GMAT Math : DSQ: Graphing complex numbers

Study concepts, example questions & explanations for GMAT Math

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Example Question #651 : Data Sufficiency Questions

Let  and  be real numbers. 

From the number , subtract its complex conjugate. What is the result?

Statement 1: 

Statement 2: 

Possible Answers:

EITHER statement ALONE is sufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question. 

Correct answer:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Explanation:

The complex conjugate of an imaginary number  is , and

.

Therefore, it is necessary and sufficient to know  in order to answer the question. Neither statement alone gives this information. However, the two statements together form a linear system that can be solved as follows:

    

             

We need go no further; since , the desired sum is .

Example Question #2762 : Gmat Quantitative Reasoning

Let  be a positive integer.

Evaluate .

Statement 1:  is a multiple of 3.

Statement 2:  is a multiple of 7.

Possible Answers:

BOTH statements TOGETHER are sufficient to answer the question, but NEITHER statement ALONE is sufficient to answer the question.

Statement 1 ALONE is sufficient to answer the question, but Statement 2 ALONE is NOT sufficient to answer the question.

EITHER statement ALONE is sufficient to answer the question.

BOTH statements TOGETHER are insufficient to answer the question.

Statement 2 ALONE is sufficient to answer the question, but Statement 1 ALONE is NOT sufficient to answer the question.

Correct answer:

BOTH statements TOGETHER are insufficient to answer the question.

Explanation:

Assume that both statements are true. The value of  a positive integer, is equal to , where  is the remainder of the division of  by 4, so we can use this fact to show that insufficient information is provided. 

Case 1: .

, so 

Case 2: .

, so 

In both cases, both statements are true, but the value of  differs.

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