Free Quantitative Reasoning MCQs with Answers

401. Kaylani used fabric measuring 5 yards in length to make each suit for a men's choir. The relationship between the number of suits that Kaylani made, x, and the total length of fabric that she purchased y, in yards, is represented by the equation y − 5x = 6. What is the best interpretation of 6 in this context?

• A. Kaylani made 6 suits.
• B. Kaylani purchased a total of 6 yards of fabric.
• C. Kaylani used a total of 6 yards of fabric to make the suits.
• D. Kaylani purchased 6 yards more fabric than she used to make the suits.

Explanation: Choice D is correct. It's given that the equation y - 5x = 6 represents the relationship between the number of suits that Kaylani made, x, and the total length of fabric she purchased, y, in yards. Adding 5x to both sides of the given equation yields y = 5x + 6. Since Kaylani made x suits and used 5 yards of fabric to make each suit, the expression 5x represents the total amount of fabric she used to make the suits. Since y represents the total length of fabric Kaylani purchased, in yards, it follows from the equation y = 5x + 6 that Kaylani purchased 5x yards of fabric to make the suits, plus an additional 6 yards of fabric. Therefore, the best interpretation of 6 in this context is that Kaylani purchased 6 yards more fabric than she used to make the suits.

402. What is the value of tan 92π/3?

• A. − √3
• B. -√3/3
• C. √3/3
• D. √3

Explanation: Choice A is correct. A trigonometric ratio can be found using the unit circle, that is, a circle with radius 1 unit. If a central angle of a unit circle in the xy-plane centered at the origin has its starting side on the positive x-axis and its terminal side intersects the circle at a point (x, y), then the value of the tangent of the central angle is equal to the y-coordinate divided by the x-coordinate. There are 2π radians in a circle. Dividing 92π/3 by 2π yields 92/6, which is equivalent to 15 + 2/3. It follows that on the unit circle centered at the origin in the xy-plane, the angle 92π/3 is the result of 15 revolutions from its starting side on the positive x-axis followed by a rotation through radians. Therefore, the angles 92π/3 and 2π/3 are coterminal angles and tan (92π/3) is equal to tan (2π/3). Since 2π/3 is greater than π/2 and less than π , it follows that the terminal side of the angle is in quadrant II and forms an angle of π/3, or 60°, with the negative x-axis. Therefore, the terminal side of the angle intersects the unit circle at the point (-1/2, √3/2). It follows that the value of tan(2π/3) is √3/2/-1/2 , which is equivalent to -√3. Therefore, the value of tan (92π/3) is -v3.

403. A right rectangular prism has a height of 9 inches. The length of the prism's base is x inches, which is 7 inches more than the width of the prism's base. Which function V gives the volume of the prism, in cubic inches, in terms of the length of the prism's base?

• A. V(x) = x(x + 9)(x + 7)
• B. V(x) = x(x + 9)(x − 7)
• C. V(x) = 9x(x + 7)
• D. V(x) = 9x(x − 7)

Explanation: Choice D is correct. The volume of a right rectangular prism can be represented by a function V that gives the volume of the prism, in cubic inches, in terms of the length of the prism's base. The volume of a right rectangular prism is equal to the area of its base times its height. It's given that the length of the prism's base is x inches, which is 7 inches more than the width of the prism's base. This means that the width of the prism's base is x-7 inches. It follows that the area of the prism's base, in square inches, is x(x - 7) and the volume, in cubic inches, of the prism is x(x - 7) (9). Thus, the function V that gives the volume of this right rectangular prism, in cubic inches, in terms of the length of the prism's base, x, is V(x) = 9x( x - 7).

404. The result of increasing the quantity x by 400% is 60. What is the value of x?

• A. 12
• B. 15
• C. 240
• D. 340

Explanation: Choice A is correct. It's given that the result of increasing the quantity x by 400% is 60. This can be written as x+ (400/100)x = 60, which is equivalent to x + 4x = 60, or 5x = 60. Dividing each side of this equation by 5 yields x = 12. Therefore, the value of x is 12.

