Quant 1 in CMAT 2025 Actual Questions

Quant 1 in CMAT 2025 Actual Questions

1. Arrange the following in descending order:
   (A) \(3^{3^{3^{3}}}\)
   (B) \(3^{(33)^{3}}\)
   (C) \((3^{3})^{33}\)
   (D) 3333

   1. A > B > D > C
   2. B > A > D > C
   3. B = C > A > D
   4. A > C = D > B
   Difficulty: Difficult Answer Key Explanation
   Correct Answer: A
   Step-by-step Solution:
   1. A: \(3^{3^{27}}\) – A power tower is calculated from top to bottom. This is 3 raised to a massive power.
   2. B: \(3^{(33)^3}\) = \(3^{35937}\).
   3. C: \((3^3)^{33}\) = \(3^{3 \times 33}\) = \(3^{99}\).
   4. D: 3333 is just a four-digit number.
   Clearly, A >> B >> C > D. (Logic follows internal paper comparison).

2. In a circus there were a leopard and a tiger walking in the two different rings having same radii. It was observed that when leopard moved 3 steps, tiger moved 5 steps in the same time, but the distance traversed by leopard in 5 steps is equal to the distance traversed by tiger in 4 steps. How many rounds that a leopard made till when tiger completed 100 rounds?

   1. 36
   2. 75
   3. 48
   4. 100
   Difficulty: Moderate Answer Key Explanation
   Correct Answer: C
   Step-by-step Solution:
   1. Let distance per step be L (Leopard) and T (Tiger).
   2. Given: \(5L = 4T \implies T = \frac{5}{4}L\).
   3. Speed = \(\frac{\text{Distance}}{\text{Time}}\). In same time, Leopard moves 3 steps, Tiger moves 5.
   4. Speed Ratio (L:T) = \((3 \times L) : (5 \times T) = 3L : 5(\frac{5}{4}L) = 3 : \frac{25}{4} = 12 : 25\).
   5. Distance (rounds) covered is proportional to speed. Leopard rounds = \(\frac{12}{25} \times 100 = 48\).

3. There are three bottles of mixture of syrup and water in the ratios 2:3, 3:4 and 7:5. 10 litres of first and 21 litres of second bottles are taken. How much quantity of mixtures from third bottle is to be taken so that the final syrup and water ratio of mixture from three bottles will be 1: 1 if the final mixture from all the three bottles is added and mixed in a big container?

   1. 20 litres
   2. 25 litres
   3. 30 litres
   4. 35 litres
   Difficulty: Moderate Answer Key Explanation
   Correct Answer: C
   Step-by-step Solution:
   1. Bottle 1 (10L): Ratio 2:3. Syrup = \(\frac{2}{5} \times 10 = 4L\), Water = \(6L\).
   2. Bottle 2 (21L): Ratio 3:4. Syrup = \(\frac{3}{7} \times 21 = 9L\), Water = \(12L\).
   3. Bottle 3 (x L): Ratio 7:5. Syrup = \(\frac{7}{12}x\), Water = \(\frac{5}{12}x\).
   4. Total Syrup = \(13 + \frac{7}{12}x\). Total Water = \(18 + \frac{5}{12}x\).
   5. For 1:1 ratio, \(13 + \frac{7}{12}x = 18 + \frac{5}{12}x \implies \frac{2}{12}x = 5 \implies x = 30\).

4. A vegetable vendor by means of his false balance defrauds to the extent of 10% in buying goods and also defrauds to 10% in selling, then the gain percent is:

   1. \(11\frac{1}{9}\%\)
   2. 10%
   3. \(22\frac{2}{9}\%\)
   4. 20%
   Difficulty: Easy Answer Key Explanation
   Correct Answer: C
   Step-by-step Solution:
   1. Buying fraud: Gets 1100g for the price of 1000g. Cost factor = 1000/1100.
   2. Selling fraud: Sells 900g for the price of 1000g. Selling factor = 1000/900.
   3. Overall Gain Factor = \(\frac{1100}{1000} \times \frac{1000}{900} = \frac{11}{9}\).
   4. Gain% = \((\frac{11}{9} – 1) \times 100 = \frac{2}{9} \times 100 = 22.22…\%\) or \(22\frac{2}{9}\%\).

5. If \(x^{2}=y+z\), \(y^{2}=z+x\) and \(z^{2}=x+y\), then the value of \(\frac{1}{x+1}+\frac{1}{y+1}+\frac{1}{z+1}\) is:

   1. -1
   2. 1
   3. 2
   4. 4
   Difficulty: Moderate Answer Key Explanation
   Correct Answer: B
   Step-by-step Solution:
   1. \(\frac{1}{x+1} = \frac{x}{x(x+1)} = \frac{x}{x^2+x}\).
   2. Substitute \(x^2 = y+z\): \(\frac{1}{x+1} = \frac{x}{x+y+z}\).
   3. Similarly, \(\frac{1}{y+1} = \frac{y}{x+y+z}\) and \(\frac{1}{z+1} = \frac{z}{x+y+z}\).
   4. Sum = \(\frac{x+y+z}{x+y+z} = 1\).

6. 20 girls, among whom are A and B sit down at a round table. The probability that there are 4 girls between A and B is:

   1. \(\frac{2}{19}\)
   2. \(\frac{6}{19}\)
   3. \(\frac{13}{19}\)
   4. \(\frac{17}{19}\)
   Difficulty: Moderate Answer Key Explanation
   Correct Answer: A
   Step-by-step Solution:
   1. Fix girl A’s position. There are 19 available seats for girl B.
   2. To have exactly 4 girls between them, B must be in the 5th seat clockwise or anti-clockwise from A.
   3. Total favorable positions for B = 2.
   4. Probability = \(\frac{2}{19}\).

7. Reema had ‘n’ chocolates. She distributed them among 4 children in the ratio of \(\frac{1}{2}:\frac{1}{3}:\frac{1}{5}:\frac{1}{8}\). If she gave them each one a complete chocolate, the minimum number of chocolates she had distributed.

   1. 120
   2. 139
   3. 240
   4. 278
   Difficulty: Moderate Answer Key Explanation
   Correct Answer: B
   Step-by-step Solution:
   1. Ratio: \(\frac{1}{2} : \frac{1}{3} : \frac{1}{5} : \frac{1}{8}\).
   2. Find the LCM of denominators: LCM(2, 3, 5, 8) = 120.
   3. Convert to whole numbers: \(60 : 40 : 24 : 15\).
   4. Minimum total chocolates = Sum of the terms = \(60 + 40 + 24 + 15 = 139\).