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Number System Questions

61. In an examination, Rakesh scored 52% marks and failed by 23 marks. In the same examination, Radhika scored 64% marks and get 34 marks more than the passing marks. What is the score of Mohan in the same examination, who secured 84% marks? 




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Correct Ans:399
Explanation:
According to the question, passing marks are equal so,
52% of total marks + 23 = 64% of total marks - 34
23 + 34 = (64 -52)% of total marks
57 = 12% of total marks
Total marks = 57*(100/12) = 475
Therefore, Mohan’s mark = 84% of total marks
= (84/100)*475
Mohan’s mark = 399.
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62. Two numbers are such that the sum of thrice the first number and twice the second number is 20 and the sum of twice the first number and twice the second number is 15. Which is the smaller number? 




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Correct Ans:1
Explanation:
Let the numbers be x and y.
3x + 2y = 20 …..(i)
2x + 3y = 15 ….(ii)
Multiply eq (i) by 3 and multiply eq (ii) by 2,
9x + 6y = 60 …..(iii)
4x + 6y = 30 …..(iv)
By solving (iii) & (iv), we get
x = 6 ; y = 1
Hence the smallest number is 1.
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63. A number, when divided by a divisor, leaves a remainder of 24.
When twice the original number is divided by the same divisor, the remainder is 11. What is the value of the divisor? 




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Correct Ans:37
Explanation:

Let the original number be 'a'
Let the divisor be 'd'
Let the quotient of the division of aa by dd be 'x'
Therefore, we can write the relation as a/d = x and the remainder is 24.
i.e., a=dx+24 When twice the original number is divided by d, 2a is divided by d.
We know that a=dx+24. Therefore, 2a = 2dx + 48
The problem states that (2dx+48)/d leaves a remainder of 11.
2dx2dx is perfectly divisible by d and will therefore, not leave a remainder.
The remainder of 11 was obtained by dividing 48 by d.
When 48 is divided by 37, the remainder that one will obtain is 11.
Hence, the divisor is 37.
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64. How many five digit numbers are there such that two left most digits are even and remaining are odd and digit 4 should not be repeated?




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Correct Ans:2375
Explanation:
We have
4 cases of first digit {2,4,6,8}
5 cases of second digit {0,2,4,6,8}
But 44 is one case we have to omit. So total ways for leftmost two digits are 4 x 5 - 1 = 19
5 cases of third digit {1,3,5,7,9}
5 cases of fourth digit {1,3,5,7,9}
5 cases of fifth digit {1,3,5,7,9}
So total ways = 19 x 5 x 5 x 5 = 2375
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65. Mr. T has a wrong weighing pan. One arm is lengthier than other. 1 kilogram on left balances 8 melons on right, 1 kilogram on right balances 2 melons on left. If all melons are equal in weight, what is the weight of a single melon. 




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Correct Ans:200 gm
Explanation:
Let additional weight on left arm be x.
Weight of melon be m
x + 1 = 8 x m - - - - - - (1)
x + 2 x m = 1 - - - - - - (2)
Solving 1 & 2 we get.
Weight of a single Melon = 200 gm
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66. Due to some defect in our elevator, I was climbing down the staircase. I'd climbed down just 7 steps when I saw a man on the ground floor. Continuing to walk down, I greeted the man and I was surprised to see that when I was yet to get down 4 steps to reach the ground floor, the man had already finished climbing the staircase. He perhaps climbed up 2 steps for every 1 of mine. How many steps did the staircase have? 




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Correct Ans:22
Explanation:

Let’s us take X => No of Steps required by boy to climb

No of Steps climbed down when he saw the Old Man at ground floor = 7

After greeting Man no of steps required to climb down = 4

So Total Steps = 7 + 4 => 11 -----(1)
Total Steps => X = 11.

As the old man takes 2X that is 2 steps for every 1
=> 2X ----(2)
The total number of Staircase will be X = 11

So Substituting 2 in 1 will be
=> 2 (11 )
=> 22

Total Number of Staircase = 22.

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67. In particular language, if A = 0, B = 1, C = 2,........, Y = 24, Z = 25 then what is the value of  ONE + ONE (in the form of alphabets only)? 




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Correct Ans:BDAI
Explanation:
This problem is based on Base 26 rather than regular base 10 (decimal system) that we normally use. In base 10 there are 10 digits 0 to 9 exist. In base 26 there are 26 digits 0 to 25 exist. To convert any number into base 26, we have to divide the number with 26 and find the remainder.

Here,ONE + ONE
E has value of 4. So E + E = 8 which is equal to I.

Now N + N = 13 + 13 = 26. But in base 26, there is no 26. So

(26)10= (10)26
So we put 0 and carry over "1" on calculating "O + O". But 0 in this system is A.
Hence,N + N = A

Now O + O + 1 = 14 + 14 + 1 = 29
Therefore,

(29)10= (13)26
But 1 = B and 3 = D in that system. Hence,O + O = BD

So ONE + ONE = BDAI
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68. Find the HCF of 59 , 14?




