A number when divided by 21 leaves a remainder 3. When thrice the number is divided by 7, the remainder isa.2b.1c.0d.3
Question
A number when divided by 21 leaves a remainder 3. When thrice the number is divided by 7, the remainder is
a. 2
b. 1
c. 0
d. 3
Solution
Let's denote the number as x.
Step 1: According to the problem, when x is divided by 21, the remainder is 3. This can be written as: x = 21k + 3, where k is the quotient.
Step 2: The problem also states that when thrice the number (3x) is divided by 7, we need to find the remainder. Substituting x from step 1, we get: 3x = 3(21k + 3) = 63k + 9.
Step 3: Now, we need to find the remainder when 63k + 9 is divided by 7. Since 63k is divisible by 7, we only need to consider the remainder when 9 is divided by 7.
Step 4: When 9 is divided by 7, the remainder is 2.
So, the answer is a.2.
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