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Directions: Solve the following question and mark the most appropriate option.
x is a natural number between 1 and 20, both inclusive, such that
1. If x is less than 10, then it is even.
2. If x is not divisible by 3, then it is prime.
3. If x is not a factor of 60, then it is a factor of 102.
4. If x, when divided by 7, leaves a remainder greater than 4, then it is greater than 14.
5. If one less than x is a perfect square, then the reciprocal of x is less than 4/7.
6. If one more than x is a perfect square, then x is not divisible by 5.
Q. What is the value of x?
  • a)
    2
  • b)
    3
  • c)
    5
  • d)
    8
Correct answer is option 'A'. Can you explain this answer?
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Directions: Solve the following question and mark the most appropriat...
From the first condition, if x is less than 10, then x = 2, 4, 6 or 8, otherwise it is 10, 11, 12, …, 20.
From the second condition, if x is divisible by 3, then x = 6, 9, 12, 15 or 18, otherwise it is 2, 5, 7, 11, 13, 17 or 19.
From the third condition, if x is a factor of 60, then x = 1, 2, 3, 4, 5, 6, 10, 12, 15 or 20, otherwise it is 17.
From the fourth condition, if x when divided by 7 leaves a remainder greater than 4, then x = 19 or 20, otherwise it is 1,2,3,4,7,8,9,10,11,14,15,16,17,18
From the fifth condition, if x – 1 is a perfect square, then x = 2, 5, 10 or 17, otherwise it is 1,3,4,6,7,8,9,11,12,13,14,15,16,18,19,20.
From the sixth condition, if x + 1 is a perfect square, then x = 3 or 8, otherwise it is 1, 2, 4, 5, 6, 7, 9,10,11,12,13,14,16, …, 20.
The only value that satisfies all of the above conditions is x = 2.
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