Free Quantitative Reasoning MCQs with Answers

361. In the figure, lines m and n are parallel. If x = 6k + 13 and y = 8k − 29, what is the value of z ?

• A. 3
• B. 21
• C. o41
• D. 139

Explanation: Choice C is correct. Vertical angles, which are angles that are opposite each other when two lines intersect, are congruent. The figure shows that lines t and m intersect. It follows that the angle with measure xo and the angle with measure yo are vertical angles, so x = y. It's given that x = 6k + 13 and y = 8k - 29. Substituting 6k + 13 k for x and 8k - 29 for y in the equation x = y yields 6k + 13 = 8k - 29. Subtracting 6k from both sides of this equation yields 13 = 2k - 29. Adding 29 to both sides of this equation yields 42 = 2k, or 2k = 42. Dividing both sides of this equation by 2 yields k = 21. It's given that lines m and n are parallel, and the figure shows that lines m and n are intersected by a transversal, line t. If two parallel lines are intersected by a transversal, then the same-side interior angles are supplementary. It follows that the same-side in angles with measures yo and zo are supplementary, so y + z = 180. Substituting 8k - 29 for y in this equation yields 8k - 29 + z = 180. Substituting 21 for k in this equation yields 8 (21) - 29 +z = 180, or 139 + z = 180. Subtracting 139 from both sides of this equation yields z = 41. Therefore, the value of z is 41.

362. In triangle JKL, 24/51= cos(K ) and angle J is a right angle. What is the value of cos(L) ?

• A. 15/17
• B. 16/21
• C. 17/15
• D. 21/16

Explanation: The correct answer is 15/17. It's given that angle J is the right angle in triangle JKL. Therefore, the acute angles of triangle JKL are angle K and angle L. The hypotenuse of a right triangle is the side opposite its right angle. Therefore, the hypotenuse of triangle JKL is side KL. The cosine of an acute angle in a right triangle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. It's given that cos(K) = 24/51. This can be written as cos(K) = 8/17. Since the cosine of angle K is a ratio, it follows that the length of the side adjacent to angle K is 8n and the length of the hypotenuse is 17n, where n is a constant. Therefore, JK = 8nand KL = 17 n. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. For triangle JKL, it follows that (JK)2 + (JL)2 = (KL)2. Substituting 8n for JK and 17n for KL yields (8n)2 + (JL)2 = (17n)2. This is equivalent to 64n2 + (JL)2 = 289n2. Subtracting 64n2 from each side of this equation yields (JL)2 = 225n2. Taking the square root of each side of this equation yields JL = 15n. Since cos(L) = JL/KL, it follows that cos(L) = 15n/17n, which can be rewritten as cos(L) = 15/17. Note that 15/17, .8824, .8823, and 0.882 are examples of ways to enter a correct answer.

363. The dot plot represents the 15 values in data set A.Data set B is created by adding 56 to each of the values in data set A. Which of the following correctly compares the medians and the ranges of data sets A and B?

• A. The median of data set B is equal to the median of data set A, and the range of data set B is equal to the range of data set A.
• B. The median of data set B is equal to the median of data set A, and the range of data set B is greater than the range of data set A
• C. The median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A
• D. The median of data set B is greater than the median of data set A, and the range of data set Bis greater than the range of data set A.

Explanation: Choice C is correct. The median of a data set with an odd number of values, in ascending or descending order, is the middle value of the data set, and the range of a data set is the positive difference between the maximum and minimum values in the data set. Since the dot plot shown gives the values in data set A in ascending order and there are 15 values in the data set, the eighth value in data set A, 23, is the median. The maximum value in data set A is 26 and the minimum value is 22, so the range of data set A is 26 - 22, or 4. It's given that data set B is created by adding 56 to each of the values in data set A. Increasing each of the 15 values in data set A by 56 will also increase its median value by 56 making the median of data set B 79. Increasing each value of data set A by 56 does not change the range, since the maximum value of data set B is 26 + 56, or 82, and the minimum value is 22 + 56, or 78, making the range of data set B 82 - 78, or 4. Therefore, the median of data set B is greater than the median of data set A, and the range of data set B is equal to the range of data set A.

