CAT Practice Question and Answer

Q: For x∈N, x>1,  and  p=logxx+1, q=logx+1x+2 then which one of the following is correct? 6979 2

  • 1
    p < q
    Correct
    Wrong
  • 2
    p = q
    Correct
    Wrong
  • 3
    p > q
    Correct
    Wrong
  • 4
    can't be determined
    Correct
    Wrong
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Answer : 3. "p > q"
Explanation :

Answer: C) p > q Explanation: kl>k+1l+1 for (k,l) > 0 and  k > l        Let     k = x+1    and   l = x       Therefore, x+1x>(x+1)+1(x)+1        (x + 1) > x       Therefore, log(x+1)log(x)>log(x+2)log(x+1)       ⇒logxx+1 >logx+1x+2

Q: A cistern has a leak which would empty the cistern in 20 minutes. A tap is turned on which admits 4 liters a minute into the cistern, and it is emptied in 24 minutes. How many liters does the cistern hold ? 6927 0

  • 1
    360 lit
    Correct
    Wrong
  • 2
    480 lit
    Correct
    Wrong
  • 3
    320 lit
    Correct
    Wrong
  • 4
    420 lit
    Correct
    Wrong
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Answer : 2. "480 lit"
Explanation :

Answer: B) 480 lit Explanation: 1/k - 1/20 = -1/24 k = 120 120 x 4 = 480 Therefore, the capacity of the cistern is 480 liters.

Q: 45% of 750  -  25% of 480 = ? 6885 0

  • 1
    337.50
    Correct
    Wrong
  • 2
    217.50
    Correct
    Wrong
  • 3
    376.21
    Correct
    Wrong
  • 4
    120
    Correct
    Wrong
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Answer : 2. "217.50"
Explanation :

Answer: B) 217.50 Explanation: Given expression = (45 x 750/100) - (25 x 480/100) = (337.50 - 120) = 217.50

Q: A cube is painted blue on two adjacent surfaces and black on the surfaces opposite to blue surfaces and green on the remaining faces .Now the cube is cut into 216 smaller cubes of equal size. 6840 0

  • 1
    56
    Correct
    Wrong
  • 2
    48
    Correct
    Wrong
  • 3
    32
    Correct
    Wrong
  • 4
    64
    Correct
    Wrong
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Answer : 4. "64"
Explanation :

Answer: D) 64 Explanation: We know that Cubes with no surface painted can be find using x-23, where x is number of cuttings. Here x=6.  ∴ 6-23=64

Q: In a party there are 5 couples. Out of them 5 people are chosen at random. Find the probability that there are at the least two couples ? 6783 0

  • 1
    6/7
    Correct
    Wrong
  • 2
    19/21
    Correct
    Wrong
  • 3
    7/31
    Correct
    Wrong
  • 4
    5/21
    Correct
    Wrong
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Answer : 4. "5/21"
Explanation :

Answer: D) 5/21 Explanation: Number of ways of (selecting at least two couples among five people selected) = (⁵C₂ x ⁶C₁) As remaining person can be any one among three couples left. Required probability = (⁵C₂ x ⁶C₁)/¹⁰C₅= (10 x 6)/252 = 5/21

Q: In a purse there are 30 coins, twenty one-rupee and remaining 50-paise coins. Eleven coins are picked simultaneously at random and are placed in a box. If a coin is now picked from the box, find the probability of it being a rupee coin? 6762 0

  • 1
    4/7
    Correct
    Wrong
  • 2
    2/3
    Correct
    Wrong
  • 3
    1/2
    Correct
    Wrong
  • 4
    5/6
    Correct
    Wrong
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Answer : 2. "2/3"
Explanation :

Answer: B) 2/3 Explanation: Total coins 30 In that, 1 rupee coins 20 50 paise coins 10Probability of total 1 rupee coins =  20C11 Probability that 11 coins are picked = 30C11 Required probability of a coin now picked from the box is 1 rupee = 20C11/30C11 = 2/3.

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Answer : 3. "23"
Explanation :

Answer: C) 23 Explanation: Let us assume the two persons who can speak two languages speak Hindi and Tamil. The third person then speaks all the three languages. Tamil – Number of persons who can speak is 6. Only Tamil 6 – 2 – 1 = 3 Hindi - Number of persons who can speak is 15. Only Hindi 15 – 2 – 1 12 Gujarati – Number of persons who can speak is 6. Only Gujarati 6 – 1 = 5 Thus the number of persons who can speak only one language is 3 + 12 + 5 = 20 Number of persons who can speak two languages = 2 Number of person who an speak all the languages = 1 Total number of persons = 23.

Q: Find the missing number? 15, 30, ? , 40, 8, 48 6733 0

  • 1
    21
    Correct
    Wrong
  • 2
    8
    Correct
    Wrong
  • 3
    19
    Correct
    Wrong
  • 4
    10
    Correct
    Wrong
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Answer : 4. "10"
Explanation :

Answer: D) 10 Explanation: Given nuber series is 15, 30, ? , 40, 8, 48  Here the number series follows a pattern that 15 15 x 2 = 30 30 ÷ 3 = 10 10 x 4 = 40 40 ÷ 5 = 8 8 x 6 = 48 Hence, the missing number in the series is 10.

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