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.

### Multiple Choice Questions Topic Outline

- MCQs in Algebraic functions | MCQs in theory of Equations | MCQs in Factorization and Algebraic functions | MCQs in Ratio, Proportion and Variation | MCQs in Matrix theory | MCQs in Arithmetic and Geometric Progression | MCQs in Equations and Inequalities | MCQs in Linear and Quadratic Equations | MCQs in Complex Number System | MCQs in Polynomials | MCQs in Mathematical Induction | MCQs in Logic and Probability | MCQs in Statistics| MCQs in System of Numbers and Conversion | MCQs in Fundamentals in Algebra | MCQS in Binomial Theorems and Logarithms | MCQs in Age Problems | MCQs in Work Problems | MCQS in Mixture Problems | MCQs in Digit Problems | MCQs in Motion Problems | MCQs in Clock Problems | MCQs in Variation | MCQs in Progression | MCQs in Miscellaneous Problems

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

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

**Algebra and General Mathematics MCQs**

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

**PART I**

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

**PART II**

**MCQs from Number 101 – 150**Answer key:

**PART III**

**MCQs from Number 151 – 200**Answer key:

**PART IV**

**MCQs from Number 201 – 250**Answer key:

**PART V**

**MCQs from Number 251 – 300**Answer key:

**PART VI**

### Continue Practice Exam Test Questions Part V 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

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

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

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%

205. 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 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

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

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

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

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

210. The arithmetic mean of a and b is

- a. (a+b)/2
- b. sqrt(ab)
- c. (ab)/2
- d. (a-b)/2

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

- a. 114
- b. 124
- c. 134
- d. 144

212. 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

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

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

- a. 75
- b. 88
- c. 90
- d. 91

215. 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

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

217. 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

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

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

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

221. 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

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

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

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

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

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

- a. 2500
- b. 2601
- c. 2501
- d. 3500

227. 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 ad so on?

- a. 210
- b. 24
- c. 156
- d. 300

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

229. 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

230. Find the fourth term of the progression 1/2, 0.2, 0.125…

- a. 1/10
- b. 1/11
- c. 0.102
- d. 0.099

231. 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

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

- a. 130
- b. 140
- c. 150
- d. 160

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

- a. 17649
- b. 17496
- c. 16749
- d. 17964

234. 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

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

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

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

- a. 14336
- b. 13463
- c. 16433
- d. 16344

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

- a. 1023
- b. 2046
- c. 225
- d. 1596

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

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

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

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

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

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

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

- a. 4/5
- b. 3/4
- c. 2/3
- d. 1/2

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

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

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

- a. 133/666
- b. 133/777
- c. 133/888
- d. 133/999

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

- a. 9/2
- b. 5/2
- c. 7/2
- d. 11/2

250. Find the sum of 1, -1/5, 1/25…

- a. 5/6
- b. 2/3
- c. 0.84
- d. 0.72

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