Basic Math Quiz 29:48 Congratulations - you have completed Basic Math Quiz. You scored 0 out of 30. Your performance has been rated as Need more practice! Post your Results on our Fanpage or the comments section below to view how well you did compared to others [UPCAT is a ranking system afterall.:D]and please dont forget to click the share button to share the quiz with your classmates!^^ps. you still have to adjust your scores for the UPCAT Penalty of correct - 1/4 wrong. Your answers are highlighted below. Question 1 WRONG Of all the participants on a camping trip last summer, 70% were over 15 years old. If 63 of those who attended were 15 years old or below, what was the total number of participants in the camp? A 210 B 330 C 120 D 200 Question 1 Explanation: let x = total number of participants (30%)x = 63 0.3x = 63 x = 63/0.3 x = 210 Question 2 WRONG Which of the following set of fractions arrange in ascending order? A 5/12, 1/9, 7/8, 11/8 B 6/19, 7/12, 3/4, 4/5 C 3/16, 1/7, 2/5, 5/6 D 13/15, 1/4, 3/8, 5/6 Question 2 Explanation: A. 0.416, 0.111, 0.875, 0.611 not in ascending order B. 0.187, 0.143, 0.400, 0.833 not in ascending order C. 0.316, 0.583, 0.750, 0.800 in ascending order D. 0.867, 0.250, 0.375, 0.833 not in ascending order Question 3 WRONG [(800 ÷ 40) + (92 ÷ (17 – 8))] – (22 + 32) = _________. A 16 B 15 C 29 D 42 Question 3 Explanation: = 20 + 981/9) - (4+9) = 20 + 9 - 13 = 16 Question 4 WRONG At first stop on his route, a driver unloaded 1/5 of the packages in his truck. After he unloaded another 9 packages at his next stop, 1/2 of the original number of packages in the truck remained. How many packages were in the van before at the first delivery? A 50 B 20 C 30 D 40 Question 4 Explanation: let x = original number of packages before the 1st delivery [4/5]x - 9 = [1/2]x [4/5]x - [1/2]x = 9 [(8-5)/10] x = 9 x = 90/3 x = 30 Question 5 WRONG For any integer n, which of the following represents the sequence of three consecutive odd integers? A n, n + 1, n + 3 B n, n + 2, n + 4 C 2n +1, 2n + 3, 2n + 5 D 2n + 1, 2n + 2, 2n + 3 Question 5 Explanation: n is any integer, let n = 1 for odd numbers & n = 2 for even numbers. If n = 1, A. n, n + 1, n + 3 = (1), (1) + 1, (1) + 3 = 1, 2, 4 not consecutive odd integers B. n, n + 2, n + 4 = (1), (1) + 2, (1) + 4 = 1, 3, 5 consecutive odd integers C. 2n + 1, 2n + 2, 2n + 3 = 2(1) + 1, 2(1) + 2, 2(1) + 3 = 3, 4, 5 not a consecutive odd integers D. 2n + 1, 2n + 3, 2n + 5 = 2(1) + 1, 2(1) + 3, 2(1) + 5 = 3, 5, 7 a consecutive odd integers If n = 2, A. n, n + 1, n + 3 = (2), (2) + 1, (2) + 3 = 2, 3, 5 not consecutive odd integers B. n, n + 2, n + 4 = (2), (2) + 2, (2) + 4 = 2, 4, 6 not consecutive odd integers but consecutive even integers C. 2n + 1, 2n + 2, 2n + 3 = 2(2) + 1, 2(2) + 2, 2(2) + 3 = 5, 6, 7 not consecutive odd integers D. 2n + 1, 2n + 3, 2n + 5 = 2(2) + 1, 2(2) + 3, 2(2) + 5 = 5, 7, 9 consecutive odd integers D satisfy both sample value for n. Question 6 WRONG If r, s, t are three consecutive integers such that r > s > t, then (r – s)(s – t)(r – t) equals: A -2 B 2 C -1 D 0 Question 6 Explanation: Given three consecutive