Free Quantitative Reasoning MCQs with Answers

381. In the given figure, shaded area is less than the un-shaded area by

• A. 10%
• B. 20%
• C. 25%
• D. 30%

Explanation: This is the correct answer. The shaded area is exactly 25% less than the un-shaded area.if we count the full figure (it's a 2×4 grid).There are 3 shaded and 5 unshaded squares → difference = 5 − 3 = 2 squares.Out of the 8 total squares, the difference is 2/8×100=25%So in this case, the shaded area is 25% less than the un-shaded area, making Option C the correct choice. Options A and B are incorrect as the percentage difference is greater than 10% and 20% respectively. Option D is incorrect because the difference is not as large as 30%.

382. In the given diagram the value of x is equal to

• A. 35°
• B. 45°
• C. 65°
• D. 75°

Explanation: 65° is correct. It satisfies the angle relationships in the diagram.The two slanted lines meet above the horizontal line, forming a triangle whose top angle is x. The angle labelled 125∘ at the left is outside that triangle, so the triangle's left base angle is its supplement:left base angle=180∘−125∘=55∘right base angle=60∘ Sum of triangle angles = 180∘ sotop angle of the triangle =180∘−(55∘+60∘)=180∘−115∘=65∘Now, angle x and the top angle of the triangle are vertically opposite angles therefore they are equal.x = 65∘Options 35°, 45°, and 75° are incorrect because they do not adhere to the angle sum properties of the shape as indicated in the diagram.

383. If the ratio between the length of sides of two cubes is 3 : 5, then the ration between their volumes will be

• A. 9: 25
• B. 18: 50
• C. 27: 75
• D. 27: 125

Explanation: The volume of a cube is determined by cubing the length of its side. Therefore, if the ratio of the lengths of the sides of two cubes is 3:5, the ratio of their volumes will be the cube of these side lengths. Calculating the cube of each gives us 3^3 = 27 and 5^3 = 125. Thus, the ratio of the volumes is 27:125.Option A (9:25) is incorrect because it implies squaring the side lengths rather than cubing them. Option B (18:50) arises from an incorrect calculation and does not follow from cubing the side lengths. Option C (27:75) is incorrect because the second value should be 125, not 75, when cubing 5.

384. Cottage A and Cottage B are 8 km apart. Cottage B and Cottage C are 3 km apart. What could be the possible distance/s between cottage A and Cottage C?I. 12kmII. 11kmIII. 8km

• A. I only
• B. II only
• C. I and II only
• D. II and III only

Explanation: To determine the possible distances between Cottage A and Cottage C, apply the triangle inequality theorem. The sum of any two sides of a triangle must be greater than the length of the remaining side. Considering the sides as 8 km, 3 km, and the unknown distance AC:For 12 km, 8 + 3 = 11, which is less than 12, making this distance not possible.For 11 km, 8 + 3 = 11, which is equal, thus a possible distance.For 8 km, 8 + 3 = 11, which is greater, hence a possible distance.Therefore, the valid distances are 11 km and 8 km, making option D (II and III only) the correct answer.

385. A teacher gives cubes each of volume 8 cubic centimeters to his students. He then asks his students to divide each side of the cube into half.The new volume of the cube in cubic centimeters.

• A. Will be 1
• B. Will be 2
• C. Will be 4
• D. Cannot be determined

Explanation: The original cube has a volume of 8 cubic centimeters. Since the volume (V) of a cube is given by V = side^3, each side of the original cube is 2 cm long (since 2^3 = 8). When each side is divided into half, the new side length is 1 cm. The volume of the cube with the new side length is calculated as 1 cm × 1 cm × 1 cm = 1 cubic centimeter. Therefore, Option A is correct. Options B and C are incorrect because they result from incorrect calculations of the volume. Option D is incorrect because the volume can be clearly determined using the given information.

386. A vehicle is inclined 26 units up a ramp whose slope is in the ratio 12:5. How many units higher is the vehicle than the ground level?

• A. 10
• B. 13
• C. 24
• D. 26

Explanation: The vehicle is inclined 26 units up the ramp. We know that for a ramp length of 13 units (from our slope ratio calculation), the vertical height is 5 units. Since the actual ramp length the vehicle traveled is 26 units, which is twice the calculated ramp length (26 / 13 = 2), we need to scale the vertical height by the same factor. The incline is typically expressed as a ratio, with the most common standards being: 1:12 (ADA Standard): For every 1 inch of rise, you need 12 inche... 4. Calculate the actual height: Actual height = Vertical height (from slope ratio) * Scaling factor Actual height = \(5*2=10\) units. The incline is typically expressed as a ratio, with the most common standards being: 1:12 (ADA Standard): For every 1 inch of rise, you need 12 inche... Therefore, the vehicle is 10 units higher than the ground level. The final answer is 10

387. Which of the following quantities is the largest?

• A. 45%
• B. 0.5
• C. 3/4
• D. 0.666

Explanation: A) 45%: To convert a percentage to a decimal, divide by 100. 45% = 45 / 100 = 0.45 * B) 0.5: This is already in decimal form. * C) 3/4: To convert a fraction to a decimal, divide the numerator by the denominator. 3 / 4 = 0.75 * D) 0.666: This is already in decimal form.Now, let's compare the decimal values: * A) 0.45 * B) 0.5 * C) 0.75 * D) 0.666Arranging them in ascending order: 0.45, 0.5, 0.666, 0.75.The largest quantity is 0.75.Therefore, the correct answer is C) 3/4.

388. Which of the following figures has the same shaded area as that of the given circle?

• A. A square with side length equal to the diameter of the circle
• B. A rectangle with length equal to the diameter of the circle and width equal to half the radius
• C. A triangle with a base equal to the circle's diameter and height equal to the radius
• D. A parallelogram with base equal to the circle's diameter and height equal to the radius

Explanation: The correct answer is the triangle with a base equal to the circle's diameter and height equal to the radius. The area of the circle is πr², while the area of the triangle is 1/2 × base × height = 1/2 × 2r × r = r². Thus, these areas are equivalent when π is approximated to 3. Option A (square) and Option B (rectangle) do not match the circle's area, while Option D (parallelogram) also does not have the same area as the circle.

389. If 4/5 of the teachers in the meeting occupied 5/6 of the seats in the hall, then the least number of teachers in a meeting could be

• A. 5
• B. 6
• C. 24
• D. 25

Explanation: To find the least number of teachers, we need to equate the fractions of teachers and seats. Let T represent the number of teachers. According to the problem:4/5 of the teachers = 5/6 of the seatsAssuming the total number of teachers is T, then 4/5 * T = 5/6 *(total seats). To find the least number of teachers, we need to find the smallest value of T such that both sides are equal. Solving this equation, we find that T = 24 is the smallest number satisfying this condition.Option A (5) and Option B (6) are too small to satisfy the equation, and Option D (25) is more than necessary. Thus, Option C (24) is the correct answer.

390. The ascending order of 0.3,1/5 and 15% is

• A. 0.3, 1/5 and 15%
• B. 1/5, 0.3 and 15%
• C. 0.3, 15% and 1/5
• D. 15%, 1/5 and 0.3

Explanation: To solve this question, convert each value to a decimal:0.3 is already a decimal.1/5 = 0.215% = 15/100 = 0.15Now, arrange them in ascending order (smallest to largest):0.15, 0.2, 0.3Therefore, the ascending order of 0.3, 1/5, and 15% is:15%, 1/5, 0.3The other options are incorrect because they do not reflect the correct ascending order of the converted decimals.