364. 210 is p% greater than 30. What is the value of p ?

• A. 600
• B. 650
• C. 700
• D. 800

Explanation: To find the value of p, we start with the equation 210 = (1 + p/100) * 30. This equation translates to 210 representing a p% increase over 30. Dividing both sides by 30 gives us 7 = 1 + p/100. Subtract 1 from both sides to get 6 = p/100. Finally, multiplying both sides by 100 results in p = 600. Therefore, the value of p is 600. The other options, 650, 700, and 800, are incorrect due to potential calculation errors or misconceptions about percentage increases.

365. X < O; X > 9Quantity A: XQuantity B: -3

• A. Quantity A is greater than Quantity B.
• B. Quantity B is greater than Quantity A.
• C. Quantities A and B are equal.
• D. The relationship cannot be determined from the information given.

Explanation: The conditions X < 0 and X > 9 cannot both be true simultaneously. This means there is no real number X that satisfies both conditions. As a result, it's impossible to determine which quantity is greater or if they are equal. Therefore, the correct answer is that the relationship between Quantity A and Quantity B cannot be determined from the information given. The other options assume values or relationships that cannot exist under the given conditions.

366. Mushtaq has three grandparents with brown eyes and one with blue eyes.Raisa has two grand parents with brown eyes and two with blue eyes.Mushtaq and Raisa marry and have two children, both with brown eyes.What is the best estimate of the probability that their next child will have blue eyes?

• A. 1/8
• B. 1/4
• C. 3/8
• D. 1/2

Explanation: Mushtaq has three grandparents with brown eyes and one with blue eyes, and Raisa has two grandparents with brown eyes and two with blue eyes. Both likely have the genotype Bb, indicating that they each have one allele for brown eyes (B) and one for blue eyes (b). When both parents are Bb, their children's possible genotypes are BB (brown eyes), Bb (brown eyes), Bb (brown eyes), and bb (blue eyes). Thus, the probability of a child having blue eyes (bb) is 1/4.Option B is correct, as it correctly identifies the probability as 1/4 based on the potential genetic combinations. Option A is incorrect as it underestimates the likelihood of the child having blue eyes. Option C is incorrect as it provides a probability not consistent with the genetic possibilities. Option D is incorrect as it overestimates the probability, not accounting for the dominance of the brown eye allele.

367. A farmer sold apples, pears, and tomatoes by the kilogram for a total receipt of Rs. 480.00. How many kilograms of apples did the farmer sell?Which two of the following statements together provide sufficient additional information to answer the question?Which two of the following statements together provide sufficient additional information to answer the question?i. Apples and pears were each sold at Rs.0.50 per kilogramii. A total of 780 kilograms of pears, and tomatoes was sold.iii. The total receipt for apples was equal to the combined receipt for pears and tomatoes.iv. The total receipt for apples was 4 times the total receipt for pears.v. The total receipt for tomatoes was 3 times the total receipt for pears.The first required additional statement is

• A. i and iii
• B. ii and iv
• C. iii and v
• D. i and iv

Explanation: To determine how many kilograms of apples were sold, we need to calculate the total receipt and the receipts for each type of produce. Statement i tells us the price per kilogram for apples and pears, and statement iv provides a ratio of the receipts for apples and pears. With this information, we can set up equations to solve for the kilograms of apples. The other options either lack sufficient data or provide redundant relationships that do not allow us to solve for the exact quantity of apples.

368. A farmer sold apples, pears, and tomatoes by the kilogram for a total receipt of Rs. 480.00. How many kilograms of apples did the farmer sell?i. Apples and pears were each sold at Rs.0.50 per kilogramii. A total of 780 kilograms of pears, and tomatoes was sold.iii. The total receipt for apples was equal to the combined receipt for pears and tomatoes.iv. The total receipt for apples was 4 times the total receipt for pears.v. The total receipt for tomatoes was 3 times the total receipt for pears.

