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 oโclock 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
Answer: Option D
Solution: Review: Solution for Number 1
Problem 2: CE Board November 1995
In how many minutes after 7 oโclock 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
Answer: Option C
Solution: Review: Solution for Number 2
Problem 3: CE Board May 1997
What time after 3 oโclock 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
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
Answer: Option B
Solution: Review: Solution for Number 4
Problem 5:
At what time between 8 and 9 oโclock 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
Answer: Option C
Solution: Review: Solution for Number 5
Problem 6: EE Board October 1990
A man left his home at past 3:00 oโclock 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
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
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
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
Answer: Option C
Solution: Review: Solution for Number 9
Problem 10: CE Board May 1993
Given that โwโ varies directly as the product of โxโ and โyโ and inversely as the square of โzโ and that w = 4 when x = 2, y = 6 and z = 3. Find the value of โwโ when x = 1, y = 4 and z = 2.
A. 3
B. 4
C. 5
D. 6
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
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
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
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%
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 tutorโs 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
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
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
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
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
Answer: Option A
Solution: Review: Solution for Number 19
Problem 20: ME Board October 1996
The arithmetic mean of a and b is?
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
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
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
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, โฆ.
A. 75
B. 88
C. 90
D. 91
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, โฆ must be taken in order that their sum will be 2600?
A. 48
B. 49
C. 50
D. 51
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
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 โฆ up to the 20th term?
A. 1030
B. 1035
C. 1040
D. 1045
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
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
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
Answer: Option C
Solution: Review: Solution for Number 30
Problem 31: CE Board May 1991
In the recent โGulf Warโ in the Middle East, the allied forces captured 6400 of Saddamโs 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
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
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
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
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
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
Answer: Option B
Solution: Review: Solution for Number 36
Problem 37:
How many times will a grandfatherโs clock strikes in one day if it strikes only at the hours and strike once at 1 oโclock, twice at 2 oโclock, thrice at 3 oโclock and so on?
A. 210
B. 24
C. 156
D. 300
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
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
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
Answer: Option B
Solution: Review: Solution for Number 40
Problem 41:
Find the 9th term of the harmonic progression 3, 2, 3/2โฆ.
A. 3/5
B. 3/8
C. 4/5
D. 4/9
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
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
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
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
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 itโs 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
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
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, โฆ
A. 1023
B. 2046
C. 225
D. 1596
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
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
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
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
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
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
Answer: Option D
Solution: Review: Solution for Number 54
Problem 55: EE Board March 1998
Determine the sum of the infinite series: S = + + + โฆ. + n
A. 4/5
B. 3/4
C. 2/3
D. 1/2
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
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
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?
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
Answer: Option A
Solution: Review: Solution for Number 59
Problem 60: CE Board May 1998
Find the sum of 1, – , , . . .
A. 5/6
B. 2/3
C. 0.84
D. 0.72
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
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
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
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
Answer: Option D
Solution: Review: Solution for Number 64
Problem 65: ECE Board April 1998
Find the 1987th in the decimal equivalent toย ย starting from the decimal point.
A. 8
B. 1
C. 7
D. 5
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:
P inoyBIX educates thousands of reviewers and students a day in preparation for their board examinations. Also provides professionals with materials for their lectures and practice exams. Help me go forward with the same spirit.
โWill you subscribe today via YOUTUBE?โ
TIRED OF ADS?
- Become Premium Member and experienced fewer ads to ads-free browsing.
- Full Content Access Exclusive to Premium members
- Access to PINOYBIX FREEBIES folder
- Download Reviewers and Learning Materials Free
- Download Content: You can see download/print button at the bottom of each post.
PINOYBIX FREEBIES FOR PREMIUM MEMBERSHIP:
- CIVIL ENGINEERING REVIEWER
- CIVIL SERVICE EXAM REVIEWER
- CRIMINOLOGY REVIEWER
- ELECTRONICS ENGINEERING REVIEWER (ECE/ECT)
- ELECTRICAL ENGINEERING & RME REVIEWER
- FIRE OFFICER EXAMINATION REVIEWER
- LET REVIEWER
- MASTER PLUMBER REVIEWER
- MECHANICAL ENGINEERING REVIEWER
- NAPOLCOM REVIEWER
- Additional upload reviewers and learning materials are also FREE
FOR A LIMITED TIME
If you subscribe for PREMIUM today!
You will receive an additional 1 month of Premium Membership FREE.
For Bronze Membership an additional 2 months of Premium Membership FREE.
For Silver Membership an additional 3 months of Premium Membership FREE.
For Gold Membership an additional 5 months of Premium Membership FREE.
Join the PinoyBIX community.