integers: r, s, t and r > s > t. let r = 3, s = 2, t = 1 (r-s)(s-t)(r-t) = (3-2)(2-1)(3-1) = (1)(1)(2) = 2 Question 7 WRONG Tuwing bakasyon, ginagamit ni Leah ang 30% ng kanyang oras sa pagbabasa ng mga nobela. Sa kabuuan, kaya niyang matapos ang isang nobela ng pitong oras. Kung siya ay natutulog ng siyam na oras araw-araw, ilang nobela ang kaya niyang tapusin sa loob ng dalawang linggo? A 5 B 7 C 9 D 8 Question 7 Explanation: 24 hours – 9 hours (sleeping) = 15 hours (awake) 30% of 15 hours = 0.3 x 15 = 4.5 hours per day reading a novel 4.5 x 14 days/2 weeks = 63 hours reading novels in 2 weeks 63 7 hours/novel = 9 novels she can read in 2 weeks Question 8 WRONG What is the sum of 2.45 multiplied by 0.06 and 0.057 divided by 0.3? A 1.66 B 0.337 C 3.37 D 2.047 Question 8 Explanation: 0.147 + 0.19 = 0.337 Question 9 WRONG The ratio of men to women at a concert was 2:3. If there were 350 people in the concert, how many women were there? A 140 B 200 C 210 D 150 Question 9 Explanation: 2:3, ratio of men to women. Let k = constant which we will use as multiplier to the ratio 2k + 3k = 350 5k = 350 k = 350/5 k = 70 the total number of women in the concert is (70)(3) = 210 Question 10 WRONG Si Gng. Gonzales ay bumili ng kotse sa halagang P pesos. Pagkalipas ng tatlong taon, ibinenta niya ang kotse ng 25% higit sa halaga ng pagkakabili niya. Binigyan siya ng babayarang buwis na 50% ng kanyang kita. Magkano ang kailangang bayaran na buwis ni Gng. Gonzales? A P/24 B P/8 C P/2 D P/4 Question 10 Explanation: let P = original cost of car selling price of car = P + 0.25P = P + [1/4]P tax = 1/2 [(1/4)P] = 1/8 P Question 11 WRONG If a and b are both odd numbers, then which of the following must be an even number? A a + b + 1 B ab + 2 C 2a + b D a + b Question 11 Explanation: a and b are odd numbers, let a = 1 and b = 3 A. 5 = not an even number B. 5= not an even number C. 4 = an even number D. 5 = not an even number Question 12 WRONG The sum of five consecutive integers is 35. How many of the five consecutive integers are prime numbers? A 1 B 4 C 3 D 2 Question 12 Explanation: five consecutive integers: x, x +1, x + 2, x +3, x + 4 x + [x+1] + [x+2] + [ x+3] + [x+4] = 35 5x + 10 = 35 x = 5 so the five consecutive integers are: 5, 6, 7, 8, 9 let check if their sum is 35: 5 + 6 + 7 + 8 + 9 = 11 + 7 + 8 + 9 = 18 + 8 + 9 = 26 + 9 = 35 the prime numbers are 5 and 7. Question 13 WRONG The age of Jennilyn 3 years ago is ¼ her age 6 years from now. How old is Jennilyn? A 12 B 4 C 18 D 6 Question 13 Explanation: Let the present age of Jennilyn be equal to x. Present age = x 3 years ago = x-3 6 yrs from now = x +6 x – 3 = ¼ (x + 6) 4(x – 3) = x + 6 4x – 12 = x + 6 3x = 18 x = 6 , Jennilyn is 6 years old Question 14 WRONG The reservoir is at full capacity at the beginning of summer. By the first day of fall, the level in the reservoir is 40% below full capacity. Then during the fall, a period of heavy rains raises the level by 40%. After the rains, the reservoir is at what percent of its full capacity? A 84% B 90% C 80% D 100% Question 14 Explanation: first day of the fall: the reservoir is 60% of full