Solution
Given:• The equation of a line l, which is 5x + 6y = 90.
To find:• If the point (a, b) lies on the line l or not
Approach and Working: • For (a, b) to lie on the line, l. It must satisfy the equation of the line, l, that is
• Therefore, we can conclude that,
o If 5a + 6b = 90, then the point (a, b) will lie on the line, l
Analysing Statement 1“(a + b - 16) (5a + 6b - 90) = 0”
• The above equation will be equal to zero, if
o a + b - 16 = 0, or
o 5a + 6b - 90 = 0 or both
• From this, we get,
o a + b = 16, or
o 5a + 6b = 90
o From this, we cannot say whether, 5a + 6b = 90, or not. It is only a possible case.
Therefore, Statement (1) ALONE is not sufficient to answer this question
Analysing Statement 2“(b - a - 4) (5a + 6b - 90) = 0”
• The above expression will be equal to zero, if
o b – a - 4 = 0, or
o 5a + 6b - 90 = 0 or both
• From this, we get,
o b - a = 4, or
o 5a + 6b = 90
o From this, we cannot say whether, 5a + 6b = 90, or not. It is only a possible case.
Therefore, Statement (2) ALONE is not sufficient to answer this question
Combining Both Statements• Combining both the statements, we get
o 5a + 6b = 90
o Therefore, (a, b) lie on the line, 5x + 6y = 90
Thus, Statement (1) and (2) TOGETHER are sufficient to answer this question.
Hence, the correct answer is option C.
Answer: C _________________