When two numbers are separately divided by 33, the remainders are 21 and 28 respectively. If the sum of the two numbers is divided by 33, the remainder will beOptions10141612
Question
When two numbers are separately divided by 33, the remainders are 21 and 28 respectively. If the sum of the two numbers is divided by 33, the remainder will beOptions10141612
Solution
To solve this problem, we can use the concept of remainders and modular arithmetic.
Let's call the two numbers x and y. We know that when x is divided by 33, the remainder is 21, and when y is divided by 33, the remainder is 28.
Using modular arithmetic, we can express these conditions as equations: x ≡ 21 (mod 33) y ≡ 28 (mod 33)
Now, let's find the sum of x and y: x + y ≡ 21 + 28 (mod 33) x + y ≡ 49 (mod 33)
To find the remainder when the sum of x and y is divided by 33, we need to find the smallest non-negative integer that is congruent to 49 modulo 33.
To do this, we can divide 49 by 33: 49 ÷ 33 = 1 remainder 16
Therefore, the remainder when the sum of x and y is divided by 33 is 16.
So, the correct option is 16.
Similar Questions
When a number is divided by a certain divisor, the remainder is 46. If another number is divided by same divisor, it leaves remainder 31. If the sum of both the numbers is divided by the same divisor, it gives remainder 19. Find divisor
On dividing a certain number by 342, we get 47 as reminder. If the same number is divided by 18, what will be the remainder?Options :A.7B.9C.11D.13
A number when divided by 296 gives a remainder 75. The remainder when the same number is divided by 37 is
NumbersWhen a number is divided by 24, the remainder is 16. The remainder when the same number is divided by 12 isOptions4368
NumbersWhen a number is divided by 357 the remainder is 39. If that number is divided by 17, the remainder will be :Options30511
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.