102. | If the number 91876 * 2 is completely divisible by 8, then the smallest whole number in place of * will be: | |||||||||
Answer: Option C Explanation:
Then number 6x2 must be divisible by 8.
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103. | 2056 x 987 = ? | |||||||||||||||||
Answer: Option B Explanation:
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104. | On multiplying a number by 7, the product is a number each of whose digits is 3. The smallest such number is: | |||||||
Answer: Option A Explanation:
By hit and trial, we find that 47619 x 7 = 333333. |
105. |
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Answer: Option B Explanation:
Let the number be x. Then
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106. | If x and y are the two digits of the number 653xy such that this number is divisible by 80, then x + y = ? | |||||||||
Answer: Option A Explanation:
80 = 2 x 5 x 8 Since 653xy is divisible by 2 and 5 both, so y = 0. Now, 653x is divisible by 8, so 13x should be divisible by 8. This happens when x = 6.
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107. | The difference of the squares of two consecutive odd integers is divisible by which of the following integers ? | |||||||
Answer: Option D Explanation:
Let the two consecutive odd integers be (2n + 1) and (2n + 3). Then, (2n + 3)2 – (2n + 1)2 = (2n + 3 + 2n + 1) (2n + 3 – 2n – 1) = (4n + 4) x 2 = 8(n + 1), which is divisible by 8. |
108. | What is the unit digit in (4137)754? | |||||||
Answer: Option D Explanation:
Unit digit in (4137)754 = Unit digit in {[(4137)4]188 x (4137)2} =Unit digit in { 292915317923361 x 17114769 } = (1 x 9) = 9 |
109. | 587 x 999 = ? | |||||||||||||||
Answer: Option A Explanation:
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110. | A number was divided successively in order by 4, 5 and 6. The remainders were respectively 2, 3 and 4. The number is: | |||||||
Answer: Option A Explanation:
4 | x z = 6 x 1 + 4 = 10 ----------- 5 | y -2 y = 5 x z + 3 = 5 x 10 + 3 = 53 ----------- 6 | z - 3 x = 4 x y + 2 = 4 x 53 + 2 = 214 ----------- | 1 - 4 Hence, required number = 214. |