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Is the x-intercept of y = ax + b greater than 0?
(1) ab < 0
(2) a + b < 0
(2) a + b < 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)EACH statement ALONE is sufficient to answer the question asked
- e)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed
Correct answer is option 'A'. Can you explain this answer?
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Is the x-intercept of y = ax + b greater than 0?(1) ab < 0(2) a + b...
Statement (1) states that ab < 0. This means that the product of a and b is negative. If the product of a and b is negative, it implies that a and b have opposite signs. When the x-intercept of a line is greater than 0, it means that the line crosses the x-axis to the right of the origin. Given that a and b have opposite signs, it indicates that the line y = ax + b crosses the x-axis to the right of the origin. Therefore, statement (1) alone is sufficient to answer the question.
Statement (2) tells us that a + b < 0. This statement provides a relationship between the sum of a and b and 0, but it doesn't give us direct information about the x-intercept or its position. Knowing that a + b is less than 0 doesn't provide conclusive information about the position of the x-intercept. Therefore, statement (2) alone is not sufficient to answer the question.
Considering both statements together, we have the information that ab < 0 from statement (1) and a + b < 0 from statement (2). From this combined information, we can deduce that a and b have opposite signs and their sum is negative. This indicates that the line y = ax + b crosses the x-axis to the right of the origin, and thus, the x-intercept is greater than 0. Therefore, together, the statements are sufficient to answer the question.
Hence, the answer is A: Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked.
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Is the x-intercept of y = ax + b greater than 0?(1) ab < 0(2) a + b < 0a)Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question askedb)Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient to answer the question askedc)BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficientd)EACH statement ALONE is sufficient to answer the question askede)Statements (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are neededCorrect answer is option 'A'. Can you explain this answer?
Question Description
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