capacity during heavy rains, the reservoir raises 40% of 60% full capacity of the reservoir after the rain = 60% + ( 0.4 x 0.6) = 60% + 24% = 84% full capacity of the reservoir Question 15 WRONG Determine the value of k so that the line kx – 8 + 7y = 0 will be parallel to the line 2x – y + 1 = 0. A 9 B -3 C -14 D 6 Question 15 Explanation: line 1: kx - 8 +7y = 0 y = -[k/7]x + 8/7 m1= -k/7 line 2: 2x-7+1 = 0 y = 2x+1 m2 = 2 if line 1 is parallel to line 2, then their slope must be equal to each other. m1 = m2 -k/7 = 2 k = 2 X -7 k = -14 Question 16 WRONG What is the difference between 72, 846 divided by twice of three and seventy-five multiplied twice? A 24, 132 B 11, 991 C 18, 657 D 6, 516 Question 16 Explanation: [72,846 / (2 X 3)] - (75)(75) = (72,846 / 6) - 5,625 = 12,141 - 5625 = 6,516 Question 17 WRONG Rocky had a party. Midway in the party, half of the people left. A fifth of those remaining started to sing. There were 16 remaining who did not sing. How many people came to Rocky’s party? A 50 B 40 C 20 D 30 Question 17 Explanation: let x = total no. of people in Rocky’s party x[1 - 1/2] [ 1 - 1/5] = 16 x [1/2][4/5] = 16 4/10x = 16 x = 4 X 10 x = 40 Question 18 WRONG Two cars traveled at the rates of 50 kph and 60 kph respectively. The faster car traveled 2 hours longer than the slower car and went 150 kms farther. Find the time traveled by the slower car. A 4 B 5 C 7 D 3 Question 18 Explanation: Rate x Time Distance Faster Car: rate = 60 time = t + 2 distance = d + 150 Slower Car: rate = 50 time = t distance = d 60(t + 2) = d + 150 , 50 t = d 60t + 120 = 50t + 150 60t – 50t = 150 – 120 10t = 30 t = 3 hours Question 19 WRONG (0.143 + 0.27 + 0.852 + 0.009) – (0.235 + 0.51 + 0.006) = _________. A 0.523 B 0.423 C 0.751 D 0.851 Question 19 Explanation: 1.274 – 0.751 = 0.523 Question 20 WRONG What is sixty-seven less than the sum of fifty-eight and forty-two? A 43 B -33 C 23 D 33 Question 20 Explanation: (58+42)-67 = 100-67 = 33 Question 21 WRONG If k = 2 x 10-2, then what does the expression 1/k equal to? A 50 B 5 C 0.5 D 500 Question 21 Explanation: k = 0.02 1/k = 1/0.02 = [1/0.02] [100/100] = 100/2 = 50 Question 22 WRONG When buying an item, a man was given a 10% discount on its original price, and then he was charged a 10% tax on its selling price. Base from this transaction, which of the following is true? A The amount paid is 20% lower than the original price. B The original price and the selling price are the same. C The amount paid is 99% of the original price. D The amount paid is 10% lower than the original price. Question 22 Explanation: let OP = original price discounted price = OP – 0.1OP = 0.9OP tax = 0.9OP x 0.1 = 0.09OP amount paid = discounted price + tax = 0.9OP + 0.09OP = 0.99OP Question 23 WRONG What is the value of the digit x in order for 5719x to be divisible by 2, 3 and 6? A 2 B 6 C 0 D 7 Question 23 Explanation: 5719x to be divisible by 2, 3, and 6 must follow the divisibility rule for 2, 3, and 6. Divisibility rule for 2: last digit must be an even numbers (0, 2, 4, 6, 8) Divisibility rule for 3: sum of all digits must be divisible by 3. Divisibility rule for 6: must follow the divisibility rule for 2 and 3. Applying the divisibility rule for 6, we now get the sum of all digits to check if this number is divisible by 3. 