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in the xy plane, line A has slope=a and line b has slope=b.

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Re: DS-slope [#permalink]  24 Aug 2009, 23:05
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flyingbunny wrote:
suppose
f(a)=2^a
g(b)=3^b,

the graphs of these two functions have one and only one intersection.

At the point of interception of this graph, a=b=0 and the value of the function 2^a=3^b=1.
If you draw lines parallel to the X axis, you can see that different values for a and b can lead to the same y. There are other pairs (a,b) such that 2^a=3^b.

To say it in a more mathematical way:
Lets denote two functions f(x)=2^x and g(x)=3^x
at the point of interception f(0)=g(0)=1.
Howerver, there are other pairs (a,b) such that f(a)=g(b)\neq1. So there are other soulution for f(x)=g(x) other than (a,b) = (0,0)

Last edited by LenaA on 24 Aug 2009, 23:15, edited 3 times in total.
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Re: DS-slope [#permalink]  24 Aug 2009, 23:10
flyingbunny wrote:
for 2).
since 2^a=3^b, that means a=b=0,
line A, B are parallel

Not so, as a and b are not necessarily integers.

Both statements are needed. Answer is C.
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Re: DS-slope [#permalink]  24 Aug 2009, 23:14
Oh, hand't seen LenaA's explanation. Oustanding.

2^ln(3) = 2.141486064 = 3^ln(2)

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Re: DS-slope [#permalink]  25 Aug 2009, 00:17
In st. 2: a and b could have values as under:

2^a = 3^b
2^a = 2^(1.58497b)
a = 1.58497b

Also: a = b = 0 is also possible..

Quote:
lan583 wrote:
in the xy plane, line A has slope=a and line b has slope=b. are the 2 lines parallel to each other?

(1) 4^a = 2 ^b

(2) 2^a = 3^b

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Re: [#permalink]  06 Sep 2009, 01:26
terp26 wrote:
ok that makes sense, but what if the lines are equal? then are they not parallel?

is there something in the question that states they are not equal lines ?

Yeah, so I think the answer should be E.
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Re: DS-slope [#permalink]  23 Nov 2009, 22:12
What about the fact that nothing has been said about the y-intercept?

Even if you combine both statement and obtain that a=b=0, the y-intercept could also be both 0. a1=b1=0

This would leads to 2 lines on y-axis itself and hence not parallel to each other, E.

Am I reading too much into the question? Anyone has the OA?
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Re: [#permalink]  18 Sep 2011, 23:12
terp26 wrote:
im confused, just because the slopes are equal does not make the lines parallel?

if both the slopes are 0, then both lines are the X axis, and a line cannot be parallel to itself

so I say E

The slopes will tell us nothing about whether both lines are parallel or equal. Additional information about the Y-intercept is missing.
So, a vote for E.

Last edited by lawsohn on 25 Sep 2011, 18:55, edited 1 time in total.
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Re: DS-slope [#permalink]  19 Sep 2011, 08:11
Is it a GMAT question?? We are not supposed to used logarithms in GMAT. If it still is a GMAT question, can somebody explain it in GMAT language.

Thanks.
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Re: DS-slope [#permalink]  19 Sep 2011, 09:13
The GMAT Exam won't necessarily use logarithms on the exam as this is generally understood as more advanced math. But the question itself does not use any logarithms - it's merely an expression with variables in the exponent.

For the purposes of understanding the expression further it may help to do basic logs (in this case, take the log of both sides). So you should brush up on the basics here so you can better rearrange equations when there is a need. There may certainly be other ways to approach the problem rather than do some basic logs (ie randomly input numbers for x and y and see what results you get) but you are better off learning the basics of logs here.

The issue here among everyone is whether 2 lines with the same slope are parallel. And the answer here is -- for most the part.
This is where the GMAT test takers get tricky and even when you think you understand a concept, you may still get it wrong.

Parallel lines satisfy BOTH of the following:
1) Same slope - yes, this happens when we combine both statements and have a=b=0
2) Don't touch each other. Or in math terms, can draw a perpendicular line to each other, create interior angles of 90 degrees, and never cross.

So when we have two lines with the same slope, they are parallel except when they are the same line. So don't jump to answer choices right away when you follow the rule of thumb (parallel lines = same slope). You really have to think about all scenarios when it comes down to these data sufficiency problems.
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Last edited by gmatpill on 19 Sep 2011, 09:24, edited 1 time in total.
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Re: DS-slope [#permalink]  19 Sep 2011, 09:14
C from my side as well.
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Re: DS-slope [#permalink]  20 Sep 2011, 19:39
gmatpill wrote:
The GMAT Exam won't necessarily use logarithms on the exam as this is generally understood as more advanced math. But the question itself does not use any logarithms - it's merely an expression with variables in the exponent.

For the purposes of understanding the expression further it may help to do basic logs (in this case, take the log of both sides). So you should brush up on the basics here so you can better rearrange equations when there is a need. There may certainly be other ways to approach the problem rather than do some basic logs (ie randomly input numbers for x and y and see what results you get) but you are better off learning the basics of logs here.

The issue here among everyone is whether 2 lines with the same slope are parallel. And the answer here is -- for most the part.
This is where the GMAT test takers get tricky and even when you think you understand a concept, you may still get it wrong.

Parallel lines satisfy BOTH of the following:
1) Same slope - yes, this happens when we combine both statements and have a=b=0
2) Don't touch each other. Or in math terms, can draw a perpendicular line to each other, create interior angles of 90 degrees, and never cross.

So when we have two lines with the same slope, they are parallel except when they are the same line. So don't jump to answer choices right away when you follow the rule of thumb (parallel lines = same slope). You really have to think about all scenarios when it comes down to these data sufficiency problems.

From your comment above I conclude that E is the right answer for this Question.
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Re: DS-slope [#permalink]  23 Sep 2011, 11:55
B is sufficient...

but have a doubt... if a and b have the same values then there is a possibility of the y intercept to be the same for both lines.

so in that case the answer can be E....

so please let me know wat do in such type of questions...
Re: DS-slope   [#permalink] 23 Sep 2011, 11:55
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