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Is integer y divisible by 16?
1) y2 is divisible by 16
2) y3 is divisible by 16
- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
Is integer y divisible by 16?1) y2 is divisible by 162) y3 is divisibl...
Answer: D
Explanation:
To determine if integer y is divisible by 16, we need to know if y is a multiple of 16.
Statement 1: y^2 is divisible by 16
- If y^2 is divisible by 16, it means that y is a multiple of 4. However, this does not necessarily mean that y is a multiple of 16. For example, y could be 4, 8, or 12, all of which satisfy statement 1 but are not divisible by 16. Therefore, statement 1 alone is insufficient to answer the question.
Statement 2: y^3 is divisible by 16
- If y^3 is divisible by 16, it means that y is a multiple of 2 and a multiple of 4. However, this still does not guarantee that y is a multiple of 16. For example, y could be 8, which satisfies statement 2 but is not divisible by 16. Therefore, statement 2 alone is also insufficient to answer the question.
Combining both statements:
- From statement 1, we know that y is a multiple of 4. From statement 2, we know that y is a multiple of 2 and a multiple of 4. Therefore, y must be a multiple of 8. However, this still does not guarantee that y is a multiple of 16. For example, y could be 8, 16, 24, or any multiple of 8, all of which satisfy both statements but only some of which are divisible by 16. Therefore, even when both statements are considered together, we cannot determine if y is divisible by 16. Hence, more information is required to answer the question.
Therefore, the correct answer is option D - more information is required as the information provided is insufficient to answer the question.
Explanation:
To determine if integer y is divisible by 16, we need to know if y is a multiple of 16.
Statement 1: y^2 is divisible by 16
- If y^2 is divisible by 16, it means that y is a multiple of 4. However, this does not necessarily mean that y is a multiple of 16. For example, y could be 4, 8, or 12, all of which satisfy statement 1 but are not divisible by 16. Therefore, statement 1 alone is insufficient to answer the question.
Statement 2: y^3 is divisible by 16
- If y^3 is divisible by 16, it means that y is a multiple of 2 and a multiple of 4. However, this still does not guarantee that y is a multiple of 16. For example, y could be 8, which satisfies statement 2 but is not divisible by 16. Therefore, statement 2 alone is also insufficient to answer the question.
Combining both statements:
- From statement 1, we know that y is a multiple of 4. From statement 2, we know that y is a multiple of 2 and a multiple of 4. Therefore, y must be a multiple of 8. However, this still does not guarantee that y is a multiple of 16. For example, y could be 8, 16, 24, or any multiple of 8, all of which satisfy both statements but only some of which are divisible by 16. Therefore, even when both statements are considered together, we cannot determine if y is divisible by 16. Hence, more information is required to answer the question.
Therefore, the correct answer is option D - more information is required as the information provided is insufficient to answer the question.
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Community Answer
Is integer y divisible by 16?1) y2 is divisible by 162) y3 is divisibl...
- To determine if integer y is divisible by 16, let's analyze each statement.
- Statement 1: y2 is divisible by 16.
- This means that y2 = 16k for some integer k. If y is divisible by 4, then y2 would indeed be divisible by 16. However, this does not guarantee that y itself is divisible by 16. For example, if y = 4, then y2 = 16, but y is not divisible by 16. So, this statement alone is not sufficient.
- Statement 2: y3 is divisible by 16.
- This means that y3 = 16m for some integer m. If y is divisible by 2, then y3 could be divisible by 16. However, this also does not guarantee that y itself is divisible by 16. For example, if y = 2, then y3 = 8 which is not divisible by 16. Thus, this statement alone is not sufficient.
- Combining Statements 1 and 2:
- With both statements, we know:
- y2 is divisible by 16 (from Statement 1).
- y3 is divisible by 16 (from Statement 2).
- Even with both statements combined, y could be 4 (not divisible by 16) or 16 (divisible by 16). Therefore, we cannot conclusively determine if y is divisible by 16.
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Is integer y divisible by 16?1) y2 is divisible by 162) y3 is divisible by 16a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'D'. Can you explain this answer?
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