PSHS National Competitive Examination Review Mathematics Ability FRACTIONS, DECIMALS
AND
PERCENTS
[1] Evaluate the expression
5 7 + 8 12 13 1 − 6 4 [A] 5/2
[B] 1/2
[C] 569/288
[D] 2
[E] 5/4
[2] What is 80% of 400% of (0.75 · 3/4)? [A] 2
[B] 1.75
[C] 1.8
[D] 1.18
[E] 1.01
[3] 90 is what percent of 75% of 600? [A] 10% [E] 40%
[B] 15%
[C] 20%
[D] 25%
[4] 62.5% of 280 is what percent of 200? [A] 12.5%
[B] 37.5%
[C] 50%
[D] 75%
[E] 87.5%
[5] The passing score in the PSHS-NCE is 60% for the total scores combined from the four subject areas. While taking the exam, Ivan was quite sure that he already got correct 36 out the 60 Math questions, 48 out of the 60 Science questions, and 15 out of the 30 Abstract Reasoning questions. What score must he get in the English which has 100 questions to pass the PSHS-NCE? [A] 42
[B] 51
[C] 65
[D] 70
[E] 84
[6] Bryan Castillo was pronounced as The Biggest Loser in ABS-CBN’s recent run of The Biggest Loser: Pinoy Edition Doubles. He weighed 293 pounds at the start of the show but by the end, he already lost 154 pounds. By what percentage did he lose weight? [A] 47.50%
[B] 49.10%
[C] 50.52%
[D] 52.56%
[E] 54.41%
For questions [7] to [9], refer to the problem below. The total energy content (measured in calories) of foodstuffs is assumed to only come from their carbohydrate, protein and fat contents. Carbohydrates can give 4 calories per gram, proteins can give 4 calories per gram and fats can give 9 calories per gram. A certain snack consists 10% fat, 20% protein and 70% carbohydrate. [7] What percent of the snack’s total energy is provided by fat only? [A] 20%
[B] 25%
[C] 37.7…%
[D] 68.8…%
[E] 80%
[8] What percent of the snack’s total energy is provided by fat and protein only?
[A] 20%
[B] 25%
[C] 37.7…%
[D] 68.8…%
[E] 80%
[9] What percent of the snack’s total energy is provided by protein and carbohydrate only? [A] 20%
[B] 25%
[C] 37.7…%
[D] 68.8…%
[E] 80%
[10] A single cupcake costs P40.00. However, you can buy a dozen for just P300.00. How much cheaper is a piece of cupcake if bought as part of a dozen rather than bought as a single piece? [A] 12.5%
[B] 25%
[C] 37.5%
[D] 60%
[F] 62.5%
[11] Sarah wanted to buy a certain pair of ladies’ shoes, originally priced P2500, for her mother last Mother’s Day. Since it was Mother’s Day, there was a sale in the mall and the shoes were marked with a discount of 40%. How much will Sarah need to buy these shoes? [A] P2500
[B] P2000
[C] P1500
[D] P1000
[E] P500
[12] Your classmate lent you P20 for an interest. For every day (after the day you borrowed) you are not able to pay, you need to add 10% of the original amount you borrowed to the amount you will pay. How much you will need if you are to pay your classmate a week after you borrowed the money? [A] P20.00
[B] P21.40
[C] 27.00
[D] P30.00
[E] P34.00
[13] A molecule consists of atoms of various elements. Sugar, formally C 6H12O6, contains 6 atoms of carbon C, 12 atoms of hydrogen H and 6 atoms of oxygen O. It is known that of the mass of one sugar molecule, 2/5 is contributed by the carbon atoms and 1/15 is contributed by the hydrogen atoms. If a carbon atom weighs 12 units and a hydrogen atom weighs 1 unit, what is the weight of an oxygen atom? [A] 8
[B] 10
[C] 14
[D] 16
[E] 24
[14] Little Boy is the name of the nuclear bomb that was used to attack Hiroshima during the World War II. Naturally occurring uranium ores contain both uranium-235 and uranium-238, but only uranium-235 can cause the explosion. To achieve the explosive power it needed, the uranium fuel used must be enriched. Natural uranium ores contain 99.8% uranium-238 and 0.2% uranium-235. Little Boy used a 60 kg uranium fuel which is 80% enriched (80% of the uranium fuel is uranium-235). How much natural uranium ore must be obtained to produce the fuel used in Little Boy? [A] 0.096 kg
[B] 9.6 kg
[C] 240 kg
[D] 2400 kg
[E] 24000 kg
[15] A group of three students decided to paint a mural. To divide the work fairly, each student will be given 2 hours each day to work on the mural. If the first student can finish 1/20 of the work in an hour, the second student can finish 1/15 of the work in an hour, and the third student can finish 1/12 of the work in an hour, how many days will it take these students to finish the mural? [A] 1
[B] 2
[C] 3
[D] 4
[E] 5
[16] The market value of a certain firm decreased by 20%. What percent increase must be applied to return the market value to what it was before the decrease?