405. In the triangle ABC, If AB = BC = AC, theni: x ii: y

• A. (i) is greater
• B. (ii) is greater
• C. Both are Equal
• D. Can't be determined

Explanation: if AB = BC = AC i.e all the three sides of triangle are equal,the triangle is equilateral, all three angles are supposed to be equal. If the one angle mentioned is 60° than the other two should also be 60°53°+x= 60X= 7°72-y=60°Y=12°Option B is correct as (ii)Y is greater than (i) X (12>7)Option A: Not correct as x is smaller than yOption C: X and y are not equal as x= 7 and y=12Option D: The value can be determined as shown in calculation above

406. How many people are standing in the queue at the counter? I. If four more people join the queue, the number in the queue will be more than 15 II. More than 10 people are standing in the queue III. There are more men than women in the queue IV. If three people give up and leave the queue, the number remaining will be less than 10 V. Less than 20 people are standing in the queue Which two statements are sufficient to answer the question?

• A. I & III
• B. II & III
• C. II & V
• D. I & IV

Explanation: Option D provides the sufficient information to find out the number of people standing in a queue i.e It states that if 4 more people join the queue the number of people in queue would be greater than 15, considering the number of people in queue=x gives an idea that 11≤ x ≤ 15 Whereas IV states that if three people leave the queue the value of c would be less than 10 i.e 12≥x ≥10, Giving an idea that x= 11 or 12 as both the statements resonates with these two numbers and together gives sufficient information. All the other options do not give sufficient information together as they do not relate with each other.

407. What is the value for x? I. x is an integer II. The average of v, w, x, y & z is 13 III. The average of v, w, y & z is 10 IV. v + w = 12 V. y + z = 28 Which two statements are sufficient to answer the question?

• A. I & V
• B. I & III
• C. II & III
• D. IV & V

Explanation: Option C gives Sufficient information as using the information in C as the variables provided are similar in this option which can be used for calculationOption A: this option gives three different variables which cannot be used for calculation. (v,w)Option B:this option gives two equations with completely different variables which cannot be used together for calculation. Option D:this option gives two equations with completely different variables which cannot be used together for calculation.

408. If u > t, r > q, s > t, and t > r, which of the following must be true? I. u > s II. s > q III. u > r

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

Explanation: From the above data provide it can be concluded that U>s>t>r>q or s>u>t>r>q Using this information OPTION E is correct as it states that s>q and u>r both the option matching the conclusion above All the other options provide do not match the data provided above

409. Anna spent $80 buying a used bicycle and $30 repairing it. Then she sold the bicycle for 40 percent more than the total amount she spent buying and repairing it. Quantity A: The price at which Anna sold the bicycle Quantity B: $150

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

Explanation: Anna spent $80 (to buy bicycle)Anna spent. +$30 ( for it's repair)Total amount spent $ 11040% of the spent amount is $44she sold the bicycle for $154Quantity A is the total amount Anna spent i.e $154 which is greater than Quantiy B ($150 )and hence option A is correctAll the other option stated are wrong and do not match the calculation

410. A total of 300 tickets were sold for a performance of a school play. The ticket prices were $5 for each adult and $3 for each child, and the total revenue from tickets was $1,400. Solving which of the following systems of equations would yield the number of adult tickets sold, a, and the number of children's tickets sold, c?

• A. a + c = 1,400 5a + 3c = 300
• B. a + c = 300 5a + 3c = 1400
• C. a + c = 300 3a + 5c = 1,400
• D. a + c = 300 3a + 5c = 1,400 × 2

Explanation: Using the equations in Option B, the number of tickets for adults and child sold can be found out A being the number of Adults C being the number of children A+C= 300 (1) A= 300-C 5A+3C=1400 (2) Substituting A in equation 2 5(300-C) +3C=1400 1500-5C+3C=1400 1500-1400=2C 100/2=C C=50 A+C=300 A+50=300 A=300-50 A=250 Tickets sold for ADULT=250 Tickets sold for CHILDREN=50 All the other options do not consist of sufficient option to find the actual number of tickets sold to Adults and children