This data sufficiency problem consists of a q...
This data sufficiency problem consists of a question and two statements, labeled (1) and (2), in which certain data are given. You have to decide whether the data given in the statements are sufficient for answering the question. Using the data given in the statements, plus your knowledge of mathematics and everyday facts (such as the number of days in a leap year or the meaning of the word counterclockwise), you must indicate whether -
Q.
1. (y - 3)(x - 4) = 0
2. (x - 4) = 0
Numbers
All numbers used are real numbers.
• a)
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
• b)
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question asked.
• c)
BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked.
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data specific to the problem are needed.

### Related Test

 DHANSHRI WANKHEDE Aug 10, 2019
Step 1
Understand the Question Stem
What kind of an answer will this GMAT DS question fetch?
The question is an "Is" question. Answer to an "is" questions is either YES or NO.
When is the data sufficient?
The data is sufficient if we are able to get a DEFINITE YES or a DEFINITE NO from the information given in the statements.
Do we have any additional information about 'y' from the question stem?
There is no additional data available about 'y' in the question stem.
Step 2 of solving this GMAT system of equations question:
Evaluate Statement (1) ALONE: (y - 3)(x - 4) = 0
If product of the two terms (y - 3) and (x - 4) is 0, then at least one of the two terms equals 0.
(y - 3) = 0 or (x - 4) = 0 or both (y - 3) and (x - 4) equal 0.
i.e., either y = 3 or x = 4 or that both y = 3 and x = 4.
If x = 4, y could take any value. The value of 'y' could be 3 or it could be some other value and the product will still be a 0.
Example: x = 4 and y = 5. The equation holds good. y ≠ 3.
Counter example: x = 4 and y = 3. The equation holds good. y = 3
We CANNOT determine whether 'y' is 3 from this statement.
Statement 1 ALONE is NOT sufficient.
Eliminate choices A and D. Choices narrow down to B, C or E.
Step 3 of solving this GMAT algebra DS question:
Evaluate Statement (2) ALONE: (x - 4) = 0
The statement provides no information about y.
Statement 2 ALONE is NOT sufficient.
Eliminate choice B. Choices narrow down to C or E.
Step 4 of solving this GMAT DS question:
Evaluate Statements (1) & (2) Together: (y - 3)(x - 4) = 0 & (x - 4) = 0
When x = 4, (y - 3)(x - 4) will be 0 irrespective of the value that y takes.
Can 'y' be 3? Yes 'y' can be 3.
Is y = 3? Not necessary.It can take values other than 3 and the data in the two statements will still hold good.
Eliminate choice C.
Statements TOGETHER are NOT sufficient. Choice E is the answer.

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