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# MCQ in Algebra and General Mathematics Part 5 | ECE Board Exam

This is the Multiple Choice Questions Part 5 of the Series in Algebra and General Mathematics topics in Engineering Mathematics. 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 Algebraic functions | MCQ in theory of Equations | MCQ in Factorization and Algebraic functions | MCQ in Ratio, Proportion and Variation | MCQ in Matrix theory | MCQ in Arithmetic and Geometric Progression | MCQ in Equations and Inequalities | MCQ in Linear and Quadratic Equations | MCQ in Complex Number System | MCQ in Polynomials | MCQ in Mathematical Induction | MCQ in Logic and Probability | MCQ in Statistics| MCQ in System of Numbers and Conversion | MCQ in Fundamentals in Algebra | MCQ in Binomial Theorems and Logarithms | MCQ in Age Problems | MCQ in Work Problems | MCQ in Mixture Problems | MCQ in Digit Problems | MCQ in Motion Problems | MCQ in Clock Problems | MCQ in Variation | MCQ in Progression | MCQ in Miscellaneous Problems

#### Continue Practice Exam Test Questions Part 5 of the Series

Choose the letter of the best answer in each questions.

201. 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. 6

Solution:

202. 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 rate at 100 amperes can transmit 150 megawatts over 150 km. how much power, in megawatts can a 230 kilovolt line rate at 150 amperes transmit over 100 km?

a. 785

b. 485

c. 675

d. 595

Solution:

203. 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 30 seconds for a 10 hp motor to lift 100 lbs. through 50 feet, what size of motor is required to lift 800 lbs. in 40 seconds through 40 feet?

a. 42

b. 44

c. 46

d. 48

Solution:

204. 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. 37.5%

d. 34.7%

Solution:

205. 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 P 2 less. However, if there were 5 less examinees, each would have paid P 2 more. How many examinees are there in the group?

a. 14

b. 16

c. 18

d. 20

Solution:

206. A bookstore purchased a best selling price book at P 200.00 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

Solution:

207. 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 P 2,856 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

Solution:

208. 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

Solution:

209. A merchant has three items on sale, namely a radio for P 50, a clock for P 30 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 P 1,000 on the total sales. How many radios did he sale?

a. 16

b. 20

c. 18

d. 24

Solution:

210. The arithmetic mean of a and b is

a. (a + b)/2

b. sqrt(ab)

c. (ab)/2

d. (a – b)/2

Solution:

211. The sum of three arithmetic means between 34 and 42 is

a. 114

b. 124

c. 134

d. 144

Solution:

212. 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.

Solution:

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

a. 17

b. 18

c. 19

d. 20

Solution:

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

a. 75

b. 88

c. 90

d. 91

Solution:

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

a. 48

b. 49

c. 50

d. 51

Solution:

216. 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. 11

b. 12

c. 13

d. 14

Solution:

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

a. 1030

b. 1035

c. 1040

d. 1045

Solution:

218. 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

Solution:

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

a. 171

b. 182

c. 232

d. 216

Solution:

220. 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

Solution:

221. In the recent โGulf 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

Solution:

222. 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

Solution:

223. If the sum is 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

Solution:

224. Once a month, a man puts some money into the cookie jar. Each month he puts 50 centavos more into jar than the month before. After 12 years, he counted his money, he had P 5,436. How much money did he put in the jar in the last month?

a. P73.50

b. P75.50

c. P74.50

d. P72.50

Solution:

225. A girl on a bicycle coasts downhill 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

Solution:

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

a. 2500

b. 2601

c. 2501

d. 3500

Solution:

227. 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 ad so on?

a. 210

b. 24

c. 156

d. 300

Solution:

228. To conserve energy due to the present energy crisis, the Meralco tried to readjust their charges to electrical energy users who consumes more than 2000 kw-hours. 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

Solution:

229. 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

Solution:

230. Find the fourth term of the progression 1/2, 0.2, 0.125โฆ

a. 1/10

b. 1/11

c. 0.102

d. 0.099

Solution:

231. 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

Solution:

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

a. 130

b. 140

c. 150

d. 160

Solution:

233. The fourth term of a geometric progression is 216 and the 6th term is 1944. Find the 8th term

a. 17649

b. 17496

c. 16749

d. 17964

Solution:

234. 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

Solution:

235. 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

Solution:

236. A product has a current selling of P 325.00. If its 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 213.23

b. P 202.75

c. P 302.75

d. P 156.00

Solution:

237. The number 28, x + 2, 112 form a geometric progression. What is the 10th term?

a. 14336

b. 13463

c. 16433

d. 16344

Solution:

238. The sum of the first 10 terms of a geometric progression 2, 4, 8โฆ is

a. 1023

b. 2046

c. 225

d. 1596

Solution:

239. If the first term of a geometric progression is 9 and the common ratio is -2/3, find the fifth term

a. 8/5

b. 16/9

c. 15/7

d. 13/4

Solution:

240. 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 ratios are equal.

a. -2, 5/8

b. -1, 5/8

c. -1, 7/8

d. -2, 7/8

Solution:

241. 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. 32768

d. 16383

Solution:

242. In the PBA three-point shootout contest, the committee decided to give a prize in the following manner; A prize of P 1 for the first basket made, P 2 for the second, P 4 for the third, P 8 for the fourth and so on. If the contestant wants to win a prize no less than a million pesos, what is the minimum number of baskets to be converted?

a. 20

b. 19

c. 18

d. 21

Solution:

243. 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

Solution:

244. A man mailed 10 chain letters to ten of his friends with a request to continue by sending a 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 P 4 per letter?

a. P 6,000,000

b. P 60,000

c. P 2,222,220

d. P 4,444,440

Solution:

245. Determine the sum of the infinite series s = 1/3 + 1/9 + 1/27 +โฆ+ (1/3)^n

a. 4/5

b. 3/4

c. 2/3

d. 1/2

Solution:

246. Under favorable condition, a 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. 1,730,740

c. 1,073,741,823

d. 1,037,417

Solution:

247. 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. 100 feet

b. 125 feet

c. 150 feet

d. 175 feet

Solution:

248. What is the fraction in lowest term equivalent to 0.133133133?

a. 133/666

b. 133/777

c. 133/888

d. 133/999

Solution:

249. Find the sum of the infinite geometric progression 6, -2, 2/3โฆ

a. 9/2

b. 5/2

c. 7/2

d. 11/2

Solution:

250. Find the sum of 1, -1/5, 1/25โฆ

a. 5/6

b. 2/3

c. 0.84

d. 0.72

Solution:

### Online Questions and Answers in Algebra and General Mathematics Series

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

MCQ in Algebra and General Mathematics
PART 1: MCQ from Number 1 โ 50                               Answer key: PART 1
PART 2: MCQ from Number 51 โ 100                          Answer key: PART 2
PART 3: MCQ from Number 101 โ 150                        Answer key: PART 3
PART 4: MCQ from Number 151 โ 200                         Answer key: PART 4
PART 5: MCQ from Number 201 โ 250                         Answer key: PART 5
PART 6: MCQ from Number 251 โ 300                         Answer key: PART 6
PART 7: MCQ from Number 301 โ 350                         Answer key: PART 7
PART 8: MCQ from Number 351 โ 400                         Answer key: PART 8
PART 9: MCQ from Number 401 โ 450                         Answer key: PART 9
PART 10: MCQ from Number 451 โ 500                        Answer key: PART 10

### Online Questions and Answers in Fundamentals in Algebra Series

Following is the list of practice exam test questions in this brand new series:

MCQ in Fundamentals in Algebra
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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