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MCQ in Clock, Variation, and Progression Problems Part 1 | Math Board Exam

(Last Updated On: January 5, 2021)

MCQ in Clock, Variation, and Progression Problems Part 1

This is the Multiple Choice Questions Part 1 of the Series in Clock, Variation, and Progression Problems of the Engineering Mathematics topic. In Preparation for the ECE Board Exam make sure to expose yourself and familiarize in each and every questions compiled here taken from various sources including but not limited to past Board Examination Questions in Engineering Mathematics, Mathematics Books, Journals and other Mathematics References.

MCQ Topic Outline included in Mathematics Board Exam Syllabi

  • MCQ in Clock Problems | MCQ in Progression / Sequence Series | MCQ in Arithmetic Progression | MCQ in Geometric Progression | MCQ in Infinite Geometric Progression | MCQ in Harmonic Progression | MCQ in Related Sequence | MCQ in Fibonacci Numbers | MCQ in Lucas Numbers | MCQ in Figurate Numbers (Triangular Numbers, Square Numbers, Gnomons, Oblong Numbers, Pentagonal Numbers, Cubic Numbers, Tetrahedral Numbers, Square Pyramidal Numbers, Supertetrahedral Numbers | MCQ in Diophantine Equations | MCQ in Variation Problems

Start Practice Exam Test Questions Part 1 of the Series

Choose the letter of the best answer in each questions.

Problem 1: CE Board May 1995

In how many minutes after 2 oโ€™clock will the hands of the clock extend in opposite directions for the first time?

A. 42.4 minutes

B. 42.8 minutes

C. 43.2 minutes

D. 43.6 minutes

View Answer:

Answer: Option D

Solution: Review: Solution for Number 1

Problem 2: CE Board November 1995

In how many minutes after 7 oโ€™clock will the hands be directly opposite each other for the first time?

A. 5.22 minutes

B. 5.33 minutes

C. 5.46 minutes

D. 5.54 minutes

View Answer:

Answer: Option C

Solution: Review: Solution for Number 2

Problem 3: CE Board May 1997

What time after 3 oโ€™clock will the hands of the clock are together for the first time?

A. 3:02.30

B. 3:17.37

C. 3:14.32

D. 3:16.36

View Answer:

Answer: Option D

Solution: Review: Solution for Number 3

Problem 4: GE Board February 1997

At what time after 12:00 noon will the hour hand and minute hand of the clock first form an angle of 120o?

A. 12:18.818

B. 12:21.818

C. 12:22.818

D. 12:24.818

View Answer:

Answer: Option B

Solution: Review: Solution for Number 4

Problem 5:

At what time between 8 and 9 oโ€™clock will the minute hand coincide with the hour hand?

A. 8:42.5

B. 8:43.2

C. 8:43.6

D. 8:43.9

View Answer:

Answer: Option C

Solution: Review: Solution for Number 5

Problem 6: EE Board October 1990

A man left his home at past 3:00 oโ€™clock PM as indicated in his wall clock, between 2 to 3 hours after, he returns home and noticed the hands of the clock interchanged. At what time did the man leave his home?

A. 3:31.47

B. 3:21.45

C. 3:46.10

D. 3:36.50

View Answer:

Answer: Option A

Solution: Review: Solution for Number 6

Problem 7: GE Board February 1994

Form the time 6:15 PM to the time 7:45 PM of the same day, the minute hand of a standard clock describes an arc of?

A. 60ยฐ

B. 90ยฐ

C. 180ยฐ

D. 540ยฐ

View Answer:

Answer: Option D

Solution: Review: Solution for Number 7

Problem 8: EE Board April 1990

A storage battery discharges at a rate which is proportional to the charge. If the charge is reduced by 50% of its original value at the end of 2 days, how long will it take to reduce the charge to 25% of its original charge?

A. 3

B. 4

C. 5

D. 6

View Answer:

Answer: Option A

Solution: Review: Solution for Number 8

Problem 9: ECE Board April 1990

The resistance of a wire varies directly with its length and inversely with its area. If a certain piece of wire 10 m long and 0.10 cm in diameter has a resistance of 100 ohms, what will its resistance be if its is uniformly stretched so that its length becomes 12 m?

A. 80

B. 90

C. 144

D. 120

View Answer:

Answer: Option C

Solution: Review: Solution for Number 9

Problem 10: CE Board May 1993

Given that โ€œwโ€ varies directly as the product of โ€œxโ€ and โ€œyโ€ and inversely as the square of โ€œzโ€ and that w = 4 when x = 2, y = 6 and z = 3. Find the value of โ€œwโ€ when x = 1, y = 4 and z = 2.

