20 Math Trivia Questions

If
`WXY = 10`
`WYZ = 5`
`WXZ = 45`
`XYZ = 12`
What is `W + Y`?

We multiply the four given equations:
`(WXY)(WYZ)(WXZ)(XYZ)=10(5)(45)(12)`
`(WXYZ)^3=(2^3)(3^3)(5^3)`
Get the cube root
`WXYZ=2(3)(5)=30`
`W=(WXYZ)/(XYZ)=30/12=5/2`
`Y=(WXYZ)/(WXZ)=30/45=2/3`
`W+Y=(5/2)+(2/3)=19/6`
The answer is `19/6`

Let each of the characters `A, B, C, D, E` denote a single digit, and `ABCDE4` and `4ABCDE` represents six-digit numbers. If `4×ABCDE4=4ABCDE`, What is `C`?

Let `x=ABCDE`
`4(ABCDE4)=4ABCDE => 4(10x+4)=400000+x`
`x=10256`
`ABCDE=10256`, so `C=2`

Find the largest three-digit number such that the number minus the sum of its digits is a perfect square.

The answer is 919.
Let `ABC` be the three-digit number.
`(100A+10B+C)-(A+B+C)=99A+9B=9(11A+B)`
`9(11A+B)` is a perfect square.
To maximize the number `100A+10B+C`, we set `A=9`,`B=1` and `C=9`.

The integer `X` is the least among three positive integers whose product is `2160`. Find the largest possible value of `X`.

Note that `2160=(2^4)(3^3)(5)`. By trial-and-error method, one can aptly say that the set of three positive integers whose product is `2160` that will have a maximum least integer is `{10,12,18}`. Thus the value of `X` is `10`.

Find the smallest positive integer `X` such that the sum of `X, X+3, X+6, X+9, X+12` is a perfect cube.

Solution Coming Soon...

Six numbers from a list of nine integers are `7`, `8`, `3`, `5`, `9`, and `5`. What is the largest possible value of the median of all nine numbers in this list?

Arranging the data: `3`, `5`, `5`, `7`, `8`, `9`
For ungrouped data the median is the middle most entity. In this case we have six from the list of nine integers and we have to find the largest possible value of the median. Upon careful investigation, you will realize that what you have to do is to find the highest possible value of the 5th element which in this case is the median. If the three unknown numbers are greater than `8` we can say that the fifth element is `8` making it the highest possible value of our median.
Answer: `8`

All the students in an algebra class took a 100-point test. Five students scored 100, each student scored at least 60, and the mean score was 76. What is the smallest possible number of students in the class?

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In the sixth, seventh, eighth, and ninth basketball games of the season, a player scored 23, 14, 11, and 20 points, respectively. Her point-per-game average was higher after nine games than it was after the ﬁrst ﬁve games. Her average after ten games was greater than 18. What is the least number of points she could have scored in the tenth game?

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A circle in inscribed to triangle ABC. If AB=6 BC=4, CA=8 and given that P and Q are the points of tangency to BC and CA respectively, determine the length of the chord PQ.

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In how many ways can the letters of the word SPECIAL be permuted if the vowels are to appear in alphabetical order?

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Simplify the expression `i^2012+ i^2014`, where i is an imaginary number.

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Each side of the square ABCD is 12 meters long. The side AB is divided into three equal segments: AE, EF, and FB. Segments CE and DF intersect at point H. Find the area of triangle HCD.

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Seven points on a circle are numbered 1 to 7 in the clockwise direction. A grasshopper jumps in the counterclockwise direction, from one point to another on the circle. If the grasshopper is on an odd-numbered point, it moves one point, and moves two points if it is on an even-numbered point. If the grasshopper begins at the point 7, where will it be after 2012 jumps?

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Let A, B, C be three, not necessarily distinct, numbers chosen randomly form the set `{3, 4, 5, 6, 7, 8}`. Find the probability that `AB + C` is even.

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The mean of three numbers is 10 more than the least of the numbers and 15 less than the greatest. The median of the three numbers is 5. What is their sum?

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For what values of k does the equation `|x-2012|+|x+2012|=k` have `(-∞,-2012] uu [2012,+∞)` as its solution set?

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Given that `x+2` and `x-3` are factors of `p(x)=ax^3+ax^2+bx+12`; what is the remainder when `p(x)` is divided by `x-1`?

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A three digit number grows by 9 if we exchange the second and third digits and grows by 90 if we exchange the first and second digits. By how much will it grow if we exchange the first and third digits?

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A stone thrown into still water created ripples in the form of concentric circles, if the radius increases at a rate of `2``m/sec`. at what rate is the area increasing when the radius is 2m.

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Kate invited seventeen guests to her party. She assigned the numbers 1-18 to everyone in the party including her. When everyone was dancing, Kate noticed that the sum of each couple's numbers was a perfect square. If Kate assigned one for herself , what was the number of Kate's partner?

Solution Coming Soon...

Rhonnel Alburo

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