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 number is not an integer. Is the number less than .4?
(1) The number rounded to the nearest tenth is .4.
(2) The number rounded to the nearest integer is 0.
• 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...
If you chose (A), we know the “nearest” tenth is .4, so this means the number is between .35 and .45. If it were smaller than .35 (for example, .34), we would round down to .3, and if it were greater than .45 (for example, .47), we would round up to .5. Since .4 is between .35 and .45, we can’t tell if the value of the number is less than or greater than (or equal to) .4.
If you chose (B), we know the “nearest” integer is 0, so the number must be between -0.5 and .5. While most of the values in this range are less than .4, the values between .4 and .5 are greater than .4.
If you chose (C), remember we can express the information from the first statement as an inequality: .35 ≤ x < .45. And we can express the information from the second statement as an inequality: -0.5 < x < .5. Since the range of values for the first inequality is within the range of the second inequality, the range of values that satisfy both inequalities will be the same as the range of values in the first inequality (.35 ≤ x < .45). Since we already determined that the first inequality is not sufficient, combining both inequalities will not be sufficient.
If you chose (D), you may have missed the possible values between .4 and .45 in Statement 1, and the range of possible values between .4 and .5 in Statement 2.
(E) is the correct response. Even combined, we get a range between .35 and .45. There are values that are possible both above and below (and equal to) .4.
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