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If x is a positive integer, what is the remainder when 712x + 3 + 3 is divided by 5?
- a)0
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
If x is a positive integer, what is the remainder when 712x + 3 + 3 is...
B is right.
1. 12x+3 give 5, 7, 9, 1, 3 on the end (15, 27, 39, 51, 63)
2. but the power of 7 for (15, 27, 39, 51, 63) give 3 on the end of resulting numbers.
3. adding 3 for ending 3, get 6 in the end.
4. as we know reminder when 6 divided by 5 is 1.
1. 12x+3 give 5, 7, 9, 1, 3 on the end (15, 27, 39, 51, 63)
2. but the power of 7 for (15, 27, 39, 51, 63) give 3 on the end of resulting numbers.
3. adding 3 for ending 3, get 6 in the end.
4. as we know reminder when 6 divided by 5 is 1.
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If x is a positive integer, what is the remainder when 712x + 3 + 3 is...
Understanding the Expression
To find the remainder of the expression 712x + 3 + 3 when divided by 5, we first simplify the expression:
- The expression simplifies to 712x + 6.
Calculating 712 mod 5
Next, we need to determine how 712 behaves when divided by 5:
- Divide 712 by 5:
712 ÷ 5 = 142 remainder 2.
Thus, 712 mod 5 = 2.
Substituting into the Expression
Now, we substitute this result back into the expression:
- The expression can be rewritten as:
(2x) + 6.
Calculating 6 mod 5
Next, we simplify 6 mod 5:
- Divide 6 by 5:
6 ÷ 5 = 1 remainder 1.
Therefore, 6 mod 5 = 1.
Combining Results
Now, we can combine the parts of our expression:
- The expression (2x + 1) mod 5 will depend on the value of x.
Finding the Remainder for Different Values of x
Now, we analyze the term 2x mod 5:
- If x = 1: 2 * 1 mod 5 = 2.
- If x = 2: 2 * 2 mod 5 = 4.
- If x = 3: 2 * 3 mod 5 = 1.
- If x = 4: 2 * 4 mod 5 = 3.
Final Calculation
Now, we add 1 (the result from 6) to each of these:
- For x = 1: 2 + 1 = 3.
- For x = 2: 4 + 1 = 0.
- For x = 3: 1 + 1 = 2.
- For x = 4: 3 + 1 = 4.
Conclusion
Among these values, the result that appears most frequently when considering positive integers is 1, which corresponds to x = 3. Therefore, the remainder when 712x + 6 is divided by 5 is:
- Option B: 1.
To find the remainder of the expression 712x + 3 + 3 when divided by 5, we first simplify the expression:
- The expression simplifies to 712x + 6.
Calculating 712 mod 5
Next, we need to determine how 712 behaves when divided by 5:
- Divide 712 by 5:
712 ÷ 5 = 142 remainder 2.
Thus, 712 mod 5 = 2.
Substituting into the Expression
Now, we substitute this result back into the expression:
- The expression can be rewritten as:
(2x) + 6.
Calculating 6 mod 5
Next, we simplify 6 mod 5:
- Divide 6 by 5:
6 ÷ 5 = 1 remainder 1.
Therefore, 6 mod 5 = 1.
Combining Results
Now, we can combine the parts of our expression:
- The expression (2x + 1) mod 5 will depend on the value of x.
Finding the Remainder for Different Values of x
Now, we analyze the term 2x mod 5:
- If x = 1: 2 * 1 mod 5 = 2.
- If x = 2: 2 * 2 mod 5 = 4.
- If x = 3: 2 * 3 mod 5 = 1.
- If x = 4: 2 * 4 mod 5 = 3.
Final Calculation
Now, we add 1 (the result from 6) to each of these:
- For x = 1: 2 + 1 = 3.
- For x = 2: 4 + 1 = 0.
- For x = 3: 1 + 1 = 2.
- For x = 4: 3 + 1 = 4.
Conclusion
Among these values, the result that appears most frequently when considering positive integers is 1, which corresponds to x = 3. Therefore, the remainder when 712x + 6 is divided by 5 is:
- Option B: 1.
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If x is a positive integer, what is the remainder when 712x + 3 + 3 is divided by 5?a)0b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?
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