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x, y, z, w are four odd natural numbers. Let u=x2+y2+z2+w2. Consider following statements
I. U is always divisible by 4
II. U is never divisible by 8
II. U is never divisible by 8
Q. Which of the above statements) is /are true?
- a)Only I
- b)Only II
- c)Both I and II
- d)Neither I nor II
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
x, y, z, w are four odd natural numbers. Letu=x2+y2+z2+w2. Consider fo...
Statement Analysis:
We are given four odd natural numbers x, y, z, w. We need to consider the value of u = x^2 * y^2 * z^2 * w^2 and determine whether the following statements are true or false:
I. U is always divisible by 4.
II. U is never divisible by 8.
Solution:
Statement I: U is always divisible by 4.
In order to determine whether U is always divisible by 4, we need to consider the possible remainders when dividing an odd natural number by 4.
When an odd natural number is divided by 4, it leaves a remainder of either 1 or 3.
Case 1: If all the four odd numbers (x, y, z, w) leave a remainder of 1 when divided by 4, then u = (1^2) * (1^2) * (1^2) * (1^2) = 1, which is divisible by 4.
Case 2: If exactly three out of the four odd numbers (x, y, z, w) leave a remainder of 1 when divided by 4, and the remaining number leaves a remainder of 3 when divided by 4, then u = (1^2) * (1^2) * (1^2) * (3^2) = 9, which is divisible by 4.
Case 3: If exactly two out of the four odd numbers (x, y, z, w) leave a remainder of 1 when divided by 4, and the remaining two numbers leave a remainder of 3 when divided by 4, then u = (1^2) * (1^2) * (3^2) * (3^2) = 81, which is divisible by 4.
Case 4: If exactly one out of the four odd numbers (x, y, z, w) leaves a remainder of 1 when divided by 4, and the remaining three numbers leave a remainder of 3 when divided by 4, then u = (1^2) * (3^2) * (3^2) * (3^2) = 243, which is divisible by 4.
Conclusion: In all possible cases, U is divisible by 4. Therefore, statement I is true.
Statement II: U is never divisible by 8.
In order to determine whether U is divisible by 8, we need to consider the possible remainders when dividing an odd natural number by 8.
When an odd natural number is divided by 8, it leaves a remainder of either 1 or 3 or 5 or 7.
Case 1: If all the four odd numbers (x, y, z, w) leave a remainder of 1 when divided by 8, then u = (1^2) * (1^2) * (1^2) * (1^2) = 1, which is not divisible by 8.
Case 2: If exactly three out of the four odd numbers (x, y, z, w) leave a remainder
We are given four odd natural numbers x, y, z, w. We need to consider the value of u = x^2 * y^2 * z^2 * w^2 and determine whether the following statements are true or false:
I. U is always divisible by 4.
II. U is never divisible by 8.
Solution:
Statement I: U is always divisible by 4.
In order to determine whether U is always divisible by 4, we need to consider the possible remainders when dividing an odd natural number by 4.
When an odd natural number is divided by 4, it leaves a remainder of either 1 or 3.
Case 1: If all the four odd numbers (x, y, z, w) leave a remainder of 1 when divided by 4, then u = (1^2) * (1^2) * (1^2) * (1^2) = 1, which is divisible by 4.
Case 2: If exactly three out of the four odd numbers (x, y, z, w) leave a remainder of 1 when divided by 4, and the remaining number leaves a remainder of 3 when divided by 4, then u = (1^2) * (1^2) * (1^2) * (3^2) = 9, which is divisible by 4.
Case 3: If exactly two out of the four odd numbers (x, y, z, w) leave a remainder of 1 when divided by 4, and the remaining two numbers leave a remainder of 3 when divided by 4, then u = (1^2) * (1^2) * (3^2) * (3^2) = 81, which is divisible by 4.
Case 4: If exactly one out of the four odd numbers (x, y, z, w) leaves a remainder of 1 when divided by 4, and the remaining three numbers leave a remainder of 3 when divided by 4, then u = (1^2) * (3^2) * (3^2) * (3^2) = 243, which is divisible by 4.
Conclusion: In all possible cases, U is divisible by 4. Therefore, statement I is true.
Statement II: U is never divisible by 8.
In order to determine whether U is divisible by 8, we need to consider the possible remainders when dividing an odd natural number by 8.
When an odd natural number is divided by 8, it leaves a remainder of either 1 or 3 or 5 or 7.
Case 1: If all the four odd numbers (x, y, z, w) leave a remainder of 1 when divided by 8, then u = (1^2) * (1^2) * (1^2) * (1^2) = 1, which is not divisible by 8.
Case 2: If exactly three out of the four odd numbers (x, y, z, w) leave a remainder
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x, y, z, w are four odd natural numbers. Letu=x2+y2+z2+w2. Consider fo...
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x, y, z, w are four odd natural numbers. Letu=x2+y2+z2+w2. Consider following statementsI. U is always divisible by 4II. U is never divisible by 8Q. Which of the above statements) is /are true?a)Only I b)Only IIc)Both I and II d)Neither I nor IICorrect answer is option 'A'. Can you explain this answer?
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x, y, z, w are four odd natural numbers. Letu=x2+y2+z2+w2. Consider following statementsI. U is always divisible by 4II. U is never divisible by 8Q. Which of the above statements) is /are true?a)Only I b)Only IIc)Both I and II d)Neither I nor IICorrect answer is option 'A'. Can you explain this answer? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about x, y, z, w are four odd natural numbers. Letu=x2+y2+z2+w2. Consider following statementsI. U is always divisible by 4II. U is never divisible by 8Q. Which of the above statements) is /are true?a)Only I b)Only IIc)Both I and II d)Neither I nor IICorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for x, y, z, w are four odd natural numbers. Letu=x2+y2+z2+w2. Consider following statementsI. U is always divisible by 4II. U is never divisible by 8Q. Which of the above statements) is /are true?a)Only I b)Only IIc)Both I and II d)Neither I nor IICorrect answer is option 'A'. Can you explain this answer?.
x, y, z, w are four odd natural numbers. Letu=x2+y2+z2+w2. Consider following statementsI. U is always divisible by 4II. U is never divisible by 8Q. Which of the above statements) is /are true?a)Only I b)Only IIc)Both I and II d)Neither I nor IICorrect answer is option 'A'. Can you explain this answer? for Class 5 2024 is part of Class 5 preparation. The Question and answers have been prepared according to the Class 5 exam syllabus. Information about x, y, z, w are four odd natural numbers. Letu=x2+y2+z2+w2. Consider following statementsI. U is always divisible by 4II. U is never divisible by 8Q. Which of the above statements) is /are true?a)Only I b)Only IIc)Both I and II d)Neither I nor IICorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 5 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for x, y, z, w are four odd natural numbers. Letu=x2+y2+z2+w2. Consider following statementsI. U is always divisible by 4II. U is never divisible by 8Q. Which of the above statements) is /are true?a)Only I b)Only IIc)Both I and II d)Neither I nor IICorrect answer is option 'A'. Can you explain this answer?.
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