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Find the value of positive integer P that lies between 1 and 30 and is a perfect square.
(1) P has at least one Prime factor
(2) The cube of P is less than 300
- a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
- b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
- c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
- d)EACH statement ALONE is sufficient.
- e)Statements (1) and (2) TOGETHER are NOT sufficient.
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
Find the value of positive integer P that lies between 1 and 30 and is...
Steps 1 & 2: Understand Question and Draw Inferences
Given that P is positive and 1 < P < 30.
It is also given that P is a perfect square.
This means, that P is the square of an integer.
Therefore the possible values of P are 4, 9, 16, and 25.
Step 3: Analyze Statement 1
Given that P has at least one prime factor.
EVERY number greater than 1 has at least one prime factor.
This statement doesn’t help us to eliminate any value out of the four possible values of P.
So statement 1 is not sufficient to arrive at a unique answer.
Step 4: Analyze Statement 2
Given that cube of P is less than 300.
Observe that only 4 satisfies this condition.
43=64
93=729
(Since 93 itself is greater than 300, it is clear that 163 and 253 will also be greater than 300.)
Therefore the only possible value for P is 4.
Statement 2 is sufficient to arrive at a unique answer.
Step 5: Analyze Both Statements Together (if needed)
We arrived at a unique answer in step 4. Hence this step is not required.
Correct Answer: B
Most Upvoted Answer
Find the value of positive integer P that lies between 1 and 30 and is...
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1): P has at least one Prime factor
This statement tells us that P has at least one prime factor. Since a perfect square is a number that can be expressed as the product of two equal integers, we can conclude that P must have at least one prime factor that repeats.
To find a perfect square between 1 and 30, we can list the squares of all the positive integers less than or equal to the square root of 30 (which is approximately 5.5). The perfect squares between 1 and 30 are: 1, 4, 9, 16, and 25.
From this list, we can see that all the perfect squares have at least one prime factor. Therefore, statement (1) alone is sufficient to find the value of P.
Statement (2) ALONE is not sufficient.
Statement (2): The cube of P is less than 300
This statement tells us that the cube of P is less than 300. However, it does not provide any information about the prime factors or whether P is a perfect square.
Let's analyze the possible values of P using statement (2):
- If P is 1, 1^3 = 1, which is less than 300.
- If P is 2, 2^3 = 8, which is less than 300.
- If P is 3, 3^3 = 27, which is less than 300.
- If P is 4, 4^3 = 64, which is less than 300.
- If P is 5, 5^3 = 125, which is less than 300.
- If P is 6, 6^3 = 216, which is less than 300.
From this analysis, we can see that there are multiple possible values of P that satisfy statement (2), and not all of them are perfect squares. Therefore, statement (2) alone is not sufficient to find the value of P.
Conclusion:
Statement (1) alone is sufficient to find the value of P, as all the perfect squares between 1 and 30 have at least one prime factor. However, statement (2) alone is not sufficient, as it does not provide any information about the prime factors or whether P is a perfect square. Therefore, the correct answer is option (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (1): P has at least one Prime factor
This statement tells us that P has at least one prime factor. Since a perfect square is a number that can be expressed as the product of two equal integers, we can conclude that P must have at least one prime factor that repeats.
To find a perfect square between 1 and 30, we can list the squares of all the positive integers less than or equal to the square root of 30 (which is approximately 5.5). The perfect squares between 1 and 30 are: 1, 4, 9, 16, and 25.
From this list, we can see that all the perfect squares have at least one prime factor. Therefore, statement (1) alone is sufficient to find the value of P.
Statement (2) ALONE is not sufficient.
Statement (2): The cube of P is less than 300
This statement tells us that the cube of P is less than 300. However, it does not provide any information about the prime factors or whether P is a perfect square.
Let's analyze the possible values of P using statement (2):
- If P is 1, 1^3 = 1, which is less than 300.
- If P is 2, 2^3 = 8, which is less than 300.
- If P is 3, 3^3 = 27, which is less than 300.
- If P is 4, 4^3 = 64, which is less than 300.
- If P is 5, 5^3 = 125, which is less than 300.
- If P is 6, 6^3 = 216, which is less than 300.
From this analysis, we can see that there are multiple possible values of P that satisfy statement (2), and not all of them are perfect squares. Therefore, statement (2) alone is not sufficient to find the value of P.
Conclusion:
Statement (1) alone is sufficient to find the value of P, as all the perfect squares between 1 and 30 have at least one prime factor. However, statement (2) alone is not sufficient, as it does not provide any information about the prime factors or whether P is a perfect square. Therefore, the correct answer is option (a) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
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Find the value of positive integer P that lies between 1 and 30 and is a perfect square.(1) P has at least one Prime factor(2) The cube of P is less than 300a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'B'. Can you explain this answer?
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ample number of questions to practice Find the value of positive integer P that lies between 1 and 30 and is a perfect square.(1) P has at least one Prime factor(2) The cube of P is less than 300a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.b)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.c)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.d)EACH statement ALONE is sufficient.e)Statements (1) and (2) TOGETHER are NOT sufficient.Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice GMAT tests.
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