GATE Practice Question and Answer
8Q: Find the sum to 200 terms of the series 2 + 5 + 7 + 6 + 12 + 7 + .... 1183 05b5cc754e4d2b4197774fb9f
5b5cc754e4d2b4197774fb9f- 130,400true
- 230,200false
- 334,600false
- 438,400false
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Answer : 1. "30,400"
Explanation :
Answer: A) 30,400 Explanation: we can treat every two consecutive terms as one.So, we will have a total of 100 terms of the nature:(2 + 5) + (7 + 6) + (12 + 7).... => 7, 13, 19,.... We know the sum of n terms nn+12 Now, a= 7, d=6 and n=100Hence the sum of the given series is S= 100/2 x[2 x 7 + 99 x 6]=> 50[608]=> 30,400.
Q: "I am five times as old as you were, when I was as old as you are", said a man to his son. Find out their present ages, if the sum of their ages is 64 years ? 11342 05b5cc754e4d2b4197774fba4
5b5cc754e4d2b4197774fba4- 1Father = 50; Son =14false
- 2Father = 40; Son =24true
- 3Father = 60; Son =4false
- 4Father = 48; Son =16false
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Answer : 2. "Father = 40; Son =24"
Explanation :
Answer: B) Father = 40; Son =24 Explanation: Let the present age of the man be 'P' and son be 'Q',Given, P + Q = 64 or Q = (64 - P)Now the man says "I am five times as old as you were, when I was as old as you are",So, P = 5[B - (P - Q)]We get 6P = 10Q,Substitute value for Q,6P = 10(64 - P),Therefore P = 40, Q = 24.
Q: A six-digit number is formed by repeating a three-digit number; for example, 404404 or 415415 etc. Any number of this form is always exactly divisible by 1273 05b5cc754e4d2b4197774fb95
5b5cc754e4d2b4197774fb95- 1101false
- 2901false
- 31001true
- 4789false
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Answer : 3. "1001"
Explanation :
Answer: C) 1001 Explanation: Here by trial and error method, we can obseve that 404404 = 404 x 1001; 415415 = 415 x 1001, etc. So, any number of this form is divisible by 1001.
Q: What least number must be substracted from 627349 so that the remaining number is divisible by 15 ? 1026 05b5cc754e4d2b4197774fb9a
5b5cc754e4d2b4197774fb9a- 11false
- 22false
- 33false
- 44true
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Answer : 4. "4"
Explanation :
Answer: D) 4 Explanation: On dividing 627349 by 15, we get remainder = 4.Therefore, the obtained remainder is the least number to be subtracted from the given number so that the the mnumber is divisible by 15.Here 4 is the least number to be subtracted from 627349 so that it is divisible by 15.
Q: A teacher multiplies 987 by a certain number and obtains 556781 as her answer. If in the answer, both 6 and 7 are wrong but the other digits are correct, then the correct answer will be 1216 05b5cc754e4d2b4197774fb8b
5b5cc754e4d2b4197774fb8b- 1553681false
- 2555181false
- 3556581false
- 4555681true
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Answer : 4. "555681"
Explanation :
Answer: D) 555681 Explanation: Given number is 987 = 3 x 7 x 47. So, required number must be divisible by each one of 3, 7, 47. None of the numbers in 553681 and 555181 are divisible by 3. While 556581 is not divisible by 7.Correct answer is 555681.
Q: Avanthi’s age is 1/6th of her father’s age. Her father’s age will be twice of Kapil’s age after 10 years. If Kapil’s eighth birthday was celebrated two years ago, then what is Avanthi’s present age ? 1395 05b5cc754e4d2b4197774fb90
5b5cc754e4d2b4197774fb90- 16 yearsfalse
- 24 yearsfalse
- 37 yearsfalse
- 4Nonetrue
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Answer : 4. "None"
Explanation :
Answer: D) None Explanation: As given Kapil's 8th birthday was celebrated 2 years ago, Kapil’s present age = 8 + 2 = 10 years. Father's age is twice of Kapil’s age after 10 years. => F + 10 = 2 (K + 10) = 2 (10+ 10)F = 30years, Avanthi's age =1/6(F) = 30/6 = 5 years.
Q: K, L and M can do a piece of work in 20, 30 and 60 days respectively. In how many days can K do the total work if he is assisted by L and M on every third day ? 1047 05b5cc754e4d2b4197774fb86
5b5cc754e4d2b4197774fb86- 115 daystrue
- 213 daysfalse
- 312 daysfalse
- 410 daysfalse
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Answer : 1. "15 days"
Explanation :
Answer: A) 15 days Explanation: In one day work done by K = 1/20 Work done by K in 2 days = 1/10 Work done by K,L,M on 3rd day =1/20 + 1/30 + 1/60 = 1/10 Therefore, workdone in 3 days is = 1/10 + 1/10 = 1/5 1/5th of the work will be completed at the end of 3 days. The remaining work = 1 - 1/5 = 4/5 1/5 of work is completed in 3 days Total work wiil be done in 3 x 5 = 15 days.
Q: The difference between two numbers is 3355. When the larger number is divided by the smaller one, the quotient is 6 and the remainder is 15. The smaller number and larger number respectively ? 1172 05b5cc754e4d2b4197774fb81
5b5cc754e4d2b4197774fb81- 1546, 3901false
- 2415, 3770false
- 3668, 4023true
- 4404, 3759false
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Answer : 3. "668, 4023"
Explanation :
Answer: C) 668, 4023 Explanation: Let the smaller number be k.Then, larger number = (3355 + k)Therefore 3355 + k = (6k + 15)‹=› 5k = 3340‹=› k = 668. Therefore, the smaller number k = 668 and now the larger number = 3355+668 = 4023.