EASY 1. Ferb the fruit lover bought 12 apples and 20 mangoes for ₱240 and bought 30 apples and 10 mangoes for the same amount of money. How much does an apple cost? (5 pesos) 2. Carlo and Carly are doing their homework. Carlo can solve a problem in 15 minutes, while Carly can solve it for 10 minutes. How many minutes can they solve the same problem, working together? Assume that their solving rates are constant. (6 minutes) 3. How many numbers x from 1 to 2013 satisfy the following equation:
(2013) 4. Patrick the photographer loves to take pictures. He took 10 pictures on Spongebob’s house, 20 on Squidward’s house, 30 on Mr. Krabs’s, and so on, such that on every next house, he takes 10 more pictures than the house before. How many pictures does he take by the time he visits Dora’s house, which happens to be the 20th house in their neighborhood? (2100) 5. How many triangles are there in the figure? (27) 6. Perry drew a regular decagon. Then, he drew all possible lines inside the hexagon that goes from one corner to another (but not an edge). How many lines did he draw? (35) 7.
Determine whether the linear expression
is a factor of
. If not a factor, write the remainder of the division . (2) 8.
Assume that in terms of
9.
Factor
,
and
. Determine the value of
and . (x + y + z) completely. (3(x+y)^5)
10.
Let
be the unique positive integer such that
is the largest integer not
exceeding the largest 4-digit palindrome. Find . (x = 13)
AVERAGE 1. Dora and her monkey friend Boots went to a journey. For her journey, Dora packed 5 shirts, 4 caps, 3 pants, 4 shorts and 2 shades. How many sets of outfits can she have, assuming she wears one from each type of clothing? (280) 2.
Solve for
in
3.
Shelly sells seashells by the seashore in three shiny colors (white, blue and yellow). She sold
(x = 1)
of the total shells she has. The white, blue and
yellow shells she sold are in the ratio 5:7:9, respectively. If 252 shells remained, how many blue shells did Shelly sell by the seashore? (28) 4. My closet is filled with seven pairs of fuchsia, seven pairs of magenta and seven pairs of carnation socks. How many socks must I pick to ensure that I have a matching pair of magenta socks? (30) 5. Taylor is grouping consecutive counting numbers by 5 such that the first group contains the sequence 1, 2, 3, 4, 5 and the second group contains 6, 7, 8, 9, 10, while the third group contains 11, 12, 13, 14, 15. If he continues doing this until the 50th group, what is the sum of all the numbers in that group? (1240) 6. Draw 10 straight lines on a circular cardboard. What is the maximum number of parts that the cardboard can be divided into? (56) 7.
Evaluate
. (1/2)
8. A Lamborghini and a Bugatti departed at 8:00 AM from two cities which are 1600 km away from each other. They traveled towards each other, one at a speed of 250 km/h and the
other at a speed of 350 km/h. When would the two cars meet? (10:40 AM) 9.
In the figure, AA’ is parallel to CC’. If , find the value of
and
(in degrees). (78)
10. Find the largest power of 2 that divides the number 322,560. (2^10 or 1024)
DIFFICULT 1. Professor McGonagall was assigned by Professor Dumbledore to do a survey about the wizards and witches on their favorite subjects. Of the 120 students surveyed, 70 likes Transfiguration, 25 likes Defense Against the Dark Arts and 50 like Potions. 18 like both like Transfiguration and Defense Against the Dark Arts, 40 like Transfiguration and Potions, and 5 both like Defense Against the Dark Arts and Potions. Only Draco Malfoy and Hermione Granger like all three. The rest like Arithmancy. How many like Arithmancy? (36) 2.
Jack gave Rose a rose having a petal shaped like a regular hexagon. If the area of the hexagon is
cm2, what is its perimeter? (36 cm)
3. Present at Juan’s birthday party were a father-in-law, a mother-in-law, a daughter-in-law, two sons, two daughters, two sisters and a brother, four children, three grandchildren, two fathers, two mothers, a grandfather and a grandmother. However, family relationships can be complicated. One man’s brother can, of course, be another man’s brother-in-law, and at the same time, someone’s son. With that in mind, what is the smallest number of people needed at the party for the above relationships to exist? (7) 4.
Let and be two distinct 2-digit numbers where . If the product is a 4-digit number with 2 as the first digit and after striking the leading digit, the remaining number becomes the sum of and . Find at least one possible value of
and . (30, 70) and/or (24, 88)
5. Hogwarts School of Witchcraft and Wizardry sent Finn, Jake and Bubblegum each a letter of invitation to this school. But, The Ice King exchanged all letters of invitation in a way that no one receives his or her own letter. For example,
Finn does not receive his own letter, instead he receives Jake’s letter. In how many ways can The Ice King do this? (2 ways) 6. A hen and a half can lay an egg and a half for a day and a half. How many hens can lay 8 eggs in 9 days? (12 hens) 7.
In a 2013-gon (a polygon with 2013 sides), the measure of one exterior angle is . Find the average of the measures of the remaining 2012 exterior angles. (1/11)
8.
For
and
, evaluate
. (-12)
9. Benjamin Button has a curious case of aging backwards; after each year, he becomes one year younger rather than older. Also, Benjamin has a distant relative, named Zenjamin Zipper, who ages normally. Three years ago, Benjamin was twice as old as Zenjamin. The situation will be reversed 9 years from now, as by then, Zenjamin will be twice as old as Benjamin. How old are Benjamin and Zenjamin now? (B=21, Z=15) 10. Let
such that
. Evaluate
. (1/8)