[A] 10% [E] 60%
[B] 20%
[C] 25%
[D] 50%
For problems [17] and [18], refer to the problem below. In the Avatar cycle, the Avatar spirit is reincarnated into the next nation, as dictated by the cyclic order: Air, Water, Earth and Fire. The first Avatar of the first cycle was of the Air nation. [17] With the birth of the Avatar from the Water nation during the fiftieth cycle, what fraction of the Avatars that existed up to that time are from the Water nation? [A] 1/4
[B] 13/25
[C] 52/101
[D] 26/101
[E] 13/50
[18] Which of the following is TRUE about the Avatar cycle? I. II. III. IV. V.
For every reincarnation of the Avatar into the Air nation, the fraction of Avatars that existed up to that time which came from the Air nation is the same for all Avatar cycles. For every reincarnation of the Avatar into the Air nation, the fraction of Avatars that existed up to that time which came from the Air nation decreases through the progression of the Avatar cycles. For every reincarnation of the Avatar into the Fire nation, the fraction of Avatars that existed up to that time which came from the Fire nation is the same for all Avatar cycles. For every reincarnation of the Avatar into the Air nation, the fraction of Avatars that existed up to that time which came from the Air nation decreases through the progression of the Avatar cycles. For every reincarnation of the Avatar into the Air and Fire nations, for all Avatar cycles, the fraction of Avatars that existed up to that time which came from the Air nation always equals the fraction of Avatars that existed up that time which came from the Fire nation
[A] I and III [B] I and IV
[C] II and III [D] II and IV
[E] I, III and IV
For problems [19] and [20], refer to the problem. We define, for counting numbers a and b, the operation ü such that a ü b equals the sum of the fraction a/b and its reciprocal b/a. [19] What values of a and b will make a ü b equal to 25/12? [A] a = 1, b = 12 [B] a = 3, b = 4
[C] a = 7, b = 5 [D] a = 4, b = 10
[E] a = 2, b = 6
[20] Which of the following is TRUE for the operation ü? [A] For all counting numbers a and b, a ü b is always greater than one. [B] For all counting numbers a and b, a ü b is always less than one. [C] Whenever a = b, a ü b is always equal to two. [D] A and C
[E] B and C
PSHS National Competitive Examination Review Mathematics Ability SPECIAL FRACTIONS 1 1 ´ =0. 333=33 3 3 2 2 ´ =0. 666=66 3 3 1 2 ´ =0.1 66=16 6 3 5 1 ´ =0.8 33=83 6 3 1 1 ´ =0. 111=11 9 9 2 2 ´ =0. 222=22 9 9 4 4 ´ =0. 444=44 9 9
5 5 ´ =0. 555=55 9 9 7 7 ´ =0. 777=77 9 9 8 8 ´ =0. 888=88 9 9 1 1 ´ =0. 09=9 11 11 2 2 ´ =0. 18=18 11 11 1 1 =0.08 3´ =8 12 3 5 2 =0.41 6´ =41 11 3
PSHS National Competitive Examination Review Mathematics Ability WORD PROBLEMS Average problems [01] The temperature in Quezon City was measured for five days. On the first to fourth days, the city temperatures were 29⁰C, 31⁰C, 32⁰C and 35⁰C. Find the city temperature on the fifth day so that the average temperature for the five days is 33⁰C. [02] A certain class has 14 boys and 16 girls. The average score of the boys in the final exam is 84. What should be the average score of the girls so that the average score for the whole class is 86? Rate problems [03] If you shout into the Grand Canyon, your voice travels at the speed of sound (340 m/s) to the bottom of the canyon where it bounces and travels back to you. The echo you hear is the sound that travelled back to you. If you heard the echo 8 seconds after you shouted, how deep is the Grand Canyon from the spot where you shouted? [04] In order to go to work, Melissa needs to ride twice – first, a bus from her home to the MRT North Avenue station and second, the train from the MRT North Avenue to the MRT Ayala station. The distance between her home and MRT North Avenue station is 70 km while the distance between the MRT North Avenue and Ayala stations is 16 km. The speed of the bus is 50 kph and the speed of the MRT train is 60 kph, Note that Melissa needs to fall in line for around 45 minutes before she can ride the MRT. If she needs to arrive at work by 8:00 AM, what time must she leave her house everyday? [05] Tidus is up for a very important meeting. The appointed time of engagement is 02:00 PM so he decided to leave the office at 09:00 AM. His office is around 280 km away from the meeting place. Initially, he was travelling at a speed 60 kph. However, the client suddenly called around 11:00 am, asking Tidus that they need to meet by 01:00 PM. What must be Tidus’ new speed to arrive for the meeting at the new time? [06] Two cars started at the same point. One car travels north at a speed of 75 kph. Another car travels east at a speed of 90 kph. After 150 min, how far apart are the two cars? [07] Suppose a farmer can finish preparing a hectare of land in 6 days while another farmer can finish in 8 days, how long will it take the two farmers to prepare the land if they work together?
