Mathematics Challenge

Problem:
1. If 2x + y = 13 and x + 2y = 11, what is the value of x + y?
2. Determine the units digit of the integer equal to 9 + 92 + 93 + 94.
(The units digit of an integer is its rightmost digit. For example, the units digit of
the integer 1234 is 4.)

Answer ?
Solution 1
Adding the two equations gives (2x + y) + (x + 2y) = 13 + 11 or 3x + 3y = 24.
Thus, x + y = 1/3(24) = 8.

Solution 2
We note that 9 + 92 + 93+ 94 = 9(1 + 91) + 93(1 + 91) = (9 + 93)(1 + 9) = 10(9 + 93).
Therefore, 9 + 92 + 93 + 94 is an integer that is divisible by 10, so its units digit is 0.

Comments

One Response to “Mathematics Challenge”

  1. nasrullah on March 4th, 2011 11:48 am

    let a and b be real numbers such that a>b>c. determine the least possible value of

    a + 1/b(a-b)

    please send your answer to nasrul.coral@gmail.com

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