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VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
In the xy-plane, the equation of line l is 5x + 6y = 90. Does the  [#permalink]

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5 00:00

Difficulty:   75% (hard)

Question Stats: 46% (01:51) correct 54% (01:55) wrong based on 47 sessions

### HideShow timer Statistics 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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Regards,

PKN

Rise above the storm, you will find the sunshine
Math Expert V
Joined: 02 Sep 2009
Posts: 56275
Re: In the xy-plane, the equation of line l is 5x + 6y = 90. Does the  [#permalink]

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PKN wrote:
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
_________________
VP  D
Status: Learning stage
Joined: 01 Oct 2017
Posts: 1028
WE: Supply Chain Management (Energy and Utilities)
Re: In the xy-plane, the equation of line l is 5x + 6y = 90. Does the  [#permalink]

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Bunuel wrote:
PKN wrote:
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

Got it. Thank you.
_________________
Regards,

PKN

Rise above the storm, you will find the sunshine
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 2942
In the xy-plane, the equation of line l is 5x + 6y = 90. Does the  [#permalink]

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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.

_________________ In the xy-plane, the equation of line l is 5x + 6y = 90. Does the   [#permalink] 13 Aug 2018, 07:16
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# In the xy-plane, the equation of line l is 5x + 6y = 90. Does the  