If J≠0, What Is The Value Of J? GMAT Data Sufficiency

Question: If J≠0, what is the value of J ?

1. |J| = J^(-1)
2.  J^J = 1

1. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
2. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
3. BOTH statement TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
4. EACH statement ALONE is sufficient.
5. Statements (1) and (2) TOGETHER are NOT sufficient.

“If J≠0, What Is The Value Of J? GMAT Data Sufficiency”- is a topic of the GMAT Quantitative reasoning section of GMAT. GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. This question has been taken from the book "GMAT Quantitative Review". GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Solution and Explanation:

Approach Solution 1:

Explanation: Given to us that J ≠ 0. It has given two options
(1) |J| = J^(-1)
(2) J^J = 1
It is asking what could be the value of j. This is a data sufficiency problem.
It should be noted that it is important to state that J ≠ 0 because in condition
1/0 could not be defined. Also in case 2, 0 could not be raised to the power 0.
Some sources might say that 0^0 is 1 but it is not considered to be not defined by mathematicians.
It is given in the question that J ≠ 0, so we do not have to handle that case.
In the first condition it says that
|J| = \(J^{-1}\)

=> |J| = \(\frac{1}{J}\)

=> |J| * J = 1

Here the value of j can be 1 only. Taking j = -1
The value of LHS will be -1
J cannot be a negative number as modulus is always positive, so the product of negative and positive will not give a positive number.
Therefore the only value of J can be 1
Hence this condition is sufficient to answer the question.
Given in condition 2,

\(J^J\) = 1

=> J = \(1^\frac{1}{J}\)

=> J = 1 ( it is known that 1 raised to the power any number is always 1)

Here we get J = 1
Hence this condition is sufficient to answer the question.

Correct Answer: D

Approach Solution 2:

Explanation: Given to us that J ≠ 0. It has given two options
(1) |J| = J^(-1)
(2) J^J = 1

It is asking what could be the value of J.
Given in statement 1,
|J| = J^(-1)

|J| = \(\frac{1}{J}\) – (1)
It should be noted that the question it has not mentioned that J is positive or negative. So J can take any values.
But the condition 1 states that J is positive.
Looking at the equation 1,

|J| is always positive, So RHS has to be positive and hence J is positive.
Therefor |J| should not be taken as – J
|J| =\(\frac{1}{J}\)

=> |J| * J = 1

J = 1
In the second condition,

\(J^J\)= 1
=> J = 1
Both the statements are self-sufficient to find the value of J.

Correct Answer: D

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