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Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
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Another way:

If line ax+by=c does cross x axis then, there will be a point (z,0) on this line. Which means:

az=c. or z= (c/a). z should have real value and this will be possible when a is not equal to zero.

So our question now becomes: Is a = 0?

statement 1: b not equal to 0; This does not tell anything about a. NS

statement 2: ab>0. a is certainly not equal to 0. Sufficient.


B is the answer.

(Note that if we put z = (c/a) in equation; and we know that a is not equal to zero; we get: (b)(y)=0; Now because statement (2) also says b is not equal to zero, so y will have to be zero. This is what we want and this proves the point that this line cuts x axis. )
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Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
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Hi chetan2u,

I have one doubt. If a line passes through origin, then can we say that the line passes through x and y axis both...?
Please assist.
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Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
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PrakharGMAT wrote:
Hi chetan2u,

I have one doubt. If a line passes through origin, then can we say that the line passes through x and y axis both...?
Please assist.


Yes, Prakhar the line passing through ORIGIN crosses x-axis at x=0 and y-axis at y=0...
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Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
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Bunuel wrote:
Does the line with equation ax + by = c, where a, b and c are real constants, cross the x-axis?

(1) b ≠ 0
(2) ab > 0



GMATinsight's Solution



A line will always cross x-axis if the slope of line is NOT zero

ax + by = c can be written as \(y = (-\frac{a}{b})x + (\frac{c}{b})\)

Comparing it with \(y = mx+c\) where m is the slope

i.e. SLope of the given line \(= -\frac{a}{b}\)

Question REPHRASED: Is \(-\frac{a}{b}=0\)

Statement 1: b ≠ 0

but a may be 0 or non-zero hence

NOT SUFFICIENT

STatement 2: ab > 0

i.e. ab≠0

i.e. slope is non-zero i.e it will always cross x axis hence

SUFFICIENT

Answer: option B
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Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
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Equation: ax+by=c
Rearranging, we get

y = (-a/b)x + (c/b)

Q: Does the line cross the x-axis? We need to find if the slope is 0 or not.

Statements:

(1) b ≠ 0

Doesn't tell anything about a. a can be 0 (line won't cross) or a can be something else (line will cross).

Insufficient.

(2) ab>0

Either a and b are both positive or both negative. Neither a nor b is equal to 0.

Therefore, we know that a is never zero. Does the line cross the x-axis? Definitely Yes.

Sufficient

Hence, the answer is Option (B).[/b]
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Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
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Bunuel wrote:
Does the line with equation ax + by = c, where a, b and c are real constants, cross the x-axis?

(1) b ≠ 0
(2) ab > 0

Project DS Butler Data Sufficiency (DS3)


For DS butler Questions Click Here



Eqn of line y =-ax/b+c/b
#1
B not = 0
Insufficient
#2
Ab>0

Possible when both are - or +

So eqn of line y=-x+c and y =-x-c

For values of x & y line will pass x axis slope is not 0
sufficient option B
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Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
Hi Bunuel,

I got stumped with this one on the mock. Can you help me clarify something.

For the line to not cross the x-axis, is it enough for the slope to be 0, or we also have to ensure that Y-Intercept is not equal to 0 (in other words if the line is the same as the X-Axis)?

I am guessing here, B was sufficient, as it is clear that slope is not 0, but if we knew the slope was 0, would the answer be E here, as we know nothing about the Y-Intercept?
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Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
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TargetMBA007 wrote:
Does the line with equation ax + by = c, where a, b and c are real constants, cross the x-axis?

(1) b ≠ 0
(2) ab > 0

Hi Bunuel,

I got stumped with this one on the mock. Can you help me clarify something.

For the line to not cross the x-axis, is it enough for the slope to be 0, or we also have to ensure that Y-Intercept is not equal to 0 (in other words if the line is the same as the X-Axis)?

I am guessing here, B was sufficient, as it is clear that slope is not 0, but if we knew the slope was 0, would the answer be E here, as we know nothing about the Y-Intercept?


The line represented by y = 0, while having a slope of 0, coincides with the x-axis. Whether coinciding lines can be considered as crossing each other is a technicality that the GMAT does not test. Fortunately, this specific case is ruled out by the second statement because ab > 0 implies that we don't have a y = 0 line.
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Re: Does the line with equation ax + by = c, where a, b and c are real con [#permalink]
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