Directions: Each Data Sufficiency problem con...
Directions: Each Data Sufficiency problem consists of a question and two statements labeled (1) and (2), that provide data. Based on the data given plus your knowledge of mathematics and everyday facts, you must decide whether the data are sufficient for answering the question. The five answer choices are the same for every data sufficiency question.
A certain voting bloc has how many voters?
(1) If no additional voters are added to the bloc, and 4 of the current voters leave the bloc, there will be fewer than 20 voters.
(2) If 4 more voters join the bloc and all of the present voters remain, there will be at least 27 voters.
• 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;
• d)
• e)
Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed.
Directions: Each Data Sufficiency problem consists of a question and t...
The correct response is (C).
(1) If no additional voters are added to the bloc, and 4 of the current voters leave the bloc, there will be fewer than 20 voters.
We can translate the given information into an inequality: x – 4 < 20, where “x” is the number of current voters. We know x < 24, but we cannot determine an exact value for x.
(2) If 4 more voters join the bloc and all of the present voters remain, there will be at least 27 voters.
We can translate the given information into an inequality: x + 4 ≥ 27. “At least” means there could be 27 OR more than 27 in the bloc. This inequality simplifies to x ≥ 23. We do not know the exact value of x based on this inequality.
Combining both statements we know 23 ≤ x < 24. If x must be less than 24, but greater or equal to 23, the only number that satisfies both conditions is 23.
If you chose (D), keep in mind that each statement alone only allows us to limit the range of possible values for “x,” but not find the actual numerical value. For a “value” DS question, if more than one number is possible, the statement cannot be sufficient.
If you chose (E), you may not have realized that we could have expressed the information in the statements as inequalities. Both statements combined then allow us to limit the range of possible values to one, so combined they are sufficient.
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