[08] One pipe can fill a pool 1.25 times faster than a second pipe. When both pipes are open, they can fill the pool in 6 hours. How long would it take to fill the pool if only the slower pipe is used? Geometry problems [09] The complement of the supplement of an angle is 25⁰. What is the measure of this angle? [10] A right triangle has one angle which measures 45⁰ and one leg (side other than hypotenuse) which measures 8. What is the area of the right triangle?
[11] Refer to the figure in the right. If a = 7, b = 24, find the area of the square whose side measures c. [12] Still, refer to the figure in the right. If the area of the inner square (with side c) is 100 and b = 8, what is the area of the larger square which inscribes the inner square?
[13] Refer to the figure in the right. If the area of the inner circle is 36π square units, find the perimeter and area of the outer square. [14] Still, refer to the figure in the right. The outer square has an area equal to the area of a rectangle with length of 32 and width of 8. Find the circumference and area of the inner circle.
[15] In general, an Olympic-size pool is 50 m long, 25 m wide and 3 m deep. What is the total capacity of an Olympic-size pool? [16] Four cubes of ice with an edge of 4 cm each are left to melt in a box whose base is a square of side 8 cm. How high will the water rise when the ice have melted? [17] How many square tiles with 20 cm edge are needed to completely cover the walls and floor of a room which is 10 m long, 6 m wide and 6 m high?
PSHS National Competitive Examination Review Mathematics Ability WORD PROBLEMS [01] The temperature in Baguio City was measured for six days. On the first to fourth days, the city temperatures were 15⁰C, 17⁰C, 19⁰, 21⁰C and 23⁰C. What should be the city temperature on the fifth day so that the average city temperature for the six days is 20⁰C? ________________ [02] ] Sanikem’s average score for her first four exams is 93. Note that the maximum score for all exams is 103. Can Sanikem reach a target average of 94 or above if her score in the fifth exam is…. [i] 94? ____
[ii] 95? ____
[iii] 98? _____ [iv] 100? ______
[03] Class A has 12 boys and 8 girls. For Class A, the average grade of the boys is 80 while the average score of the girls is 84. Class B has 10 boys and 6 girls. For Class B, the average grade of the boys is 85. What should be the average score of the girls in Class B so that the total averages for Class A and B are the same? _____________ [04] TRUE OR FALSE: The sum of the differences of the different scores from their mean equals zero. [05] Astronomers study celestial bodies by firing light waves (speed is 300,000 km/s) into the celestial body and letting the light wave signal return for analysis. If the distance between the astronomer and the celestial body he is studying is 6,000,000,000,000,000,000 m, how long will it take for light wave signal to be observed after firing? ___________________ [06] The plane ride from Manila, Philippine to Baku, Azerbaijan requires a single stop at Dubai, UAE. The distance between Manila and Dubai is 4000 mi (miles) while the distance between Dubai and Baku is 2000 mi. For the first flight, the speed of the plane is 5000 mph (miles per hour) while for the second flight, the speed of the plane is 6000 mph. What is the total travel time from Manila to Baku? ______________ [07] A toy boat, moving at 100 m/min, travels through a 200-m long segment of a river. Take that the boat needs to travel through that segment upstream and then go back to the starting point downstream. If the speed of the water current is 20 m/min, how long will it take for the toy boat to do the entire upstream-then—downstream course? ______________
[08] Two toy cars started at the same point. One car travels north at a speed of 1.5 m/s. Another car, which moves at 2 m/s, first travelled south for 1 s and then for the rest of trip, it travelled east. After 4 seconds, what is the distance between the two toy cars? ______________ [09] A certain sculptor can finish a replica of the Venus de Milo in 15 days. Another sculptor can finish the replica in 18 days. How long will it take for the two sculptors to finish the replica if they work together? _____________ [10] Three pipes are connected to a water reservoir – the first two brings water while the third drains water. The first pipe can fill the reservoir in 30 days and the second pipe can fill it in 40 days. The drain can empty the reservoir in 60 days. If all the pipes are open, how long will it take to completely fill up the empty reservoir? ______________ [11] Two angles are equal and complementary. What is the measure of the supplement of this angle? __________-
[12] Consider the parallel lines with a transversal on the right. It is always true for this figure that angles 5 and 3 are supplementary. Answer the following questions. [i] TRUE OR FALSE. Angles 4 and 6 are also supplementary. [ii] If angle 5 measures 135⁰, what is the measure of all the other angles in the figure? [13] Consider the figure on the right. The radius of the circle is 4. Answer the following questions. [i] What is the area of the outer square? [ii] What is the area of the inner square? [iii] What is the area of the shaded figure? [14] Consider the figure on the right. The circle has an area of 36 square units. What is the area of the square inside the circle?
[15] The figure on the right shows an annulus. For this figure, the radius r of the smaller circle has length 5 while the length d of the segment AB is 12. Note that AQ is perpendicular to AB. [i] What is the area and perimeter of the triangle formed by r, d and R (radius of larger outer circle)? [ii] What is the difference between the circumferences of the outer and inner circle? [iii] What is the area of the annulus (the shaded figure)?
