GATE Practice Question and Answer

Q: A group of men can complete a job in K hours. After every 4 hours, half the number of men working at that point of time leave the job. Continuing this way if the job is finished in 16 hours, what is the value of K ? 3359 0

  • 1
    7 hrs
    Correct
    Wrong
  • 2
    7.5 hrs
    Correct
    Wrong
  • 3
    8 hrs
    Correct
    Wrong
  • 4
    8.25 hrs
    Correct
    Wrong
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Answer : 2. "7.5 hrs"
Explanation :

Answer: B) 7.5 hrs Explanation: Let there are L men job requires LK man hours.   job completed in first 4 hrs = L x 4 = 4L job completed in next 4 hrs = 4 x L/2 = 2L job completed in next 4 hrs = 4 x L/4 = L job completed in last 4 hrs = 4 x L/8 = L/2 4L + 2L + L + L/2 = KL K = 7+1/2 = 7.5 hours.

Q: 5 years ago Sushma was 5 times as old as her Son. 5 years hence her age will be 8 less than three times the corresponding age of her Son. Find their ages ? 2958 0

  • 1
    24 and 13 years
    Correct
    Wrong
  • 2
    48 and 24 years
    Correct
    Wrong
  • 3
    35 and 11 years
    Correct
    Wrong
  • 4
    33 and 15 years
    Correct
    Wrong
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Answer : 3. "35 and 11 years"
Explanation :

Answer: C) 35 and 11 years Explanation: Let the age of sushma be x and the age of her son is yThen five years before x-5=5(y-5) ...(1)Five years hence x+5 = 3(y+5)-8 .....(2) By soving (1) & (2), we get5y - 15 = 3y + 7y = 11 => x = 35 Therefore, the age of Sushma = 35 and her son = 11.

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Answer : 4. "E = 4 & Y = 2"
Explanation :

Answer: D) E = 4 & Y = 2 Explanation: Let the the age of the elder boy = E   Let the the age of the younger boy = Y   Given that Y = cube root of EY   => Y3 = EY => E = Y2 .....(1)By the condition of number replacement the age of the father is YE   The Mother's age = EY/2   But she is 3 years less than father => EY/2 + 3 = YE2YE = EY + 6 ......(2)   Then now from the given options we can identify which satisfies the all the conditions.   Here Y =2 and E = 4 satisfies all the conditions.

Q: Equal quantities of three mixtures of milk and water are mixed in the ratio 1:2, 2:3 and 3:4. The ratio of water and milk in the mixture is ? 2852 0

  • 1
    193 : 122
    Correct
    Wrong
  • 2
    97 : 102
    Correct
    Wrong
  • 3
    115 : 201
    Correct
    Wrong
  • 4
    147 : 185
    Correct
    Wrong
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Answer : 1. "193 : 122"
Explanation :

Answer: A) 193 : 122 Explanation: Given the three mixtures ratio as (1:2),(2:3),(3:4) (1+2),(2+3),(3+4) Total content = 3,5,7   Given equal quantities of the three mixtures are mixed, then LCM of 3, 5, 7 = 105 105/3 = 35 , 105/5 = 21 , 105/7 = 15   Now, the individual equal quantity ratios are (35x1, 35x2), (21x2, 21x3), (15x3, 15x4)  i.e (35,70), (42,63), (45,60)   So overall mixture ratio of milk and water is 35+42+45 : 70+63+60 122:193   But in the question asked the ratio of water to milk = 193 : 122

Q: A man has only 20-paise and 25-paise coins in a bag. If he has 50 coins in all totaling to Rs.10.25, then the number of 20-paise coins is 895 0

  • 1
    42
    Correct
    Wrong
  • 2
    45
    Correct
    Wrong
  • 3
    38
    Correct
    Wrong
  • 4
    36
    Correct
    Wrong
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Answer : 2. "45"
Explanation :

Answer: B) 45 Explanation: Let number of 20 ps coins = x and number of 25 ps coins = y Given total coins in the bag = 50 x + y = 50.......(1) But the total money in the bag = Rs. 10.25 0.20x + 0.25y = 10.25 20x + 25y = 1025.........(2) Now multiplying (1) by 25 we get 25x+25y=1250.............(3) By solving (2) and (3) 20x + 25y = 1025; => x = 45; Then, the no. of 20 ps coins are 45.

Q: The sum of 3rd and 15th elements of an arithmetic progression is equal to the sum of 6th, 11th and 13th elements of the same progression. Then which element of the series should necessarily be equal to zero ? 1820 1

  • 1
    14th element
    Correct
    Wrong
  • 2
    9th element
    Correct
    Wrong
  • 3
    12th element
    Correct
    Wrong
  • 4
    7th element
    Correct
    Wrong
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Answer : 3. "12th element"
Explanation :

Answer: C) 12th element Explanation: If we consider the third term to be ‘x”The 15th term will be (x + 12d)6th term will be (x + 3d)11th term will be (x + 8d) and 13th term will be (x + 10d).Thus, as per the given condition, 2x + 12d = 3x + 21d.Or x + 9d = 0.x + 9d will be the 12th term. Thus, 12th term of the A.P will be zero.

Q: 20 men went to a restaurant. Ninteen of them paid Rs.70 each and the twentieth man paid Rs.90.25 more than the average of all the 20 men. What is the total bill ? 1480 0

  • 1
    Rs. 1495
    Correct
    Wrong
  • 2
    Rs. 548
    Correct
    Wrong
  • 3
    Rs. 850
    Correct
    Wrong
  • 4
    Rs. 1750
    Correct
    Wrong
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Answer : 1. "Rs. 1495"
Explanation :

Answer: A) Rs. 1495 Explanation: Let the average bill paid by twenty members = 'x' But 19 men paid each = Rs. 70 20th man paid Rs. 90.25 more than the avg bill of 20 = x + 90.25 20x = 19(70) + x + 90.2519x = 1330 + 90.2519x = 1420.25x = 1420.25/19 = Rs. 74.75 But the total bill = 20 x 74.75 = Rs. 1495.

Q: If 4th december 1999 is Monday then what day is 3rd january 2000 ? 2343 0

  • 1
    Sunday
    Correct
    Wrong
  • 2
    Monday
    Correct
    Wrong
  • 3
    Tuesday
    Correct
    Wrong
  • 4
    Wednesday
    Correct
    Wrong
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Answer : 4. "Wednesday"
Explanation :

Answer: D) Wednesday Explanation: Here from 4th December 1999 to 3rd January 2000,there is a difference of 30 days.Number of odd days = 30/7 = 2 odd days Then no. of odd days = 2 => tuesday and wednesday(from monday). Hence on 3rd january it is wednesday.

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