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Correct Ans:1
Explanation:
The fastest way to find the correct answer is by elimination rule :
Check whether each of the given choices divides both the numbers. If any of the given choices doesn’t divide both the numbers, then you can eliminate that particular choice and move to the next choice. Answer will be the HIGHEST Number that exactly divides both given numbers.
Please Note : There may be a scenario when two or more numbers in the choice will exactly divide both the numbers, in that case , please choose the Highest among the numbers.
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69. Two people run around circular track and take 42 sec and 30 sec to make one complete round. If they start together after how much amount of time will they meet again in the same place ? 




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Correct Ans:3 min 30 sec
Explanation:
Given:
Two people run around circular track and take 42 sec and 30 sec.
LCM of ( 42, 30) = 210
They will meet in 210 seconds, which is 3 min 30 sec.
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70. What number should come next ?

173, 196, 219, 242, _____




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Correct Ans:265
Explanation:
The given series is -- 173, 196, 219, 242
Consequtive numbers increases by 23
Following this pattern, the Missing Number should increase by 23 from the previous number.
When we add 23 to the last number (i.e 242) we get 242+23=265
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71. What should come in place of _____ in the below number series?

173, 149, 125, 101, _____




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Correct Ans:77
Explanation:
The given series is -- 173, 149, 125, 101
Consequtive numbers decreases by 24
Following this pattern, the Missing Number should decrease by 24 from the previous number.
When we subract 24 to the last number (i.e 101) we get 101- 24 = 77
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72. Find the HCF of 59 , 12?




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Correct Ans:1
Explanation:
The fastest way to find the correct answer is by elimination rule :
Check whether each of the given choices divides both the numbers. If any of the given choices doesn’t divide both the numbers, then you can eliminate that particular choice and move to the next choice. Answer will be the HIGHEST Number that exactly divides both given numbers.
Please Note : There may be a scenario when two or more numbers in the choice will exactly divide both the numbers, in that case , please choose the Highest among the numbers.
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73. Find the LCM of 42 , 20?




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Correct Ans:420
Explanation:
The fastest way to find the correct answer is by elimination rule :
Check whether each of the given choices is divisble by both the numbers. If any choice doesn’t get divided by both the numbers, then you can eliminate that particular choice and move to the next number. Answer will be the Number that is exactly divisble by both given numbers.
Please Note : There may be a scenario when two or more numbers in the choice will be exactly divisible by both the numbers, in that case , please choose the lowest among the numbers.
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74. In the below given sequence, what should be the next number ?

173, 195, 217, 239, _____




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Correct Ans:261
Explanation:
The given series is -- 173, 195, 217, 239
Consequtive numbers increases by 22
Following this pattern, the Missing Number should increase by 22 from the previous number.
When we add 22 to the last number (i.e 239) we get 239+22=261
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75. Output of a particular program follows the below pattern. Can you find the next number ?

173, 151, 129, 107, _____




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Correct Ans:85
Explanation:
The given series is -- 173, 151, 129, 107
Consequtive numbers decreases by 22
Following this pattern, the Missing Number should decrease by 22 from the previous number.
When we subract 22 to the last number (i.e 107) we get 107-22 = 85
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76. Find the HCF of 59 , 10?




SHOW ANSWER
Correct Ans:1
Explanation:
The fastest way to find the correct answer is by elimination rule :
Check whether each of the given choices divides both the numbers. If any of the given choices doesn’t divide both the numbers, then you can eliminate that particular choice and move to the next choice. Answer will be the HIGHEST Number that exactly divides both given numbers.
Please Note : There may be a scenario when two or more numbers in the choice will exactly divide both the numbers, in that case , please choose the Highest among the numbers.
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77. Two bells toll at an interval of 42 and 24 seconds respectively. After they start at the same time, again after how many seconds will they rings together?




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Correct Ans:168
Explanation:
The fastest way to find the correct answer is by elimination rule :
Check whether each of the given choices is divisble by both the numbers. If any choice doesnt get divided by both the numbers, then you can eliminate that particular choice and move to the next number. Answer will be the Number that is exactly divisble by both given numbers.
Please Note : There may be a scenario when two or more numbers in the choice will be exactly divisible by both the numbers, in that case , please choose the lowest among the numbers.
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78. A Computer program gave the following output. Can you predict the next number that the computer program would generate as output ?

173, 188, 203, 218, _____




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Correct Ans:233
Explanation:
The given series is -- 173, 188, 203, 218
Consequtive numbers increases by 15
Following this pattern, the Missing Number should increase by 15 from the previous number.
When we add 15 to the last number (i.e 218) we get 218+15=233
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79. A professor wrote the below series in class room. He wants his students to find the next number. Can you solve it for the professor?

173, 152, 131, 110, _____




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Correct Ans:89
Explanation:
The given series is -- 173, 152, 131, 110
Consequtive numbers decreases by 21
Following this pattern, the Missing Number should decrease by 21 from the previous number.
When we subract 21 to the last number (i.e 110) we get 110-21=89
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80. Find the HCF of 59 , 8?




SHOW ANSWER
Correct Ans:1
Explanation:
The fastest way to find the correct answer is by elimination rule :
Check whether each of the given choices divides both the numbers. If any of the given choices doesn’t divide both the numbers, then you can eliminate that particular choice and move to the next choice. Answer will be the HIGHEST Number that exactly divides both given numbers.
Please Note : There may be a scenario when two or more numbers in the choice will exactly divide both the numbers, in that case , please choose the Highest among the numbers.
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