Question : If a number x is divisible by 8, 12 and 16, and it leaves the remainder of 3 in each case, the possible value of x is:
Option 1: 148
Option 2: 149
Option 3: 150
Option 4: 147
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Correct Answer: 147
Solution : Given: A number x is divisible by 8, 12, and 16. It leaves a remainder of 3 in each case. Taking the LCM of 8, 12 and 16 = ( 2×2×2×3×2) = 48 So, the number x = 48k + 3 (let k be any integer) put k = 3 and then, ⇒ x = (48 × 3) + 3 = 147 Hence, the correct answer is 147.
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Question : A number x, when divided by 289, leaves 18 as the remainder. The same number when divided by 17 leaves y as a remainder. The value of y is:
Option 1: 5
Option 2: 2
Option 3: 7
Option 4: 1
Question : What is the value of x in the number 3426x if the number is divisible by 6 but NOT divisible by 5?
Option 1: 3
Option 2: 4
Option 3: 6
Option 4: 8
Question : What is the least value of $x$ for which the number $712x816$ is divisible by 12?
Option 1: 41
Option 2: 1
Option 3: 0
Option 4: 2
Question : A number when divided by 78 gives the quotient 280 and the remainder 0. If the same number is divided by 65, what will be the value of the remainder?
Option 1: 1
Option 2: 3
Question : If a 10-digit number $620x976y52$ is divisible by 88, then the least value of $(x^2+y^2)$ will be:
Option 1: 8
Option 2: 7
Option 3: 11
Option 4: 10
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