ALGEBRA RECENT BOARD EXAM QUESTION

REE - Apr. 2011. A four-pound mixture of raisins and nuts is 2/3 raisins. How many pounds of nuts are there? A. 1.3 pounds B. 1.6 pounds C. 2.4 pounds D. 2.6 pounds

A. 1.3 pounds

PAST BOARD 2019/2021. The square of a number added to 25 equals 10 times the number. What is the number? A. -5 B. 5 C. -10 D. 10

B. 5

PAST BOARD 2021. Find the sum of the first five terms of the geometric progression if the 3rd term is 144 and the 6th term is 486. A. 844 B. 749 C. 978 D. 540

A. 844

REE - May 2010 / Sept. 2017. How many liters of water must be added to 1 liter of 35% boric acid solution in order to produce 20% boric acid solution? A. 0.75 liter B. 0.5 liter C. 1.5 liters D. 1.0 liter

A. 0.75 liter

PAST BOARD 2019. z varies directly as x and inversely as y^2. If x^2. Find x =1 andy = 2 then z = 2. Find z when x = 3 and y = 4. A. 1.5 B. 2.5 C. 3.5 D. 3.0

A. 1.5

REE - Feb. 2014 / Apr. 2017 / Sept. 2017 / Sept. 2018. What is the next term in the geometric sequence 16, −4, 1, −1/4, ...? A. 1/16 B. 1/8 C. −1/8 D. 0

A. 1/16

REE- May 2009. Kevin flies (in his private jet) from Los Angeles (LA) to San Francisco (SF), a distance of 450 miles, in 3 hours. He flies back in 2-7/19 hours. If the wind is blowing from the north at a steady rate during both flights, find the airspeed of the plane in mph. A. 170 B. 120 C. 150 D. 160

A. 170

PAST BOARD 2017/2019. A and B can do a piece of work in 3 days, B and C in 4 days, while A and C in 2.5 days. In how many days can all of them do the work together? A. 2.03 C. 1.02 B. 3.17 D. 3.83

A. 2.03

REE - Mar. 1998 If the polynomial x 3 + 4x2 - 3x + 8 is divided by x - 5, determine the remainder. A. 218 B. 45 C. 42 D. 210

A. 218

REE - Sept. 2011 / Sept. 2018. Find the sum of all odd integers between 100 and 1000. A. 247500 B. 374200 C. 148500 D. 454500

A. 247500

PAST BOARD 2013. Maria is 10 years older than Jake, who is 16 years old. How old is Maria? A. 26 years old C. 10 years old B. 22 years old D. 6 years old

A. 26 years old

PAST BOARD 2022. A certain two-digit number is equal to five times the sum of its digit. If 9 were added to the number, its digits would be reversed. Find the number? A. 45 B. 84 C. 54 D. 48

A. 45

PAST BOARD 2022. Melissa is four times as old as Jim. Pat is 5 years older than Melissa. If Jim is "y" years old, how old is Pat? A. 4y + 5 C. 4 x 5y B. 5y + 4 D. y+5

A. 4y + 5

PAST BOARD 2022. Rick can paint a room in an hour and a half and James can paint the same room in 2 hours. How many minutes will it take them to paint the room if they do it together? A. 51 B. 30 C. 64 D. 210

A. 51

PAST BOARD 2011/2015/2022. A ball is dropped from a height of 18 meters. On each rebound it rises 2/3 of the height from which it last fell. What distance has it travelled at the instant it strikes the ground for the fifth time? A. 75.78 m B. 36.49 m C. 57.87 m D. 63.94 m

A. 75.78 m

REE - Apr. 2003. What is the value of (sq.rt. of -10) x (sq.rt. of -7)? A. (sq.rt. of 70)i B. -(sq.rt. of 70) C. -(sq.rt. of 70)i D. sq.rt. of 70

B. -(sq.rt. of 70)

PAST BOARD 2019. If 1 is added to the difference when 10x is subtracted from -18x, the result is 57. What is the value of x? A 7 B. -2 C. 2 D. -7

B. -2

PAST BOARD 2010/2017. How many liters of water must be added to 1 liter of 35% boric acid solution in order to produce 20% boric acid solution? A. 1.20 L B. 0.75 L C. 1.00 L D. 0.40 L

B. 0.75 L

REE - Sept. 2003 / Apr. 2004 / Sept. 2004 25. Binoy, Boboy and Bata are hired to paint signs. In 8 hours Binoy can paint 1 sign, Boboy can paint 2 signs, and Bata can paint 1 1/3 signs., They all come to work the first day, but Bata doesn't like the job and quits after 3 hours. Boboy works half an hour longer than Bata and quits. How long will it take Binoy to finish the two signs they were supposed to paint? A. 2 hrs B. 1 1/2 hrs C. 2 1/3 hrs D. 3 hrs

B. 1 -1/2 hrs

REE - Oct. 2000. What time after one o'clock will the hands of the clock coincide for the first time? A. 1:7-5/11min B. 1:5-5/11min C. 1:6-5/11min D. 1:4-5/11min

B. 1:5-5/11min

PAST BOARD 2019. How many positive real roots are there in the polynomial: x^4 - 4x^3 + 7x^2 - 6x -18 = 0 A. 1 or 2 B. 3 or 1 C. 3 or 0 D. 1 or 0

B. 3 or 1

REE - May 2010 / Apr. 2019 / Aug. 2019. How many possible positive real roots are there in x^4 - 4x^3 + 7x2 - 6x - 18 = 0? A. 1 or 2 B. 3 or 1 C. 3 or 0 D. 1 or 0

