Numbers - General Questions (14)
| 105. | On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ? |
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Answer: Option D Explanation: Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder.
= (25k2 + 30k + 9) = 5(5k2 + 6k + 1) + 4
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x = 5k + 3
x2 = (5k + 3)2| 106. | What will be remainder when (6767 + 67) is divided by 68 ? |
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Answer: Option C Explanation: (xn + 1) will be divisible by (x + 1) only when n is odd.
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| 107. | 107 x 107 + 93 x 93 = ? |
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Answer: Option C Explanation:
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| 108. | If n is a natural number, then (6n2 + 6n) is always divisible by: |
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Answer: Option B Explanation: (6n2 + 6n) = 6n(n + 1), which is always divisible by 6 and 12 both, since n(n + 1) is always even. |
| 109. | On dividing a number by 56, we get 29 as remainder. On dividing the same number by 8, what will be the remainder ? |
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Answer: Option B Explanation: Formula: (Divisor*Quotient) + Remainder = Dividend. Soln: (56*Q)+29 = D -------(1) D%8 = R -------------(2) From equation(2), ((56*Q)+29)%8 = R. => Assume Q = 1. => (56+29)%8 = R. => 85%8 = R => 5 = R. |
| 110. | The difference between a positive proper fraction and its reciprocal is 9/20. The fraction is: |
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Answer: Option C Explanation:
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| 111. | The difference between the local value and the face value of 7 in the numeral 32675149 is |
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Answer: Option D Explanation: (Local value of 7) - (Face value of 7) = (70000 - 7) = 69993 |
| 112. | If the number 481 * 673 is completely divisible by 9, then the smallest whole number in place of * will be: |
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Answer: Option D Explanation: Sum of digits = (4 + 8 + 1 + x + 6 + 7 + 3) = (29 + x), which must be divisible by 9.
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