = 16d = 64c = 256b = 1024a
To have least amount of coins, you use the larger value coins as many as possible.
2012 = (1 x 1024) + (3 x 256 ) + ( 3 x 64) + (1 x 16) + ( 3 x 4)
The lease number of coins are 1 + 3 + 3 + 1 + 3 = 11 coins
#219: For m < n and m + n is even, you need m and n both to be either even or both to be odd.
There are 50 even numbers and 50 odd numbers in that list.
50C2 + 50C2 = 2450 {Only 1 way that gives you m < n after you choose two even from the list of
even numbers.)
C
#220: CE = 7
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