Quantitative Aptitude for CAT/XAT/CSAT/SSC CGL/GATE/GRE-2021

1. Is |p+2| > |q-2|

Statement (1): ‘p’ is an even prime number. This is not possible since all prime numbers are odd. An even prime number does not exist as the definition of a prime number requires it to be divisible only by 1 and itself, whereas an even number is divisible by 2. Therefore, statement (1) alone cannot answer the question.

Statement (2): ‘q’ is a highest common factor of 4 and 6. The highest common factor (HCF) of two numbers is the largest positive integer that divides both numbers without leaving a remainder. The HCF of 4 and 6 is 2. Absolute values are always non-negative, so |p+2| and |q-2| would be the same or different based on what p and q are. Without knowing the values of p and q, we cannot determine if |p+2| is greater than |q-2|. Therefore, statement (2) alone is not sufficient to answer the question.

The correct answer is: E. Statement (1) & (2) together are not sufficient to answer the question.

2. Is P > 2?

Statement 1: |p + 1| < 3. This means that the value of p is within -2 to 4, inclusive. However, for p to be greater than 2, p must be in the range from 3 to 4 (since -2 to 2 includes the boundary point 0 and 2 but not 3). Therefore, statement (1) alone is insufficient because p could be 3 or 4, which would satisfy the condition but not necessarily be greater than 2.

Statement 2: |p – 1| < 3. Similarly, this means that p is within -2 to 4, inclusive. Again, for p to be greater than 2, it must be in the range from 3 to 4. This statement also does not provide enough information because p could be 3 or 4.

Combining both statements provides no additional information because both scenarios where p is 3 or 4 satisfy both conditions. Therefore, neither statement alone, nor both statements together, are sufficient to determine if P > 2.

The correct answer is: D. Neither statement alone, nor both statements together, provide a sufficient answer.

3. P = HCF of 4 and 6

Since the highest common factor (HCF) of 4 and 6 is 2, the absolute value of their difference will always be 2, regardless of the signs of 4 and 6. So |4-6| = |-2| = 2, and |6-4| = |2| = 2. Therefore, p (which represents the HCF) is indeed 2.

The correct answer to the question is: P = 2.

4. P = q = 2 in this context

Both statements given for the first question are incorrect in terms of their original contexts, but when considering the absolute values of expressions involving p and q as HCFs, both statements become correct for the context of the second question. This is a classic example of misleading information.

The correct answers for the options provided for the second question are:

• Statement (1): Incorrect, as 'p' cannot be an even prime number.
• Statement (2): Correct, as 'q' is the HCF of 4 and 6, which is indeed 2.

5. p < q or p = q or p > q

Since we have determined that p and q are both equal to 2, none of the relationships p < q, p = q, or p > q holds true for their values in this context. However, if we consider the original statements, 'p' cannot be less than 'q' because they are both equal to 2, and they cannot be greater than each other either since they are equal.

The correct answer for the fifth question is: D. Relationship cannot be determined (based on the original context of the statements). However, based on the context where p and q are HCFs, both are equal to 2, so there is no relationship between them in this specific scenario.

I hope this clarifies the solutions to the questions and provides insight into why the given options are correct or incorrect. If you have any more doubts or questions, feel free to ask!

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