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Basic Math Quiz
Directions: This subtest is a measure of ability to think out solutions to quantitative problems. Solve each problem carefully and then decide which is the best among the answer choices. Notes: ► Calculators of any kind are not permitted. All numbers used are real numbers. ► Figures which accompany problems in this subtest are intended to provide information useful in solving the problems. They are drawn as accurately as possible except when it is stated in a specific problem that its figure is not drawn to scale. All figures lie in a plane unless otherwise indicated.
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Your answers are highlighted below.
Question 1
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For any integer n, which of the following represents the sequence of three consecutive odd integers?
n, n + 1, n + 3
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n, n + 2, n + 4
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2n + 1, 2n + 2, 2n + 3
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2n +1, 2n + 3, 2n + 5
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Question 1 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 2
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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?
79
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75
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81
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77
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Question 2 Explanation:
[83+86+89+90+x]/5 = 85 [348 + x]/5 = 85 x = 77
Question 3
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If a and b are both odd numbers, then which of the following must be an even number?
a + b
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ab + 2
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a + b + 1
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2a + b
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Question 3 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 4
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[(800 ÷ 40) + (92 ÷ (17 – 8))] – (22 + 32) = _________.
16
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29
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42
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15
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Question 4 Explanation:
= 20 + 981/9) - (4+9) = 20 + 9 - 13 = 16
Question 5
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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.
4
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3
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7
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5
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Question 5 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 6
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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?
6
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12
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9
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8
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Question 6 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 7
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Which of the following set of fractions arrange in ascending order?
13/15, 1/4, 3/8, 5/6
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3/16, 1/7, 2/5, 5/6
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5/12, 1/9, 7/8, 11/8
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6/19, 7/12, 3/4, 4/5
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Question 7 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 8
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If r, s, t are three consecutive integers such that r > s > t, then (r – s)(s – t)(r – t) equals:
0
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-1
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-2
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2
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Question 8 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 9
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If k = 2 x 10-2, then what does the expression 1/k equal to?
5
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50
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500
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0.5
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Question 9 Explanation:
k = 0.02 1/k = 1/0.02 = [1/0.02] [100/100] = 100/2 = 50
Question 10
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Determine the value of k so that the line kx – 8 + 7y = 0 will be parallel to the line 2x – y + 1 = 0.
6
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-3
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-14
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9
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Question 10 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 11
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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?
The amount paid is 99% of the original price.
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The amount paid is 20% lower than the original price.
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The amount paid is 10% lower than the original price.
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The original price and the selling price are the same.
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Question 11 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 12
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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?
7/10 days
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2 days
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5/13 days
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1/2 days
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Question 12 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 13
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What is the sum of 2.45 multiplied by 0.06 and 0.057 divided by 0.3?
0.337
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1.66
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2.047
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3.37
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Question 13 Explanation:
0.147 + 0.19 = 0.337
Question 14
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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?
50
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30
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40
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20
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Question 14 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 15
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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?
90%
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100%
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80%
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84%
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Question 15 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 16
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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?
150
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140
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210
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200
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Question 16 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 17
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What is the value of the digit x in order for 5719x to be divisible by 2, 3 and 6?
2
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0
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6
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7
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Question 17 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 18
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The sum of five consecutive integers is 35. How many of the five consecutive integers are prime numbers?
3
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4
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2
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1
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Question 18 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 19
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What is the difference between 72, 846 divided by twice of three and seventy-five multiplied twice?
24, 132
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6, 516
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11, 991
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18, 657
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Question 19 Explanation:
[72,846 / (2 X 3)] - (75)(75) = (72,846 / 6) - 5,625 = 12,141 - 5625 = 6,516
Question 20
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Simplify the expression: 5y – {3y + (2y – 5) – [3 – (2 + 4y)]}
6 – 4y
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4y
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4y + 6
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14y – 6
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Question 20 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
Question 21
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The age of Jennilyn 3 years ago is ¼ her age 6 years from now. How old is Jennilyn?
