Question : When positive numbers a,b, and c are divided by 13, the remainder are 9, 7, and 10, respectively. What will be the remainder when (a + 2b + 5c) is divided by 13?
Option 1: 8
Option 2: 9
Option 3: 5
Option 4: 10
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Correct Answer: 8
Solution : Let the quotient be 1. a = 13 × 1 + 9 = 22 b = 13 × 1 + 7 = 20 c = 13 × 1 + 10 = 23 Now, putting the values, we get: a + 2b + 5c = 22 + 2 × 20 + 5 × 23 = 22 + 40 + 115 = 177 Remainder = $\frac{177}{13}$ = 8 Hence, the correct answer is 8.
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Question : M is the largest 4-digit number which, when divided by 4, 5, 6, and 7, leaves the remainder as 2, 3, 4, and 5, respectively. What will be the remainder when M is divided by 9?
Question : If A : B = 2 : 3 and B : C = 3 : 7, then (A + B) : (B + C) : (C + A) is:
Question : Let $x$ be the least number which, when divided by 5, 6, 7, and 8, leaves a remainder of 3 in each case, but when divided by 9, leaves no remainder. The sum of the digits of $x$ is:
Question : When m is divided by 7, the remainder is 5. When 3m is divided by 7, the remainder is:
Question : On dividing a certain number by 363, we get 17 as the remainder. What will be the remainder when the same number is divided by 11?
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