Question: If non-zero x is the reciprocal of y, then which of the following may be true?

A. x/(1/y) = 0.5
B. (1/x)/y = 2
C. (1/y)/x = 0.5
D. (1/x)/(1/y) = 0.5
E. y/(1/x) = 2

Answer: D

Solution and Explanation:

Approach Solution 1:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with algebra. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Given to us that x = 1/y
Xy = 1
x*(1/y) = 0.5 (it is false)
(1/x)/y = 1/xy = 1/1 = 1 (not equal to 2) False
(1/y)/x = 1/xy = 1/1 = 1 (not equal to 0.5) False
(1/x) / (1/y) = y/x = 1/x² (it can be equal to 0.5)
y/(1/x) = xy = x*1/x = 1 (not equal to 2)
Hence,
Correct option: D

Approach Solution 2:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with algebra. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
First off, this is a hypothetical that might be accurate:
The formula x=1/y or xy=1 is provided to us.
Let's attempt to determine the value of xy in each of the following options:
x/(1/y) = x * y = xy = 0.5, not 1, is the answer. Thus, false.
(1/x)/y = (1/x * 1/y)/(1/x) = (1/xy)/(1/y), where xy = 0.5 and not 1. Again, untrue!
(1/y)/x = 1/y * 1/x = 1/xy = 0.5, where xy = 1/0.5 = 2 and therefore not 1. Again, untrue
If we are unable to determine the value of xy, (1/x)/(1/y) = 1/x * y = y/x = 0.5, this may be the case.
The result y/(1/x) = xy = 2 is not 1. So false!
about selections 1, 2, 3, and 5. We can demonstrate that xy's value is not equal to 1.
We cannot, however, establish or refute the statement that xy = 1. Well, this might be accurate!
Correct option: D

Approach Solution 3:
Apply the information in the question to the GMAT question at hand. These problems apply to numerous disciplines of mathematics. This question has to do with algebra. It is challenging to select the best option because of the way the options are presented. Candidates must be able to comprehend the appropriate approach to eliciting the desired response. Out of the five possible answers, there is only one that is correct.
Take note that the question states which of the following Might be true, not which of the following MUST be true.
If x is y's reciprocal, then x=1/y (y=1/x). Now change 1/x or 1/y in the options to:
x/(1/y) = 0.5 --> x/x = 0.5 --> 1 = 0.5 - INACCURATE.
WRONG: (1/x)/y = 2; y/y = 2; 1 = 2.
FALSE: (1/y)/x = 0.5, x/x = 0.5, 1 = 0.5.
(1/x)/(1/y) = 0.5; (1/x)/x = 1/2 —> 1/x² = 1/2 —> x² = 2. Well, if x= 2x =2 or x = -2x = -2, this is feasible.
y/(1/x) = 2 —> y/y = 2 --> 1 = 2 is incorrect.
Correct option: D

“If non-zero x is the reciprocal of y, then which of the following may" - 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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