A. 3

B. 4

C. 5

D. 6

View Answer:

Answer: Option A

Solution: Review: Solution for Number 10

Problem 11: ECE Board November 1993

If x varies directly as y and inversely as z, and x = 14 when y =7 and z = 2, find the value of x when y = 16 and z = 4.

A. 14

B. 4

C. 16

D. 8

View Answer:

Answer: Option C

Solution: Review: Solution for Number 11

Problem 12: EE Board March 1998

The electric power which a transmission line can transmit is proportional to the product of its design voltage and current capacity, and inversely to the transmission distance. A 115-kilovolt line rated at 100 amperes can transmit 150 megawatts over 150 km. How much power, in megawatts can a 230 kilovolt line rated at 150 amperes transmit over 100 km?

A. 785

B. 485

C. 675

D. 595

View Answer:

Answer: Option C

Solution: Review: Solution for Number 12

Problem 13: ME Board October 1992

The time required for an elevator to lift a weight varies directly with the weight and the distance through which it is to be lifted and inversely as the power of the motor. If it takes 30s seconds for a 10hp motor to lift 100 lbs through 50 feet, what size of motor is required to lift 800 lbs in 40s seconds through 40 feet?

A. 42

B. 44

C. 46

D. 48

View Answer:

Answer: Option D

Solution: Review: Solution for Number 13

Problem 14:

The selling price of TV set is double that of its cost. If the TV set was sold to a customer at a profit of 25% of the net cost, how much discount was given to the customer?

A. 33.7%

B. 35.7%

C. 37.7%

D. 34.7%

View Answer:

Answer: Option C

Solution: Review: Solution for Number 14

Problem 15:

A group of EE examinees decided to hire a mathematics tutor from Excel Review Center and planned to contribute equal amount for the tutorโ€™s fee. If there were 10 more examinees, each would have paid P2 less. However, if there were 5 less examinees, each would have paid P2 more. How many examinees are there in the group?

A. 14

B. 16

C. 18

D. 20

View Answer:

Answer: Option D

Solution: Review: Solution for Number 15

Problem 16: EE Board March 1998

A bookstore purchased a best selling price book at P200.00 per copy. At what price should this book be sold so that, giving a 20% discount, the profit is 30%?

A. P 450

B. P 500

C. P 357

D. P 400

View Answer:

Answer: Option C

Solution: Review: Solution for Number 16

Problem 17: ECE Board November 1993

Jojo bought a second hand Betamax VCR and then sold it to Rudy at a profit of 40%. Rudy then sold the VCR to Noel at a profit of 20%. If Noel paid P2, 856 more than it cost to Jojo, how much did Jojo paid for the unit?

A. P 4,000

B. P 4,100

C. P 4,200

D. P 4,300

View Answer:

Answer: Option C

Solution: Review: Solution for Number 17

Problem 18: EE Board March 1998

In a certain community of 1,200 people, 60% are literate. Of the males, 50% are literate and of the females 70% are literate. What is the female population?

A. 850

B. 500

C. 550

D. 600

View Answer:

Answer: Option D

Solution: Review: Solution for Number 18

Problem 19: ECE Board March 1996

A merchant has three items on sale, namely a radio for P50, a clock for P30 and a flashlight for P1. At the end of the day, he sold a total of 100 of the three items and has taken exactly P1000 on the total sales. How many radios did he sale?

A. 16

B. 20

C. 18

D. 24

View Answer:

Answer: Option A

Solution: Review: Solution for Number 19

Problem 20: ME Board October 1996

The arithmetic mean of a and b is?

A. clip_image002[4]_thumb

B. clip_image004[4]_thumb

C. clip_image006[4]_thumb

D. clip_image008[4]_thumb

View Answer:

Answer: Option A

Solution: Review: Solution for Number 20

Problem 21:

The sum of three arithmetic means between 34 and 42 is?

A. 114

B. 124

C. 134

D. 144

View Answer:

Answer: Option A

Solution: Review: Solution for Number 21

Problem 22: EE Board March 1998

Gravity causes a body to fall 16.1 ft in the first second, 48.3 in the 2nd second, 80.5 in the 3rd second. How far did the body fall during the 10th second?

A. 248.7 ft

B. 308.1 ft

C. 241.5 ft

D. 305.9 ft

View Answer:

Answer: Option D

Solution: Review: Solution for Number 22

Problem 23:

If the first term of arithmetic progression is 25 and the fourth term is 13, what is the third term?