12
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4
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18
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6
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Question 21 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 22
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Determine the equation of the line which passes through (4, -2) and has a slope of 3.
y = 3x - 10
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y = -7x + 5
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y = 3x - 42
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y = 4x - 2
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Question 22 Explanation:
Use point-slope formula, y - y1 = (x= x1)m y – (-2) = (x – 4)(3) y + 2 = 3x – 12 y = 3x – 10
Question 23
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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?
75
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60
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30
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45
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Question 23 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 24
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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?
40
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20
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50
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30
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Question 24 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 25
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What is sixty-seven less than the sum of fifty-eight and forty-two?
23
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43
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33
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-33
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Question 25 Explanation:
(58+42)-67 = 100-67 = 33
Question 26
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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?
120
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330
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210
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200
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Question 26 Explanation:
let x = total number of participants (30%)x = 63 0.3x = 63 x = 63/0.3 x = 210
Question 27
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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?
7
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5
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8
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9
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Question 27 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 28
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(0.143 + 0.27 + 0.852 + 0.009) – (0.235 + 0.51 + 0.006) = _________.
0.523
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0.751
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0.423
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0.851
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Question 28 Explanation:
1.274 – 0.751 = 0.523
Question 29
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Six consecutive integers are given. The sum of the first three is 27. What is the sum of the last three?
32
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33
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36
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30
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Question 29 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 30
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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?
P/8
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P/24
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P/2
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P/4
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Question 30 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
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In the question Determine the value of k so that the line kx – 8 + 7y = 0 will be parallel to the line 2x – y + 1 = 0…
The given answer is -14…
If so, given that answer isn’t it asking for the value of k so that it would be PERPENDICULAR to line 2x-y+1=0.
I’m not a math whiz like the rest of you here so I only checked…
Like I was saying, it was asking for a line perpendicular to the given equation. Why?
I tried getting the x and y coordinates of -14x -8 + 7y.
X coordinate
-14x -8 + 7(0) = 0
-14x = 8
x = -14/8 or -7/4
Y coordinate
-14(0) -8 + 7y = 0
7y = 8
y = 7/8
You can get the slope of the line using rise/run which means:
(7/8) / (-7/4)
7/8 x (-4/7)
-28 / 56
m = -1/2
Line 2x-y+1 has a slope of 2.
None of the choices give us an equation with a slope of 2.
The equation -14x-8+7y=0 gives us a slope of -1/2, thus, it is PERPENDICULAR TO THE LINE 2x-y+1=0
I’m not some math genius so then again, I could be wrong…
di ga po mali ang sagot sa 13? ang explanation po eh tama na 0.99 ang sagot, pero ang marked as correct eh letter C instead of B ..
sa 29 din po.. diga po un ay:
1 = (1/ days of Mrs.Isagani)x + (1/ days of Mrs.Rosas)x
1 = (1/10)x + (1 / (5/2))x
1 = (1/10)x + (2/5)x
1 = (1/10)x + (4/10)x
1 = (5/10)x
1 = (1/2)x
x = 2
awaiting reply po kung tama.. .. thanks!
Yung question number 9 explanation doesn’t support question number 9′s correct answer. please check po. mukhang baliktad lang po yung B and C.
question number 8 po pala.
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I think there’s something wrong with the answer in Q#18. The rate of Mr. Rosas should be x/(5/2). Simplifying it should be 2x/5.
x/10 + 2x/5 = 1
5x/10=1
5x=10
x=2.
So the time should be 2.
OMG. This so hard, even basic math I can’t pass, lol. But I got 44/50 in Vocabulary. Being American is a great advantage in taking the UPCAT. lmao. Goodluck to all of us.
Question 14 Explanation:
= 20 + 981/9) – (4+9) = 20 + 9 – 13 = 16
merong mali … ung 981/9 dpat 81 lng.. un lang
Typo error lng yun, yun 981/9) should be (81/9) kaya tama pa rin…