• A. 0.125%
• B. 12.5%
• C. 125%
• D. 1250%

Explanation: To solve the problem, we need to analyze the relationships between the quantities sold and their respective receipts.1. Let the price per kilogram for apples and pears be Rs. 0.50 each. From the given information, the total receipt for apples is equal to the combined receipt for pears and tomatoes.2. The total receipt for apples is also 4 times the total receipt for pears, and the total receipt for tomatoes is 3 times the total receipt for pears.3. Let the total receipt for pears be Rs. x. Then, the receipt for apples is 4x, and for tomatoes, it is 3x.4. The sum of the receipts is 4x (apples) + x (pears) + 3x (tomatoes) = 8x. Since the total receipt is Rs. 480, we have 8x = Rs. 480, thus x = Rs. 60.5. Therefore, the receipt for apples is 4x = 4 * Rs. 60 = Rs. 240. Since apples are sold at Rs. 0.50 per kilogram, the farmer sold 240 / 0.50 = 480 kilograms of apples.Thus, the correct percentage of apples in the total kilograms sold is 1250%.The other options fail to meet all these conditions as illustrated.

369. In a class of girls and boys, the average (arithmetic mean) height of the girls is 44.3 inches. What is theaverage height of all of the students in the class?Which two of the following statements together provide sufficient additional information to answer thequestion?(i) The number of girls in the class is 18.(ii) The sum of the heights of all of the students in the class is 1,379.4 inches.(iii) The average height of the boys in the class is 48.5 inches.(iv) The ratio of the number of girls to the number of boys in the class is 3 to 2.(v) The difference between the number of girls and the number of boys in the class is 6.The required additional statements are

• A. (i) and (ii)
• B. (ii) and (iii)
• C. (iii) and (iv)
• D. (iv) and (v)

Explanation: To find the average height of all students, you need to know both the total height of all students and the total number of students. Statement (i) gives the number of girls, and statement (ii) provides the total height of all students. With these two pieces of information, you can calculate the number of boys (since you know the number of girls), and therefore the total number of students. Once you have the total number of students and the total height, you can determine the average height of the class.Other options are insufficient because they either lack total height information or the exact number of students needed for the calculation.

370. What is the cost of a banana?Which two of the following statements together provide sufficient information to answer thequestion?i. 7 mangoes and 9 bananas cost Rs. 14.80ii. 4 mangoes and 8 bananas cost Rs. 11.60iii. 3 mangoes and 7 oranges cost Rs. 9.15iv. 5 bananas, 2 mangoes and 3 oranges cost Rs. 12.65

• A. (i) and (ii)
• B. i and iv
• C. ii and iv
• D. (iii) and (iv)

Explanation: To find the cost of a banana, we need to determine the price per banana from the given statements.Let's analyze which two statements together provide sufficient information:i. 7 mangoes and 9 bananas cost Rs. 14.80 ii. 4 mangoes and 8 bananas cost Rs. 11.60 iii. 3 mangoes and 7 oranges cost Rs. 9.15 iv. 5 bananas, 2 mangoes and 3 oranges cost Rs. 12.65 Let's start by expressing the cost equations for statements i and ii in terms of mangoes and bananas:From statement i:\[ 7m + 9b = 14.80 \]From statement ii:\[ 4m + 8b = 11.60 \]Now, we need to eliminate mangoes to find the cost per banana. Let's multiply the equations appropriately to achieve this:Multiply equation ii by 7:\[ 28m + 56b = 81.20 \]Multiply equation i by 4:\[ 28m + 36b = 59.20 \]Now, subtract equation i from the modified equation ii:\[ (28m + 56b) - (28m + 36b) = 81.20 - 59.20 \]\[ 20b = 22 \]\[ b = \frac{22}{20} = 1.1 \]So, the cost of one banana is Rs. 1.10.To verify, substitute \( b = 1.1 \) back into one of the original equations. Using statement ii:\[ 4m + 8 \times 1.1 = 11.60 \]\[ 4m + 8.8 = 11.60 \]\[ 4m = 11.60 - 8.8 \]\[ 4m = 2.8 \]\[ m = \frac{2.8}{4} = 0.70 \]Now, check with statement i:\[ 7 \times 0.70 + 9 \times 1.1 = 14.80 \]\[ 4.90 + 9.90 = 14.80 \]\[ 14.80 = 14.80 \]Everything checks out. Therefore, the cost of a banana is Rs. 1.10, and the two statements that together provide sufficient information to answer the question are i and ii.