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PKN
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In the xy-plane, the equation of line l is 5x + 6y = 90. Does the 12 Aug 2018, 09:10
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C
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Difficulty:

65% (hard)

Question Stats:

53% (01:47) correct 48% (01:54) wrong based on 200 sessions

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In the xy-plane, the equation of line l is 5x + 6y = 90. Does the point (a, b) lie on line l?

(1) (a + b - 16) (5a + 6b - 90) = 0
(2) (b - a - 4) (5a + 6b - 90) = 0

Source:- Time4education
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C
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In the xy-plane, the equation of line l is 5x + 6y = 90. Does the 12 Aug 2018, 11:53
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PKN
In the xy-plane, the equation of line l is 5x + 6y = 90. Does the point (a, b) lie on line l?
(1) (a + b - 16) (5a + 6b - 90) = 0
(2) (b - a - 4) (5a + 6b - 90) = 0

Source:- Time4education
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Copy of the following question: https://gmatclub.com/forum/in-the-xy-pl ... 00399.html

Similar question: https://gmatclub.com/forum/in-the-xy-pl ... 40975.html
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In the xy-plane, the equation of line l is 5x + 6y = 90. Does the 12 Aug 2018, 12:00
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PKN
In the xy-plane, the equation of line l is 5x + 6y = 90. Does the point (a, b) lie on line l?
(1) (a + b - 16) (5a + 6b - 90) = 0
(2) (b - a - 4) (5a + 6b - 90) = 0

Source:- Time4education

Copy of the following question: https://gmatclub.com/forum/in-the-xy-pl ... 00399.html

Similar question: https://gmatclub.com/forum/in-the-xy-pl ... 40975.html
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Got it. Thank you.
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In the xy-plane, the equation of line l is 5x + 6y = 90. Does the 13 Aug 2018, 07:16
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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
      o 5a + 6b = 90.
    • 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

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In the xy-plane, the equation of line l is 5x + 6y = 90. Does the 19 Jul 2021, 00:50
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State 1:
(a + b - 16) (5a + 6b - 90) =
Either of the 2 can happen
a + b - 16 = 0, 5a + 6b - 90 = 0 or both
It is only a possible case.
Hence INsuff
Statement 2:
(b - a - 4) (5a + 6b - 90) = 0
b – a - 4 = 0, 5a + 6b - 90 = 0 or both
It is only a possible case.
Statement (2) ALONE is INsuff

Combining Both 1 and 2
5a + 6b = 90
Lies on the line sufficient
hence IMO C
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In the xy-plane, the equation of line l is 5x + 6y = 90. Does the 19 Apr 2022, 06:43
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EgmatQuantExpert

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
      o 5a + 6b = 90.
    • 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
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EgmatQuantExpert Bunuel

IMO to add to the concluding part of the solution, we should simultaneously solve the 2 equations- a + b - 16 = 0 and b – a - 4 = 0 to get a=6 and b=10, these values then to be substituted in the equation 5a + 6b - 90 = 0. Since it satisfies this equation, the answer is C. If it wouldn't have satisfied this equation, then the answer would have been E like in this ques.
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