A. 17

B. 18

C. 19

D. 20

View Answer:

Answer: Option A

Solution: Review: Solution for Number 23

Problem 24: ECE Board November 1998

Find the 30th term of the arithmetic progression 4, 7, 10, โ€ฆ.

A. 75

B. 88

C. 90

D. 91

View Answer:

Answer: Option D

Solution: Review: Solution for Number 24

Problem 25: CE Board May 1993, CE Board May 1994, CE Board November 1994

How many terms of the progression 3, 5, 7, โ€ฆ must be taken in order that their sum will be 2600?

A. 48

B. 49

C. 50

D. 51

View Answer:

Answer: Option C

Solution: Review: Solution for Number 25

Problem 26: ME Board April 1995

In 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. 11

B. 12

C. 13

D. 14

View Answer:

Answer: Option D

Solution: Review: Solution for Number 26

Problem 27: CE Board May 1995

What is the sum of the progression 4, 9, 14, 19 โ€ฆ up to the 20th term?

A. 1030

B. 1035

C. 1040

D. 1045

View Answer:

Answer: Option A

Solution: Review: Solution for Number 27

Problem 28: EE Board April 1997

A stack of bricks has 61 bricks in the bottom layer, 58 bricks in the second layer, 55 bricks in the third layer, and so on until there are 10 bricks in the last layer. How many bricks are there all together?

A. 638

B. 637

C. 639

D. 640

View Answer:

Answer: Option C

Solution: Review: Solution for Number 28

Problem 29: CE Board May 1998

Determine the sum of the progression if there are 7 arithmetic mean between 3 and 35.

A. 171

B. 182

C. 232

D. 216

View Answer:

Answer: Option A

Solution: Review: Solution for Number 29

Problem 30: ECE Board April 1995

A besiege fortress is held by 5700 men who have provisions for 66 days. If the garrison losses 20 men each day, for how many days can the provision hold out?

A. 72

B. 74

C. 76

D. 78

View Answer:

Answer: Option C

Solution: Review: Solution for Number 30

Problem 31: CE Board May 1991

In the recent โ€œGulf Warโ€ in the Middle East, the allied forces captured 6400 of Saddamโ€™s soldiers and with provisions on hand it will last for 216 meals while feeding 3 meals a day. The provision lasted 9 more days because of daily deaths. At an average, how many died per day?

A. 15

B. 16

C. 17

D. 18

View Answer:

Answer: Option D

Solution: Review: Solution for Number 31

Problem 32: GE Board July 1993

A Geodetic Engineering student got a score of 30% on Test 1 of the five number test in Surveying. On the last number he got 90% in which a constant difference more on each number that he had on the immediately preceding one. What was his average score in Surveying?

A. 50

B. 55

C. 60

D. 65

View Answer:

Answer: Option C

Solution: Review: Solution for Number 32

Problem 33: ME Board April 1999

If the sum of 220 and the first term is 10, find the common difference if the last term is 30.

A. 2

B. 5

C. 3

D. 2/3

View Answer:

Answer: Option A

Solution: Review: Solution for Number 33

Problem 34: EE Board April 1997

Once a month, a man puts some money into the cookie jar. Each month he puts 50 centavos more into the jar than the month before. After 12 years, he counted his money, he had P5, 436. How much money did he put in the jar in the last month?

A. P 73.50

B. P 75.50

C. P 74.50

D. P 72. 50

View Answer:

Answer: Option A

Solution: Review: Solution for Number 34

Problem 35: EE Board April 1997

A girl on a bicycle coasts downhill is covering 4 feet the first second, 12 feet the second second, and in general, 8 feet more each second than the previous second. If she reaches the bottom at the end of 14 seconds, how far did she coasts?

A. 782 feet

B. 780 feet

C. 784 feet

D. 786 feet

View Answer:

Answer: Option C

Solution: Review: Solution for Number 35

Problem 36:

When all odd numbers from 1 to 101 are added, the result is?

A. 2500

B. 2601

C. 2501

D. 3500

View Answer:

Answer: Option B

Solution: Review: Solution for Number 36

Problem 37:

How many times will a grandfatherโ€™s clock strikes in one day if it strikes only at the hours and strike once at 1 oโ€™clock, twice at 2 oโ€™clock, thrice at 3 oโ€™clock and so on?

