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When a number is divided by 114, remainder is 82. What will be the remainder when the cube of the number is divided by 19?
- a)17
- b)7
- c)5
- d)13
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
When a number is divided by 114, remainder is 82. What will be the rem...
GIVEN:
When a number is divided by 114, remainder is 82.
When a number is divided by 114, remainder is 82.
CALCULATION:
114)N( x
82 ← remainder
N = 114 × x + 82
When cube is divided = ((114x + 82)³)/19
When, 114 is divided by 19, remainder = 0
When 82 is divided by 19, remainder = 6
Now, 6³/19 = 7 remainder
114)N( x
82 ← remainder
N = 114 × x + 82
When cube is divided = ((114x + 82)³)/19
When, 114 is divided by 19, remainder = 0
When 82 is divided by 19, remainder = 6
Now, 6³/19 = 7 remainder
Most Upvoted Answer
When a number is divided by 114, remainder is 82. What will be the rem...
Given:
- When a number is divided by 114, the remainder is 82.
To find:
- The remainder when the cube of the number is divided by 19.
Explanation:
Let's assume the number is 'x'. According to the given information, we have:
- x ≡ 82 (mod 114)
To find the remainder when the cube of the number is divided by 19, we need to find:
- x^3 ≡ ? (mod 19)
Using Modular Arithmetic:
We can use modular arithmetic to simplify the equation and find the remainder.
Step 1: Simplify the given congruence relation:
- x ≡ 82 (mod 114)
Step 2: Rewrite the congruence relation in terms of a smaller modulus:
- x ≡ 82 (mod 19)
- 114 is congruent to 1 (mod 19) since 114 = (6 * 19) + 0 ≡ 0 (mod 19)
Step 3: Substitute the congruence relation in terms of the smaller modulus into the equation we need to solve:
- x^3 ≡ 82^3 (mod 19)
Step 4: Simplify the equation:
- Since 82 ≡ 4 (mod 19), we have:
- x^3 ≡ 4^3 (mod 19)
- x^3 ≡ 64 (mod 19)
Step 5: Reduce the modulus:
- 64 ≡ 7 (mod 19)
Step 6: Substitute the reduced modulus back into the equation:
- x^3 ≡ 7 (mod 19)
Step 7: Therefore, the remainder when the cube of the number is divided by 19 is 7.
Answer:
The remainder when the cube of the number is divided by 19 is 7. Therefore, the correct option is (b).
- When a number is divided by 114, the remainder is 82.
To find:
- The remainder when the cube of the number is divided by 19.
Explanation:
Let's assume the number is 'x'. According to the given information, we have:
- x ≡ 82 (mod 114)
To find the remainder when the cube of the number is divided by 19, we need to find:
- x^3 ≡ ? (mod 19)
Using Modular Arithmetic:
We can use modular arithmetic to simplify the equation and find the remainder.
Step 1: Simplify the given congruence relation:
- x ≡ 82 (mod 114)
Step 2: Rewrite the congruence relation in terms of a smaller modulus:
- x ≡ 82 (mod 19)
- 114 is congruent to 1 (mod 19) since 114 = (6 * 19) + 0 ≡ 0 (mod 19)
Step 3: Substitute the congruence relation in terms of the smaller modulus into the equation we need to solve:
- x^3 ≡ 82^3 (mod 19)
Step 4: Simplify the equation:
- Since 82 ≡ 4 (mod 19), we have:
- x^3 ≡ 4^3 (mod 19)
- x^3 ≡ 64 (mod 19)
Step 5: Reduce the modulus:
- 64 ≡ 7 (mod 19)
Step 6: Substitute the reduced modulus back into the equation:
- x^3 ≡ 7 (mod 19)
Step 7: Therefore, the remainder when the cube of the number is divided by 19 is 7.
Answer:
The remainder when the cube of the number is divided by 19 is 7. Therefore, the correct option is (b).
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Community Answer
When a number is divided by 114, remainder is 82. What will be the rem...
GIVEN:
When a number is divided by 114, remainder is 82.
When a number is divided by 114, remainder is 82.
CALCULATION:
114)N( x
82 ← remainder
N = 114 × x + 82
When cube is divided = ((114x + 82)³)/19
When, 114 is divided by 19, remainder = 0
When 82 is divided by 19, remainder = 6
Now, 6³/19 = 7 remainder
114)N( x
82 ← remainder
N = 114 × x + 82
When cube is divided = ((114x + 82)³)/19
When, 114 is divided by 19, remainder = 0
When 82 is divided by 19, remainder = 6
Now, 6³/19 = 7 remainder
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When a number is divided by 114, remainder is 82. What will be the remainder when the cube of the number is divided by 19?a)17b)7c)5d)13Correct answer is option 'B'. Can you explain this answer?
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