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Line K defined by y = ax + b. Does line K intersect positive y axis?

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Intern
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Line K defined by y = ax + b. Does line K intersect positive y axis?  [#permalink]

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New post 06 Aug 2019, 23:02
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (01:43) correct 17% (01:30) wrong based on 29 sessions

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Line K is represented by the equation y = ax + b. Does line K intersect the positive y-axis on the x-y plane?

1. ab < 0

2. a + b < 0
Intern
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Re: Line K defined by y = ax + b. Does line K intersect positive y axis?  [#permalink]

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New post 07 Aug 2019, 08:32
1
y=ax+b
b is actually the point where line y touches the y axis,
is b is positive , line cuts y axis at positive point
if b is negative line cuts at negative y axis

so the ques is about getting if b>0 or not

by a : ab<0 , either a or b , one of them will be -ve and other +ve, not enough to answer the ques
both can not be + , both cannot be -

by b:a+b<0 , , both can be - , and a and b can be +- combination

so by both statement we cant say for sure whether b is + or -

hence E

Need kudos, thnx
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Re: Line K defined by y = ax + b. Does line K intersect positive y axis?  [#permalink]

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New post 09 Aug 2019, 08:02
The question can be rephrased to ask “ Is the y-intercept of the line positive?”.
In the equation y = ax + b, the y-intercept is b. This means, the question now becomes “Is b>0?”.

From statement I, ab<0. This means that a and b are of opposite signs.

If a>o, b<0. In this case, the answer to the main question will be a NO.
If a<0, b>0. In this case, the answer to the main question will be a YES.

Statement I alone is insufficient. Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II, a + b < 0. This can be satisfied by a range of values of a and b.

For example, if a = - 5 and b = 1, a+b<0. Here, b>0.

If a = -5 and b = -5, a+b<0. Here, b<0.

Clearly, this is insufficient. Answer option B can be eliminated.

Combining statements I and II, let’s take the following values:

If a = -5 and b = 1, ab<0, a+b<0 and b>0.

If a = 1 and b = -5, ab<0 and a+b<0, but b<0.

Even after combining the statements, the data is insufficient to find if the y-intercept of the line is positive.

The correct answer option is E.
Hope this helps!
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Re: Line K defined by y = ax + b. Does line K intersect positive y axis?   [#permalink] 09 Aug 2019, 08:02
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