B. 3 or 1

REE - Apr. 2003 / Apr. 2004 What are the values of n if (2n - 6) is greater than 1 but less than 14? A. 4,5,6,7,8,9,10 B. 4,5,6,7,8,9 C. 3,4,5,6,7,8 D. 2,3,4,5,6,7

B. 4,5,6,7,8,9

PAST BOARD 2019/2023 Joseph gave 1/4 of his candies to Joy and Joy gave 1/5 of what she got to Tim. If Tim received 2 candies, how many candies did Joseph have originally? A. 20 B. 40 C. 30 D. 50

B. 40

PAST BOARD 2019. If Jim and Jerry together they can finish a job in 4 hours. If working alone takes Jim 10 hours to finish the job, how many hours would it take Jerry to do the job alone? A. 16 B. 6.7 C. 6.0 D. 5.6

B. 6.7

REE - Apr. 2012 / Sept. 2016 If f(x) = 10^x + 1, then f(x + 1) - f(x) is equal to A. 10(10^x) B. 9(10^x) C. 1 D. 9(10^x + 1)

B. 9(10^x)

PAST BOARD 2017/2019. Find the sum of a geometric progression if there are 4 geometric means between 3 and 729. A. 1,352 B. 1,110 C. 1,092 D. 1,074

C. 1,092

PAST BOARD 2011. A four-pound mixture of raisins and nuts is two-thirds raisins. How many pounds of nuts are there? A. 3.7 pounds C. 1.3 pounds B. 2.8 pounds D. 1.9 pounds

C. 1.3 pounds

PAST BOARD 2011. A boat can travel 10 miles downstream and at the same time can travel 6 miles upstream. If the current of water is 3 mph, find the speed of the boat in still water. A. 14 mph B. 6 mph C. 12 mph D. 9 mph

C. 12 mph

PAST BOARD 2012/2019. In a pile of logs, each layer contains one more log than the layer above and the top contains just one log. If there are 105 logs in the pile, how many layers are there? A. 18 B. 12 C. 14 D. 10

C. 14

REE - Apr. 2011. A bus leaves Manila at 12 NN for Baguio 250 km away, traveling an average of 55 kph. At the same time, another bus leaves Baguio for Manila traveling 65 kph. At what time will they meet? A. 3:25 PM B. 4:25 PM C. 2:05 PM D. 3:05 PM

C. 2:05 PM

PAST BOARD 2022. What is the greatest factor of 24 and 64? A. 4 B. 10 C. 8 D. 12

C. 8

PAST BOARD 2022. Toby, a Golden Retriever, gained 5.1 pounds this month. If Toby now weights 65.1 pounds, what is the percent increase in Toby's weight? A. 5.9% B. 8.5% C. 6% D. 9.1%

C. 8.5%

PAST BOARD 2019. If the graph of y = f(x) is transformed into a graph of 2y - 6 = -4 f(x - 3), point (a,b) on the graph of y = f(x) becomes point (A,B) where A and B are expressed as: A. A = a + 4, B = 2b + 3 B. A = a + 6, B = 2b + 6 C. A = a + 3, B = -2b + 3 D. A = a + 2, B = 2b + 3

C. A = a + 3, B = -2b + 3

REE - Sept. 2015 / Apr. 2018 An equation of the form a/b = c/d is A. an inequality B. an equality C. a proportion D. a ratio

C. a proportion

REE - Sept. 2011. A boat can travel 10 miles downstream and at the same time can travel 6 miles upstream. If the current of water is 3 mph, find the speed of a boat in still water. A. 8 mph B. 9 mph C. 7 mph D. 12 mph

D. 12 mph

REE - May 2010. Find the term involving x squared in the expansion of (x^3 + k/x)^10. A. 210 k sq. x sq. B. 32 k sq. x sq. C. 92 k sq. x sq. D. 120 k^7 x sq.

D. 120 k^7 x sq.

REE - April 2017 / Apr. 2019 / Aug. 2019. A and B can do a piece of work in 3 days, B and C in 4 days, while A and C in 2.5 days. In how many days can all of them do the work together? A. 3.17 B. 1.02 C. 3.83 D. 2.03

D. 2.03

REE- Sept. 2009. Kevin flies (in his private jet) from Los Angeles (LA) to San Francisco (SF), a distance of 450 miles, in 3 hours. He flies back in 2-7/19 hours. If the wind is blowing from the north at a steady rate during both flights, find the velocity of the wind. A. 24 mph B. 18 mph C. 25 mph D. 20 mph

D. 20 mph

PAST BOARD 2021. Which of the following is not a multiple of 11? A. 231 B. 121 C. 1,111 D. 221

D. 221

PAST BOARD 2011/2018. Find the sum of all odd integers between 100 and 1,000. A. 758,065 B. 274,050 C. 587,650 D. 247,500

D. 247,500

PAST BOARD 2023. Joey participated in a dance-a-thon. His team started dancing at 10 A.M. on Friday and stopped at 6 P.M. on Saturday. How many hours did Joey's team dance? A. 52 B. 30 C. 56 D. 32

D. 32

REE - Feb. 2014 / Sept. 2015 / Apr. 2019 / Aug. 2019 5. A group consists of n engineers and n nurses. If two of the engineers are replaced by two other nurses, then 51% of the group members will be nurses. Find the value of n. A. 100 B. 110 C. 80 D. 5

D. 5

PAST BOARD 2017/2019/2022. The geometric mean and the arithmetic mean of two numbers are 8 and 10 respectively. What is the harmonic mean? A. 3.8 B. 8.4 C. 7.2 D. 6.4

D. 6.4

PAST BOARD 2022. The distance from the sun to the earth is approximately 9.3 x 10~7 miles. What is the distance expressed in standard notation? A. 930,000,000 C. 0.00000093 B. 93,700,000 D. 93,000,000

D. 93,000,000