A. 210

B. 24

C. 156

D. 300

View Answer:

Answer: Option C

Solution: Review: Solution for Number 37

Problem 38: CE Board May 1992

To conserve energy due to the present energy crisis, the Meralco tried to re-adjust their charges to electrical energy users who consume more than 2000 kw-hrs. For the first 100 kw-hr, they charged 40 centavos and increasing at a constant rate more than the preceding one until the fifth 100 kw-hr, the charge is 76 centavos. How much is the average charge for the electrical energy per 100 kw-hr?

A. 58 centavos

B. 60 centavos

C. 62 centavos

D. 64 centavos

View Answer:

Answer: Option A

Solution: Review: Solution for Number 38

Problem 39: CE Board November 1993

The 3rd term of a harmonic progression is 15 and the 9th term is 6. Find the 11th term.

A. 4

B. 5

C. 6

D. 7

View Answer:

Answer: Option B

Solution: Review: Solution for Number 39

Problem 40: ECE Board November 1995

Find the fourth term of the progression ยฝ, 0.2, 0.125, . . .

A. 1/10

B. 1/11

C. 0.102

D. 0.099

View Answer:

Answer: Option B

Solution: Review: Solution for Number 40

Problem 41:

Find the 9th term of the harmonic progression 3, 2, 3/2โ€ฆ.

A. 3/5

B. 3/8

C. 4/5

D. 4/9

View Answer:

Answer: Option A

Solution: Review: Solution for Number 41

Problem 42:

Find the sum of 4 geometric means between 160 and 5.

A. 130

B. 140

C. 150

D. 160

View Answer:

Answer: Option C

Solution: Review: Solution for Number 42

Problem 43: EE Board October 1991

The fourth term of a G.P. is 216 and the 6th term is 1944. Find the 8th term.

A. 17649

B. 17496

C. 16749

D. 17964

View Answer:

Answer: Option B

Solution: Review: Solution for Number 43

Problem 44: ECE Board April 1999

Determine x so that: x, 2x + 7, 10x โ€“ 7 will be a geometric progression.

A. 7, -7/12

B. 7, -5/6

C. 7, -14/5

D. 7, -7/6

View Answer:

Answer: Option D

Solution: Review: Solution for Number 44

Problem 45: ECE Board April 1999

If one third of the air in a tank is removed by each stroke of an air pump, what fractional part of the total air is removed in 6 strokes?

A. 0.7122

B. 0.9122

C. 0.6122

D. 0.8122

View Answer:

Answer: Option B

Solution: Review: Solution for Number 45

Problem 46: ME Board October 1996

A product has a current selling of P325.00. If itโ€™s selling price is expected to decline at the rate of 10% per annum because of obsolescence, what will be its selling price four years hence?

A. P 213.33

B. P 202.75

C. P 302.75

D. P156.00

View Answer:

Answer: Option A

Solution: Review: Solution for Number 46

Problem 47: CE Board May 1995

The numbers 28, x + 2, 112 form a G.P. What is the 10th term?

A. 14336

B. 13463

C. 16433

D. 16344

View Answer:

Answer: Option A

Solution: Review: Solution for Number 47

Problem 48: ECE Board April 1998

The sum of the first 10 terms of geometric progression 2, 4, 8, โ€ฆ

A. 1023

B. 2046

C. 225

D. 1596

View Answer:

Answer: Option B

Solution: Review: Solution for Number 48

Problem 49:

If the first term of G.P. is 9 and the common ration is -2/3, find the fifth term.

A. 8/5

B. 16/9

C. 15/7

D. 13/4

View Answer:

Answer: Option B

Solution: Review: Solution for Number 49

Problem 50: EE Board April 1997

The seventh term is 56 and the twelfth term is -1792 of a geometric progression. Find the common ratio and the first term. Assume the rations are equal.

A. -2, 5/8

B. -1, 5/8

C. -1, 7/8

D. -2, 7/8

View Answer:

Answer: Option D

Solution: Review: Solution for Number 50

Problem 51:

A person has 2 parents, 4 grandparents, 8 great grandparents and so on. How many ancestors during the 15 generations preceding his own, assuming no duplication?

A. 131070

B. 65534

C. 32766

D. 16383

View Answer:

Answer: Option B

Solution: Review: Solution for Number 51

Problem 52:

If the PBA three-point shootout-contest, the committee decided to give a prize in the following manner. A price of P1 for the first basket made, P2 for the second, P4 for the third, P8 for the fourth and so on. If the contestant wants to win a prize of no less than a million pesos, what is the minimum number of baskets to be converted?

