This is the Multiples 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.

### Multiple Choice Questions Topic Outline

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

### Online Questions and Answers in Clock, Variation, and Progression Problems Series

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

**Clock, Variation, and Progression Problems MCQs**

**MCQs from Number 1 – 50**Answer key:

**PART I**

**MCQs from Number 51 – 100**Answer key:

**PART II**

### Start Practice Exam Test Questions Part I 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 o’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

**Problem 2: CE Board November 1995**

In how many minutes after **7 o’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

**Problem 3: CE Board May 1997**

What time after **3 o’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

**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 120^{o?}

- A. 12:18.818
- B. 12:21.818
- C. 12:22.818
- D. 12:24.818

**Problem 5:**

At what time between **8 and 9 o’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

**Problem 6: EE Board October 1990**

A man left his home at past **3:00 o’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

**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. 60
^{o} - B. 90
^{o} - C. 180
^{o} - D. 540
^{o}

**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

**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

**Problem 10: CE Board May 1993**

Given that “**w**” varies directly as the product of “**x**” and “**y**” and inversely as the square of “**z**” and that w = 4 when x = 2, y = 6 and z = 3. Find the value of “w” when x = 1, y = 4 and z = 2.

- A. 3
- B. 4
- C. 5
- D. 6

**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

**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

**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

**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 %

**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 tutor’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

**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

**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

**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

**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

**Problem 20: ME Board October 1996**

The arithmetic mean of a and b is?

**Problem 21:**

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

- A. 114
- B. 124
- C. 134
- D. 144

**Problem 22: EE Board March 1998**

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

- A. 248.7 ft
- B. 308.1 ft
- C. 241.5 ft
- D. 305.9 ft

**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

**Problem 24: ECE Board November 1998**

Find the 30^{th} term of the arithmetic progression 4, 7, 10, ….

- A. 75
- B. 88
- C. 90
- D. 91

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

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

- A. 48
- B. 49
- C. 50
- D. 51

**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

**Problem 27: CE Board May 1995**

What is the sum of the progression 4, 9, 14, 19 … up to the 20^{th} term?

- A. 1030
- B. 1035
- C. 1040
- D. 1045

**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

**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

**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

**Problem 31: CE Board May 1991**

In the recent “Gulf War” in the Middle East, the allied forces captured 6400 of Saddam’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

**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

**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

**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

**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

**Problem 36:**

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

- A. 2500
- B. 2601
- C. 2501
- D. 3500

**Problem 37:**

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

- A. 210
- B. 24
- C. 156
- D. 300

**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

**Problem 39: CE Board November 1993**

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

- A. 4
- B. 5
- C. 6
- D. 7

**Problem 40: ECE Board November 1995**

Find the **fourth term** of the progression ½, 0.2, 0.125, . . .

- A. 1/10
- B. 1/11
- C. 0.102
- D. 0.099

**Problem 41:**

Find the **9 ^{th} term** of the harmonic progression 3, 2, 3/2….

- A. 3/5
- B. 3/8
- C. 4/5
- D. 4/9

**Problem 42:**

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

- A. 130
- B. 140
- C. 150
- D. 160

**Problem 43: EE Board October 1991**

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

- A. 17649
- B. 17496
- C. 16749
- D. 17964

**Problem 44: ECE Board April 1999**

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

- A. 7, -7/12
- B. 7, -5/6
- C. 7, -14/5
- D. 7, -7/6

**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

**Problem 46: ME Board October 1996**

A product has a current selling of P325.00. If it’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

**Problem 47: CE Board May 1995**

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

- A. 14336
- B. 13463
- C. 16433
- D. 16344

**Problem 48: ECE Board April 1998**

The sum of the first 10 terms of geometric progression 2, 4, 8, …

- A. 1023
- B. 2046
- C. 225
- D. 1596

**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

**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

**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

**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

**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

**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

**Problem 55: EE Board March 1998**

Determine the sum of the infinite series: S = + + + …. + ^{n}

- A. 4/5
- B. 3/4
- C. 2/3
- D. 1/2

**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

**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

**Problem 58: EE Board April 1990**

What is the fraction in lowest term equivalent to 0.133133133?

**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

**Problem 60: CE Board May 1998**

Find the sum of 1, - , , . . .

- A. 5/6
- B. 2/3
- C. 0.84
- D. 0.72

**Problem 61: ECE Board November 1998**

Find the ratio of an infinite geometric progression if the sum is **2** and the first term is **½**.

- A. 1/3
- B. 1/2
- C. 3/4
- D. 1/4

**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

**Problem 63:**

Find the **6 ^{th} term** of the sequence 55, 40, 28, 19, 13, . . .

- A. 10
- B. 9
- C. 8
- D. 11

**Problem 64: EE Board October 1997**

In the series 1, 1, ½, 1/6, 1/24, . . .determine the **6 ^{th} term**.

- A. 1/80
- B. 1/74
- C. 1/100
- D. 1/120

**Problem 65: ECE Board April 1998**

Find the 1987^{th} in the decimal equivalent to starting from the decimal point.

- A. 8
- B. 1
- C. 7
- D. 5

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