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# In the figure to the right, the equation of the line is y = 9x/10 + k

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Math Expert
Joined: 02 Sep 2009
Posts: 64949
In the figure to the right, the equation of the line is y = 9x/10 + k  [#permalink]

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09 Apr 2019, 02:20
00:00

Difficulty:

25% (medium)

Question Stats:

77% (01:50) correct 23% (01:58) wrong based on 92 sessions

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In the figure to the right, the equation of the line is y = 9x/10 + k . Which one of the following must be true about line segments AO and BO ?

(A) AO > BO
(B) AO < BO
(C) AO ≤ BO
(D) AO = BO
(E) AO = BO/2

Source: Nova GMAT
Difficulty Level: 600

Attachment:

2019-04-09_1418.png [ 13.2 KiB | Viewed 918 times ]

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Re: In the figure to the right, the equation of the line is y = 9x/10 + k  [#permalink]

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09 Apr 2019, 02:50
1
To get the length of BO, Substitute x=0 in equation y = 9x/10 + k, We get y=k . Hence BO= k

To get the length of AO, Substitute y=0 in th equation above and you get x= -10k/9 (Distance (AO= 10k/9)) (As distance can never be a negative quantity)

Clearly from above two values we know AO>BO

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Re: In the figure to the right, the equation of the line is y = 9x/10 + k  [#permalink]

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14 Apr 2019, 00:18
1
no need to find exact values, i think

M is the rate of change in y, for a change in x

since m is 9/10... for every 10 unit increase in x, y increases by 9... so OB (height of the triangle) will be shorter than OA (base)

hence A
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Re: In the figure to the right, the equation of the line is y = 9x/10 + k  [#permalink]

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16 May 2020, 07:44
Bunuel wrote:

In the figure to the right, the equation of the line is y = 9x/10 + k . Which one of the following must be true about line segments AO and BO ?

(A) AO > BO
(B) AO < BO
(C) AO ≤ BO
(D) AO = BO
(E) AO = BO/2

Source: Nova GMAT
Difficulty Level: 600

Attachment:
2019-04-09_1418.png

We know the slope is less than 1, we may change it to $$y = \frac{x}{10} + k$$ for an extreme case to visualize $$AO > BO$$. Note k doesn't have to be positive, this is true when k is negative as well.

Ans: A
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Re: In the figure to the right, the equation of the line is y = 9x/10 + k   [#permalink] 16 May 2020, 07:44