A. 20

B. 19

C. 18

D. 21

View Answer:

Answer: Option A

Solution: Review: Solution for Number 52

Problem 53: CE Board November 1994

In a benefit show, a number of wealthy men agreed that the first one to arrive would pay 10 centavos to enter and each later arrive would pay twice as much as the preceding man. The total amount collected from all of them was P 104,857.50. How many wealthy men paid?

A. 18

B. 19

C. 20

D. 21

View Answer:

Answer: Option C

Solution: Review: Solution for Number 53

Problem 54:

A man mailed 10 chain letters to ten of his friends with a request to continue by sending similar letter to each of their ten friends. If this continue for 6 sets of letters and if all responded, how much will the Phil. Postal Office earn if minimum postage costs P4 per letter?

A. P 6,000,000

B. P 60,000

C. P 2,222,220

D. P 4,444,440

View Answer:

Answer: Option D

Solution: Review: Solution for Number 54

Problem 55: EE Board March 1998

Determine the sum of the infinite series: S = clip_image010[1]_thumb + clip_image012[1]_thumb + clip_image014_thumb + โ€ฆ. + clip_image016_thumbn

A. 4/5

B. 3/4

C. 2/3

D. 1/2

View Answer:

Answer: Option D

Solution: Review: Solution for Number 55

Problem 56:

Under the favourable condition, single cell bacteria divided into two about every 20 minutes. If the same rate of division is maintained for 10 hours, how many organisms is produced from a single cell?

A. 1,073,741

B. 1,730.74

C. 1,073,741,823

D. 1,037,417

View Answer:

Answer: Option C

Solution: Review: Solution for Number 56

Problem 57: EE Board October 1994

A rubber ball is made to fall from a height of 50 feet and is observed to rebound 2/3 of the distance it falls. How far will the ball travel before coming to rest if the ball continues to fall in this manner?

A. 200 feet

B. 225 feet

C. 250 feet

D. 275 feet

View Answer:

Answer: Option C

Solution: Review: Solution for Number 57

Problem 58: EE Board April 1990

What is the fraction in lowest term equivalent to 0.133133133?

A. clip_image002[6]_thumb

B. clip_image004[6]_thumb

C. clip_image006[6]_thumb

D. clip_image008[6]_thumb

View Answer:

Answer: Option D

Solution: Review: Solution for Number 58

Problem 59: ECE Board April 1998

Find the sum of the infinite geometric progression 6, -2, 2/3, . . .

A. 9/2

B. 5/2

C. 7/2

D. 11/2

View Answer:

Answer: Option A

Solution: Review: Solution for Number 59

Problem 60: CE Board May 1998

Find the sum of 1, – clip_image026_thumb, clip_image028_thumb, . . .

A. 5/6

B. 2/3

C. 0.84

D. 0.72

View Answer:

Answer: Option A

Solution: Review: Solution for Number 60

Problem 61: ECE Board November 1998

Find the ratio of an infinite geometric progression if the sum is 2 and the first term is ยฝ.

A. 1/3

B. 1/2

C. 3/4

D. 1/4

View Answer:

Answer: Option C

Solution: Review: Solution for Number 61

Problem 62: EE Board April 1997

If equal spheres are piled in the form of a complete pyramid with an equilateral; triangle as base, find the total number of spheres in the pile if each side of the base contains 4 spheres.

A. 15

B. 20

C. 18

D. 21

View Answer:

Answer: Option B

Solution: Review: Solution for Number 62

Problem 63:

Find the 6th term of the sequence 55, 40, 28, 19, 13, . . .

A. 10

B. 9

C. 8

D. 11

View Answer:

Answer: Option A

Solution: Review: Solution for Number 63

Problem 64: EE Board October 1997

In the series 1, 1, ยฝ, 1/6, 1/24, . . .determine the 6th term.

A. 1/80

B. 1/74

C. 1/100

D. 1/120

View Answer:

Answer: Option D

Solution: Review: Solution for Number 64

Problem 65: ECE Board April 1998

Find the 1987th in the decimal equivalent toย  clip_image030_thumbย  starting from the decimal point.

A. 8

B. 1

C. 7

D. 5

View Answer:

Answer: Option A

Solution: Review: Solution for Number 65

Online Question and Answer in Clock, Variation, and Progression Problems Series

Following is the list of multiple choice questions in this brand new series:

MCQ in Clock, Variation, and Progression Problems
PART 1: MCQ from Number 1 โ€“ 50                               Answer key: PART 1
PART 2: MCQ from Number 51 โ€“ 100                          Answer key: PART 2
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