Mathematics — All MCQs
1905 questions available
Q1641.What is the value of (1,000,001)² − (999,999)² ?
Correct Answer: B
Applying the difference of squares identity (a² - b²) = (a - b)(a + b). Let a = 1,000,001 and b = 999,999. Thus, (1,000,001 - 999,999)(1,000,001 + 999,999) = 2 × 2,000,000 = 4,000,000.
Q1642.If -2x - 5 = 48, what is the value of 2x + 57?
Correct Answer: D
From -2x - 5 = 48, we get -2x = 53, which means 2x = -53. Substituting this into the target expression: 2x + 57 = -53 + 57 = 4.
Q1643.One day a super market received a delivery of 25 frozen turkeys. If the average (arithmetic mean) weight of a turkey was 14 pounds, what was the total weight in pounds of all the turkeys?
Correct Answer: A
Total weight = Average weight × Number of items. Total weight = 14 pounds × 25 turkeys = 350 pounds.
Q1644.In 1999, Danish read 10 English books and 7 Urdu books. In 2000, he read twice as many Urdu books as English books. If 60% of the books that he read during the two years were Urdu, how many books did he read in 2000?
Correct Answer: D
Let English books in 2000 = x, so Urdu books in 2000 = 2x. Total Urdu over two years = 7 + 2x. Total books over two years = (10 + 7) + (x + 2x) = 17 + 3x. Given (7 + 2x) / (17 + 3x) = 0.60. Solving: 7 + 2x = 10.2 + 1.8x => 0.2x = 3.2 => x = 16. In 2000, total books read = 3x = 3(16) = 48.
Q1645.Rabia's average (arithmetic mean) on her six math tests this marking period is 75. Fortunately for Rabia, her teacher drops each student's lowest grade, thus raising Rabia's average to 85. What was her lowest grade?
Correct Answer: B
Total marks for 6 tests = 6 × 75 = 450. After dropping the lowest test, the average of 5 tests is 85, so the total of the best 5 tests = 5 × 85 = 425. The lowest dropped test grade is 450 − 425 = 25.
Q1646.If 2a – 3b = 10, what is the value of (2a – 3b)³ ?
Correct Answer: B
Since (2a - 3b) is equal to 10, then (2a - 3b)³ = 10³ = 10 × 10 × 10 = 1000.
Q1647.If 12 years are added to 2/7 of the age of JAVED he will be 3 years younger to the present age of his elder brother OW AIS who is now 30 years. What is the present age of JAVED?
Correct Answer: D
Let Javed's age be j. Elder brother Owais is 30, and 3 years younger is 27. Equation: (2/7)j + 12 = 27 => (2/7)j = 15 => 2j = 105 => j = 52.5.
Q1648.If a/3 = b/2, then what is the value of (2a+3b)/(3a-2b)?
Correct Answer: A
From a/3 = b/2, we have 2a = 3b or a = 1.5b. Substituting this into the expression: (2a + 3b) / (3a - 2b) = (3b + 3b) / (4.5b - 2b) = 6b / 2.5b = 12/5.
Q1649.If 2x + y = 5, then 4x + 2y is equal to ____?
Correct Answer: A
Multiplying both sides of the equation 2x + y = 5 by 2 yields 2(2x + y) = 2(5), which simplifies to 4x + 2y = 10.
Q1650.If the average of five numbers is -10, and the sum of three of the numbers is 16, then what is the average of the other two numbers?
Correct Answer: D
Sum of 5 numbers = 5 × (-10) = -50. Sum of 3 numbers = 16. Sum of other 2 numbers = -50 - 16 = -66. Average of these 2 numbers = -66 ÷ 2 = -33.
Q1651.If a + b = 3(c + d), which of the following is the average (arithmetic mean) of a, b, c, and d?
Correct Answer: D
Average of 4 numbers = (a + b + c + d) / 4. Substituting (a + b) = 3(c + d) into the numerator gives [3(c + d) + (c + d)] / 4 = [4(c + d)] / 4 = c + d.
Q1652.The volume of a cylinder is to be calculated using the formula V = πr²L. If the radius (r) is 3 cm and the length (L) is 10 cm, what is the volume?
Correct Answer: A
V = π × r² × L = π × 3² × 10 = π × 9 × 10 = 90π cm³.
Q1653.There are 40 animals in a zoo and per animal 20 packets of milk is required. One pack of milk contains 200 ml of milk, and milk costs 4.6 pesos per litre. If the employees of the zoo fulfil only 80% of the animal's intake of milk what will be the expenditure of the zoo?
Correct Answer: D
Total packets needed = 40 × 20 = 800. Total volume in ml = 800 × 200 ml = 160,000 ml = 160 liters. At 80% fulfillment: 160 liters × 0.80 = 128 liters. Total cost = 128 liters × 4.6 pesos/liter = 588.8 pesos.
Q1654.Convert 158°F into Celsius (°C)?
Correct Answer: C
Using the Celsius conversion formula: °C = (°F - 32) × 5/9. Substituting 158: °C = (158 - 32) × 5/9 = 126 × 5/9 = 70°C.
Q1655.If 4x + y = 3x + 5y, find the value of 3x/16y ?
Correct Answer: C
From 4x + y = 3x + 5y, we subtract 3x and y from both sides to get x = 4y. Now, 3x / 16y = 3(4y) / 16y = 12y / 16y = 3/4.
Q1656.The volume of a cone is 245π cm³ and its radius is 7 cm. Find its height?
Correct Answer: A
Volume of a cone = (1/3)πr²h. Substituting the known values: 245π = (1/3)π × 7² × h => 245 = (49/3)h => h = (245 × 3) / 49 = 5 × 3 = 15 cm.
Q1657.A truck weighs 6500 kg. If 81% is load, what is the weight of the load?
Correct Answer: A
Weight of the load = 81% of 6500 kg = (81 / 100) × 6500 = 81 × 65 = 5265 kg.
Q1658.If T³ - 3T + 1 = 0, find the value of T³ + 1/T³?
Correct Answer: D
Dividing T³ - 3T + 1 = 0 by T gives T² - 3 + 1/T = 0, so T + 1/T = 3. Using the algebraic identity (T + 1/T)³ = T³ + 1/T³ + 3(T + 1/T), we substitute 3: 3³ = T³ + 1/T³ + 3(3) => 27 = T³ + 1/T³ + 9 => T³ + 1/T³ = 18.
Q1659.A room is 16 feet in length, 15 feet in width, and 12 feet in height. What is the maximum distance possible in feet along a straight line between any two points in the room?
Correct Answer: C
The maximum distance is the 3D space diagonal: d = √(l² + w² + h²) = √(16² + 15² + 12²) = √(256 + 225 + 144) = √625 = 25 feet.
Q1660.In January, 55 percent of a hospital's 300 patients were women. In February, 30 percent of its 440 patients were women. What was the percent change in the number of women patients from January to February?
Correct Answer: A
January women = 55% of 300 = 165. February women = 30% of 440 = 132. Change = 132 - 165 = -33. Percent change = (-33 / 165) × 100 = -20% (decrease of 20%).