5+7+1+9+x = 22+x, since we need an even number for the last digit so that it can be divisible by 2, x = 2 so that 22 + 2 = 24, 24 is divisible by 3. Question 24 WRONG Six consecutive integers are given. The sum of the first three is 27. What is the sum of the last three? A 32 B 30 C 33 D 36 Question 24 Explanation: six consecutive integers: x, x +1, x + 2, x +3, x + 4, x + 5 sum of first three terms: x + [x+1] + [x+2] = 27 3x + 3 = 27 3x = 24 x = 8 so the six consecutive integers are: 8, 9, 10, 11, 12, 13. The sum of last three integers: 11 + 12 + 13 = 36 Question 25 WRONG Determine the equation of the line which passes through (4, -2) and has a slope of 3. A y = 4x - 2 B y = -7x + 5 C y = 3x - 42 D y = 3x - 10 Question 25 Explanation: Use point-slope formula, y - y1 = (x= x1)m y – (-2) = (x – 4)(3) y + 2 = 3x – 12 y = 3x – 10 Question 26 WRONG Lovely’s grade in four of her quizzes are 83, 86, 89, and 90. There is one more quiz for the grading period and she does not want an average lower than 85, what is the lowest possible grade that she can get on her fifth quiz to maintain that average? A 81 B 77 C 75 D 79 Question 26 Explanation: [83+86+89+90+x]/5 = 85 [348 + x]/5 = 85 x = 77 Question 27 WRONG Mrs. Isagani can embroider a tablecloth in 10 days while Mrs. Rosas can embroider the same tablecloth in 2 ½ days. How long will it take both of them to embroider one such tablecloth? A 1/2 days B 2 days C 5/13 days D 7/10 days Question 27 Explanation: Mrs. Isagani: rate = 1/10 time = x work = x/10 Mrs. Rosas rate = 5/2 time = x work = 5/2 x The work Mrs. Isagani and Mrs. Rosas did together equals one whole job = x/10 + 5x/2 = 1 Manipulating the equation, x + 25x = 10 26x = 10 x = 10/26 or 5/13 days Question 28 WRONG A rope is cut into three and one-third is used. Then one-fourth of the remaining rope is cut of and used. The piece left is 6 meters long. How many meters long was the rope originally? A 9 B 6 C 8 D 12 Question 28 Explanation: x [1-1/3] [ 3/4] = 6 x [2/3] [3/4] = 6 6/12 x = 6 x = 6 [12/6] x = 12 Question 29 WRONG A fruit salad mixture consists of apples, banana and peaches in the ratio of 6:5:4 respectively by weight. If 225 grams of mixture is prepared, how many more grams of apples than peaches? A 30 B 75 C 45 D 60 Question 29 Explanation: 6:5:4 – ratio of apples, banana, & peaches respectively. Let k = constant which we will use as multiplier to the ratio 6k + 5k + 4k = 225 15k = 225 k = 225/15 k= 15 weight of apple = (6)(15) = 90, weight of banana = (5)(15) = 75, weight of peaches = (4)(15) = 60 weight of apple – weight of peaches = 90 – 60 = 30 grams Question 30 WRONG Simplify the expression: 5y – {3y + (2y – 5) – [3 – (2 + 4y)]} A 14y – 6 B 6 – 4y C 4y + 6 D 4y Question 30 Explanation: 5y – {3y + (2y – 5) – [3 – (2 + 4y)]} = 5y – {3y + (2y – 5) – [3 – 2 – 4y)]} = 5y – {3y + 2y – 5 – (1 – 4y)} = 5y – {3y + 2y – 5 – 1 + 4y} = 5y – (9y – 6) = 5y – 9y + 6 = 6 – 4y
Posted on: Wed, 10 Jul 2013 07:16:07 +0000