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13 Jun 2019, 00:24
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
69% (02:06) correct
31%
(02:16)
wrong
based on 195
sessions
History
Date
Time
Result
Not Attempted Yet
2ax + 5y = 17
4x + 6by = 11
In the x-y plane, the above two straight lines, intersect at the point (3, c). Find the value of a+b?
(1) c = 3
(2) The y-intercept of 2ax + 5y = 17 is 3.4
4x + 6by = 11
In the x-y plane, the above two straight lines, intersect at the point (3, c). Find the value of a+b?
(1) c = 3
(2) The y-intercept of 2ax + 5y = 17 is 3.4
13 Jun 2019, 10:59
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2ax + 5y = 17
4x + 6by = 11
intersect at the point (3, c)
Put x = 3 and y = c in both the equations.
6x+5c = 17
12+6bc = 11
From S1:
c = 3
Then, 6x+15 = 17, x = 1/3
6bc = -1
b = -1/18
use this in first equation, 2ax + 5y = 17, 2ax = 2, a = 1/x = 3
SUFFICIENT.
From S2:
The y-intercept of 2ax + 5y = 17 is 3.4
Rearranging the equation, 5y = -2ax+17
y = -2ax/5+17/5 = -2ax/5+3.4
No extra info.
INSUFFICIENT.
A is the answer.
4x + 6by = 11
intersect at the point (3, c)
Put x = 3 and y = c in both the equations.
6x+5c = 17
12+6bc = 11
From S1:
c = 3
Then, 6x+15 = 17, x = 1/3
6bc = -1
b = -1/18
use this in first equation, 2ax + 5y = 17, 2ax = 2, a = 1/x = 3
SUFFICIENT.
From S2:
The y-intercept of 2ax + 5y = 17 is 3.4
Rearranging the equation, 5y = -2ax+17
y = -2ax/5+17/5 = -2ax/5+3.4
No extra info.
INSUFFICIENT.
A is the answer.
14 Jun 2019, 07:39
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A moderately difficult question on Co-ordinate geometry, made to look more difficult by the presence of additional variables, a, b and c. However, if you are strong with your concepts on the topic, you’ll mostly sail through this question smoothly.
If a line passes through a point, the co-ordinates of the point should satisfy the equation of the straight line.
If two lines intersect at a point, the co-ordinates of the point should satisfy the equations of both the lines.
Since the two lines intersect at (3,c), we can rewrite the given equations as:
6a + 5c = 17
12 + 6bc = 11.
From the above equations, it’s not hard to figure out that, if we have the value of c, we can find out unique values of a and b from the individual equations and hence find out a unique value of a+b.
Statement I gives the value of c. This is sufficient. Possible answer options are A or D. Answer options B, C and E can be eliminated.
Reorganising the equation given in statement II, we have,
y = -\(\frac{2ax}{5}\) + \(\frac{17}{5}\).
\(\frac{17}{5}\), which is 3.4, represents the y-intercept of the line 2ax + 5y = 17, when written in the y = mx + c form. So, the statement is reiterating what we already know and not giving us any data about c.
So, statement II alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
Hope this helps!
If a line passes through a point, the co-ordinates of the point should satisfy the equation of the straight line.
If two lines intersect at a point, the co-ordinates of the point should satisfy the equations of both the lines.
Since the two lines intersect at (3,c), we can rewrite the given equations as:
6a + 5c = 17
12 + 6bc = 11.
From the above equations, it’s not hard to figure out that, if we have the value of c, we can find out unique values of a and b from the individual equations and hence find out a unique value of a+b.
Statement I gives the value of c. This is sufficient. Possible answer options are A or D. Answer options B, C and E can be eliminated.
Reorganising the equation given in statement II, we have,
y = -\(\frac{2ax}{5}\) + \(\frac{17}{5}\).
\(\frac{17}{5}\), which is 3.4, represents the y-intercept of the line 2ax + 5y = 17, when written in the y = mx + c form. So, the statement is reiterating what we already know and not giving us any data about c.
So, statement II alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.
Hope this helps!
