Free Quantitative Reasoning MCQs with Answers

191. x is a strictly negative integer. Which is the biggest?

• A. -2x
• B. 2x
• C. 6x+2
• D. x - 2

Explanation: Here assuming x is 1, the answer becomes 2, thus it is clearly seen that the only positive hence largest integer is 2.

192. Thirty kilograms of solution A contains 80 percent water and 20 percent liquid M. if 50 percent water evaporates from this solution, what percentage in the new solution is liquid M?

• A. 10%
• B. 12%
• C. 13%
• D. 33.5%

Explanation: To solve this problem, first determine the initial composition of the solution: 30 kg of solution A contains 80% water and 20% liquid M. Therefore, there is 24 kg of water and 6 kg of liquid M. When 50% of the water evaporates, 12 kg of water remains, making the new solution total 18 kg (12 kg water + 6 kg liquid M). The percentage of liquid M in the new solution is calculated as (6 kg / 18 kg) × 100%, which equals 33.3%. Hence, the correct answer is 33.3%. The other options reflect incorrect calculations of this percentage.

193. The price of a candy bar is Rs. 80. The price of a box containing the same 12 candy bars is Rs. 720. The box of 12 Candy bars is what percentage cheaper than purchasing 12 candy bars individually?

• A. 25%
• B. 30%
• C. 40%
• D. 50%

Explanation: To find out how much cheaper it is to buy the box of candy bars than buying them individually, first calculate the cost of buying 12 candy bars individually: 12 * Rs. 80 = Rs. 960. The box costs Rs. 720, so the difference is Rs. 960 - Rs. 720 = Rs. 240. To find the percentage discount, divide the savings by the original cost: (Rs. 240 / Rs. 960) * 100% = 25%. Thus, buying the box is 25% cheaper. Options B, C, and D are incorrect because they do not accurately represent the percentage savings calculated.

194. Question is given as an image.

• A. The quantity on the left is greater
• B. The quantity on the right is greater
• C. Both are equal
• D. The relationship cannot be determined without further information

Explanation: Factors of 36 are those numbers that divide 36 completely without leaving any remainder. There are 9 factors of 36 among which 36 is the biggest factor and 2 and 3 are its prime factors. So, the prime factors of 48 are 2 × 2 × 2 × 2 × 3 or we can also write them as 24 × 3, where 2 and 3 both are prime numbers. Hence 3 is the answer to both.

195. The value of cube root 729x21y51 is

• A. 1x63y115
• B. 9x7y17
• C. 243x7y17
• D. None of these

Explanation: To find the cube root of 729x21y51, apply the cube root to each component separately. The cube root of 729 is 9 because 93 = 729. For the exponents, divide by 3: 21/3 = 7 for x and 51/3 = 17 for y. Therefore, the correct expression is 9x7y17. Options A and C miscalculate the numbers involved, and 'None of these' is incorrect because there is a correct answer provided.

196. Which of the following is NOT a solution (x-5)(x-3)(x+3)(x+9)= 0

• A. 5
• B. 3
• C. -3
• D. -5

Explanation: In order to solve this nonlinear equation, we will apply the zero product theorem. That means that each variable factor in the original equation needs to be set to zero. x - 5 = 0; x - 3 = 0; x + 3 = 0; x + 9 = 0 x∈ {5,3,-3,-9}

197. For which of the following values of c will there be 2 distinct real solutions to the equation 5x2+16x+ c = 0?

• A. 3
• B. 12
• C. 14
• D. 15

Explanation: The discriminant of a quadratic equation ax2 + bx + c = 0 is given by b2 - 4ac. For the equation to have two distinct real solutions, the discriminant must be greater than 0. Plugging the values into the equation with c = 3 gives a discriminant of 196, which is positive, thus allowing for two distinct real solutions. Other values for c either result in a negative discriminant (no real solutions) or do not yield distinct integer solutions even if positive.

198. For all n, (3n+5)2 = ?

• A. 6n2+15n+ 10
• B. 6n2+30n+25
• C. 9n2+6n+ 10
• D. 9n2+30n+25

Explanation: Expand the expression using (a+b)² =a2+2ab+b²: (3n)²+2x3n×5+52 Simplify using exponent rule with same exponent (ab)" =ar.b": 32 xn²+2x3n×5+ 52 Calculate the power: 9n²+2x3n×5+25 Multiply the monomials: 9n2+30n+25 get the result: True

199. The average of 8 numbers is 7.5. If one of them is deleted, the average of the remaining 7 numbers becomes 8.5. What is the deleted number?

• A. 0.2
• B. 0.3
• C. 0.4
• D. 0.5

Explanation: If the eight numbers are a, b, c, d, e, f, g, h. Following equation can be formed (a+b+c+d+e+f+g+h)/8= 7.5 ---- (1) If h is deleted, the equation becomes (a+b+c+d+e+f+g)/7=8.5 (a+b+c+d+e+f+g)= 8.5×7= 59.5 Putting this value in equation (1) ((a+b+c+d+e+f+g) +h)/8= 7.5 (59.5+h)/8=7.5 59.5+h=7.5×8 59.5+h=60 h=60-59.5 h=0.5

200. 43, 83, 54, 35, 77, x, yIf the median of the set of numbers is 54 and the mean is 56, which of the following could be the values of x and y?

• A. 41 and 59
• B. 65 and 72
• C. 56 and 80
• D. 21 and 52

Explanation: Known numbers in ascending order are; 35, 43, 54, 77, 83 For 54 to remain median, one of the x and y should be greater and other less than 54, as satisfied by option A. Further, we need to confirm if the mean is 56, if x= 41 and y= 59. 35, 41, 43, 54, 59, 77, 83 (35+41+43+54+59+77+83)/7 = 392/7=56