Free Quantitative Reasoning MCQs with Answers

1. State whether a ∈ C, if {a} ⊂ A: i: A ⊆ B ii: B ⊆ C

• A. Statement (i) is sufficient
• B. Statement (ii) is sufficient
• C. Statements (i) and (ii) are each sufficient on their own
• D. Statements (i) and (ii) together are sufficient

Explanation: Option D is correct. The chain of relationships {a} ⊂ A, A ⊆ B, and B ⊆ C allows us to conclude that a ∈ C. Statements (i) and (ii) must be combined to establish this link. Options A, B, and C are incorrect because they do not utilize the full chain of subset relationships.

2. If 2m=4x and 2w = 8x, what is m in terms of w?

• A. w - 1
• B. w + 1
• C. 2w - 1
• D. 2w + 1

Explanation: To determine m in terms of w, we first rewrite the equations with the same base.Given: 2^m = 4x 2^w = 8xConvert 4x and 8x into powers of 2: 4x = 2^2 * x 8x = 2^3 * xDivide the two equations: (2^m) / (2^w) = (4x) / (8x)Simplify the right side: (4x) / (8x) = 1/2So: 2^(m - w) = 1/2Write 1/2 as a power of 2: 1/2 = 2^(-1)Thus: m - w = -1Therefore: m = w - 1Other options (w + 1, 2w - 1, and 2w + 1) suggest incorrect relationships as they imply different mathematical connections between m and w based on the original equations.

3. The sum of the Series will be i) Tn = 7n -5 ii) 𝑑 = −5 iii) 𝑎 = 2 iv) 𝑛 = 16 Which two statements are sufficient to solve the given question?

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

Explanation: The correct answer is Option A: (i) and (iv). Statement (i) provides the formula for the nth term Tn = 7n - 5, and statement (iv) gives the specific value of n = 16. Using these, you can calculate Tn as 7(16) - 5 = 107, which is essential for solving the series sum.Option B is incorrect because the initial term a from statement (iii) is not needed with the given Tn formula.Option C is incorrect because the common difference d from statement (ii) and n from statement (iv) do not provide enough information to calculate the series sum without a formula for Tn.Option D is incorrect because the initial term a and n alone do not provide the necessary information without the Tn formula.

4. If Lines AB||CD, then e = ?

• A. 83
• B. 111
• C. 69
• D. None

Explanation: When two lines, such as AB and CD, are parallel, and a transversal crosses them, the angles on the same side of the transversal are supplementary. This means their measures add up to 180°. Given one angle is 69°, the supplementary angle, denoted as e, is calculated as 180° - 69° = 111°. Therefore, e = 111° is the correct answer. Option A and C provide incorrect values, and Option D is invalid as Option B already provides the correct answer.

5. Find the number of degrees in angle B?I. AC < BCII. Angle BCD = 100°III. Angle A + Angle B + Angle C = 180°IV. AB = BCV. ABC is an isosceles triangle Which two statements are sufficient to answer the question?

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

Explanation: Option C is correct as the information is to find the angle at B(ii) states that Angle BCD= 100° i.e Angle BCA= 180°-100° =80°(as angle on a straight line =180°)If AB=BC,then the triangle is isosceles which means that both these lines would have the same angle i.e BAC=80° alsoSum of triangle =180°Angle ABC+BAC+BCA=180°Angle ABC+80+80=180°180-160=20°Angle at `b=20°The information provided is sufficient to find the angle at BAll the other options does not provide sufficient information to find the angle at B

6. If u > t, r > q, s > t, and t > r, which of the following must be true?I. u > sII. s > qIII. u > r

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

Explanation: The solution involves organizing the given inequalities to find the necessary logical relationships between variables:u > tr > qs > tt > rFrom these, we can deduce:t > r and r > q, which means t > q.s > t means s > q.u > t and t > r implies u > r.Thus, statements II (s > q) and III (u > r) are true. Statement I (u > s) cannot be confirmed because there is no information directly comparing u and s.Therefore, the correct answer is Option E: II and III.

7. If i2k= 1, and i2= -1. Which of the following must be true about k ?

• A. k is a multiple of 2.
• B. k is a positive integer.
• C. When 2k is divided by 4, the remainder is 1.
• D. k/4 is an even integer.

Explanation: in = 1 if and only if n is a multiple of 4. (i4 = 1, i8= 1, i12 = 1, etc.) Therefore, if i2k = 1, then 2k must be a multiple of 4, and therefore, k must be a multiple of 2. When the power is even the answer is 1 or else it is -1. Option B: K is not a positive integer as the answer would then be negative Option C: k is a multiple of 2 and multiplying k with 2, the answer produced would be an even number which would not be completely divisible by 4 and would not give 1 as the remainder, for e.g 2(4)/4=2 Option D: k is supposed to be a multiple of 2 e.g 10/4 = 2.5 , the answer is not going to be an even integer.

8. In the figure above, squares PQRV and VRST have sides of length 6 cm.Quantity A: The area of the shaded region PQS.Quantity B: 36cm2

• 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: To find the area of the shaded region PQS, note that PQS forms a right triangle with base PQ and height QS. Since squares PQRV and VRST have sides of 6 cm, the diagonal PQ (or QS) is 6√2 cm, but for the triangle's area calculation, we consider the base and height along the sides of the square. The area of triangle PQS is 1/2 * base * height = 1/2 * 12 * 6 = 36 cm2, which equals Quantity B. Therefore, Quantity A and Quantity B are equal.

9. If x =2 and y =5 then 4x+9y =

• A. 48
• B. 29
• C. 53
• D. 40

Explanation: To solve the equation 4x + 9y when x = 2 and y = 5, substitute the values into the equation: 4(2) + 9(5). This simplifies to 8 + 45, which equals 53. Therefore, the correct answer is 53 (Option C). Options A, B, and D result from incorrect calculations, such as errors in multiplication or addition.

10. John and Peter are hostel fellows too. Each of them pays the rent, according to their room's size. Peter's room is twice as big as John. How much rent does Peter pay if the total rent of two rooms is $600?

• A. $600
• B. $400
• C. $200
• D. $240

Explanation: To solve this, we set John's rent as $x and Peter's rent as $2x because his room is twice as big. Therefore, the equation is:$x + $2x = $600Solving for x gives:$3x = $600x = $200Thus, Peter pays $2x, which is $400.Option A ($600) suggests Peter pays all the rent, which is incorrect. Option C ($200) suggests Peter pays the same as John, which contradicts the problem. Option D ($240) does not align with the proportional rent based on room size. ORWe're told:Peter's room is twice as big as John'sTotal rent = $600Rent is proportional to room sizeStep 1: Let John's rent be xSince Peter's room is twice as big, his rent is 2xStep 2: Set up the equationx+2x=600⇒3x=600⇒x=200x + 2x = 600 , 3x = 600 , x = 200Step 3: Find Peter's rent2x=2×200=4002x = 2 x 200 = 400✅ Final Answer: Peter pays $400 in rent.