If p/q < 1, and p and q are positive integers, which of the GMAT Problem-Solving

Question: If p/q < 1, and p and q are positive integers, which of the following must be greater than 1?

A. √(p/q)
B. p/q²
C. p²/q
D. q/p²
E. q/p

Answer: E

Solution and Explanation:

Approach Solution 1:
Use the facts in the question to help you answer the current GMAT question. Several areas of mathematics can use these issues. This query relates to algebra. The way the options are presented makes it difficult to decide which is the best. Applicants need to be able to understand the proper strategy for getting the desired result. Only one of the five potential responses is accurate.
Q/p>0, since p and q are both positive integers. To get 1 < q/p, multiply p/q < 1 by q/p.
Conversely, given that this is a must-be-true question, even if we uncover one instance in which one of the options is false, it will mean that this choice is not always true and is, thus, an incorrect response.
Suppose p=2 and q=3.
Correct option: E

Approach Solution 2:
Use the facts in the question to help you answer the current GMAT question. Several areas of mathematics can use these issues. This query relates to algebra. The way the options are presented makes it difficult to decide which is the best. Applicants need to be able to understand the proper strategy for getting the desired result. Only one of the five potential responses is accurate
To resolve this issue, we can use some actual numbers. P/Q is less than 1, as may be seen. As a result, we have a suitable fraction that is positive when q is bigger than p. Assuming p = 1 and q = 4, p/q is 1/4.
We now consider each possible response:
Option A: The value of (p/q) is (1/4) = 12, which is less than 1. Option A is incorrect.
Using Option B, p/q2 is 1/42 = 1/16, which is less than 1. B is the incorrect answer.
Option C: Less than 1 is obtained by p/(2q) = 1/(2 x 4) = 1/8. The answer is not C.
In the case of option D, q/p2 = 4/1 = 4, which is greater than 1. This might be the solution.
q/p = 4/1 = 4, which is more than 1, according to option E. This might be the solution.
For fraction 14, options D and E work.
Let's take p = 3 and q = 4 into consideration as extra numbers for the initial fraction p/q.
Now, the number for option D is q/p2 = 4/32 = 4/9, which is less than 1. As a result, we can now rule out Option D.
The new q/p value for option E is 4/3, which is more than 1. Thus, option E is the right one. In fact, we can see that if p/q is smaller than 1, then its reciprocal, q/p, will always be bigger than 1. This is true regardless of the values of p and q.
Correct option: E

Approach Solution 3:
Use the facts in the question to help you answer the current GMAT question. Several areas of mathematics can use these issues. This query relates to algebra. The way the options are presented makes it difficult to decide which is the best. Applicants need to be able to understand the proper strategy for getting the desired result. Only one of the five potential responses is accurate.
By the question stem, we are aware that 0 p/q 1 and p,q are both positive integers. This means that it is conceivable for the answer to fall anywhere between 0 and 1, but only when the numerator P is less than the denominator Q, or when p q.
As we already know that the smaller the fraction's value, the less we need to examine each choice. Only E is the option that satisfies our criterion because it reduces the denominator rather than increasing it.
Nevertheless, if we test with p = 2 and q = 3, it results in p/q = 2/3 = 0.666. However, if we test with (option E, q/p = 3/2 = 1.5, which is more than 1, then E is the correct answer.
Correct option: E

“If p/q < 1, and p and q are positive integers, which of the" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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