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If y is an integer, is y3 divisible by 9?
1) y is divisible by 4
2) y is divisible by 6.
1) y is divisible by 4
2) y is divisible by 6.
- 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 'B'. Can you explain this answer?
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Verified Answer
If y is an integer, is y3 divisible by 9?1) y is divisible by 42) y is...
(1) Take multiples of 4 and 9 and the answer is yes, but say for numbers that are only multiples of 4, the answer is No
(2) is sufficient because y is divisible by 6 means that y has 3 as factor, hence y^3 will have 3^3 as factor
=> y^3 is divisible by 9.
Most Upvoted Answer
If y is an integer, is y3 divisible by 9?1) y is divisible by 42) y is...
Solution:
We need to determine whether y^3 is divisible by 9 or not.
We know that 9 = 3^2. So, for a number to be divisible by 9, it must be divisible by 3^2.
Let's evaluate the given statements.
Statement 1: y is divisible by 4
4 = 2^2. So, if y is divisible by 4, it must also be divisible by 2^2.
Let's consider some values of y to see whether y^3 is divisible by 9 or not.
If y = 4, then y^3 = 64, which is not divisible by 9.
If y = 8, then y^3 = 512, which is not divisible by 9.
If y = 12, then y^3 = 1728, which is divisible by 9.
From the above values, we can see that statement 1 alone is not sufficient to answer the question.
Statement 2: y is divisible by 6
6 = 2 x 3. So, if y is divisible by 6, it must also be divisible by both 2 and 3.
Let's consider some values of y to see whether y^3 is divisible by 9 or not.
If y = 6, then y^3 = 216, which is divisible by 9.
If y = 12, then y^3 = 1728, which is divisible by 9.
If y = 18, then y^3 = 5832, which is divisible by 9.
From the above values, we can see that statement 2 alone is sufficient to answer the question.
Combining both statements, we know that y is divisible by 4 and 6. This means y must be divisible by 2^2 and 2 x 3. So, y must be divisible by 3 and hence, y^3 must be divisible by 3^2 = 9.
Therefore, both statements together are required to answer the question.
Hence, the correct answer is option (B).
We need to determine whether y^3 is divisible by 9 or not.
We know that 9 = 3^2. So, for a number to be divisible by 9, it must be divisible by 3^2.
Let's evaluate the given statements.
Statement 1: y is divisible by 4
4 = 2^2. So, if y is divisible by 4, it must also be divisible by 2^2.
Let's consider some values of y to see whether y^3 is divisible by 9 or not.
If y = 4, then y^3 = 64, which is not divisible by 9.
If y = 8, then y^3 = 512, which is not divisible by 9.
If y = 12, then y^3 = 1728, which is divisible by 9.
From the above values, we can see that statement 1 alone is not sufficient to answer the question.
Statement 2: y is divisible by 6
6 = 2 x 3. So, if y is divisible by 6, it must also be divisible by both 2 and 3.
Let's consider some values of y to see whether y^3 is divisible by 9 or not.
If y = 6, then y^3 = 216, which is divisible by 9.
If y = 12, then y^3 = 1728, which is divisible by 9.
If y = 18, then y^3 = 5832, which is divisible by 9.
From the above values, we can see that statement 2 alone is sufficient to answer the question.
Combining both statements, we know that y is divisible by 4 and 6. This means y must be divisible by 2^2 and 2 x 3. So, y must be divisible by 3 and hence, y^3 must be divisible by 3^2 = 9.
Therefore, both statements together are required to answer the question.
Hence, the correct answer is option (B).
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If y is an integer, is y3 divisible by 9?1) y is divisible by 42) y is...
Exactly one statement is enough i.e., y is divisible by 6
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If y is an integer, is y3 divisible by 9?1) y is divisible by 42) y is divisible by 6. a)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 'B'. Can you explain this answer?
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