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

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in the xy plane, line A has slope=a and line b has slope=b. [#permalink]  22 Sep 2006, 14:11
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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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E?

Case 1: 4^a = 2^b
=> 2a = b
What if a = b = 0?
Insufficient

Same problem with Case 2.

Also, don't think the two cases can be combined, hence cannot be C.
2^a = 3^b
=> alog2 = blog3
=> a/b = log3/log2
If we use 2a = b,
then 1/2 = log3/log2; which is certainly not true.
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Looks like everyone except me thinks this is E... back to the study room...

Last edited by haas_mba07 on 22 Sep 2006, 15:20, edited 1 time in total.
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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

For two lines to be parallel, they need to have same slope but different y-intercept. So two parallel lines will look like this:

y1 = mx + b1
y2 = mx + b2

From 1) they have different slope and no knowledge of y intercept. So INSUFF

2) Same as 1)

E.
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Re: DS-slope [#permalink]  22 Sep 2006, 15:41
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

(1) As 4^a=2^(2a)=2^b, it follows that b=2a, in which case both could be 0 (horizontal lines) or a and b would be different NOT SUFF

(2) Quite the same as (1) NOT SUFF

(1) and (2): 4^a=2^(2a)=(2^a)^2=(3^b)^2=3^(2b)=9^b=2^b

Thus b=0 and so a=0 too. The lines are parallel

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E?

Case 1: 4^a = 2^b
=> 2a = b
What if a = b = 0?
Insufficient

Same problem with Case 2.

Also, don't think the two cases can be combined, hence cannot be C.
2^a = 3^b
=> alog2 = blog3
=> a/b = log3/log2
If we use 2a = b,
then 1/2 = log3/log2; which is certainly not true.

The two cases can ALWAYS be combined. Since 1/2 is not equal to log3/log2, it must be that a=b=0
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kevincan wrote:
E?

Case 1: 4^a = 2^b
=> 2a = b
What if a = b = 0?
Insufficient

Same problem with Case 2.

Also, don't think the two cases can be combined, hence cannot be C.
2^a = 3^b
=> alog2 = blog3
=> a/b = log3/log2
If we use 2a = b,
then 1/2 = log3/log2; which is certainly not true.

The two cases can ALWAYS be combined. Since 1/2 is not equal to log3/log2, it must be that a=b=0

Thank you!
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Re: DS-slope [#permalink]  25 Sep 2006, 16:01
kevincan wrote:
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

(1) As 4^a=2^(2a)=2^b, it follows that b=2a, in which case both could be 0 (horizontal lines) or a and b would be different NOT SUFF

(2) Quite the same as (1) NOT SUFF

(1) and (2): 4^a=2^(2a)=(2^a)^2=(3^b)^2=3^(2b)=9^b=2^b

Thus b=0 and so a=0 too. The lines are parallel

why not B?.. what values other than 0 will satify 2^a = 3^b??
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Re: DS-slope [#permalink]  13 Feb 2007, 05:26
gk3.14 wrote:
kevincan wrote:
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

(1) As 4^a=2^(2a)=2^b, it follows that b=2a, in which case both could be 0 (horizontal lines) or a and b would be different NOT SUFF

(2) Quite the same as (1) NOT SUFF

(1) and (2): 4^a=2^(2a)=(2^a)^2=(3^b)^2=3^(2b)=9^b=2^b

Thus b=0 and so a=0 too. The lines are parallel

why not B?.. what values other than 0 will satify 2^a = 3^b??

there are obviously some non zero real values that have a solution.

But why is the answer not C?

in transforming a. logb = c . logd => a/c = logb/logd ... you are inherenty assuming that c =! 0

which is not true ... THe answer is C ... if you have both the equations the only solution is a=b= 0
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in fact C is indeed the answer...

a=b=0 solves both st1 and st2, and it is the only solution.
so if both st1 and st2 are true... then it must be that the lines are parallel.
hence C.
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Re: DS-slope [#permalink]  13 Feb 2007, 18:35
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

from 1, 2^2a = 2^b
=> either a=b=0 or a=b/2.

from 2, 2^a=3^b
=> a=0=b OR 2 = 3^(b/a) there could be a value possible.

from 1 and 2, a=b=0 definitely
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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
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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

No ... A slope equal to 0 creates a family of lines that are parallel to each others and to the X axis.

Ex:
> y=0 : is the X axis
> y=1
> y=2
> y=100
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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 ?
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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 ?

Yes... It's also a possibility ... Both lines are finally only one ... And thus, yes, a line cannot be parellel to itself
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Re: DS-slope [#permalink]  20 Aug 2009, 20:09
Answer is C as explained above by Kevincan.
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Re: DS-slope [#permalink]  23 Aug 2009, 19:20
Can we get the OA? I'm liking c.

I don't see any way that you can make both statements true without making a=b=0.

The two equations come out as:

1. 2a = b (not suff)
2. 2/3a = b (not suff)

So the only way both can be true is if a=b=0?
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Re: DS-slope [#permalink]  24 Aug 2009, 20:04
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

for 1).
4^a = 2 ^b ==>> 2a=b
if a<>b, then line A, B are not parallel; if a=b=0, they are parallel, thus insuf.

for 2).
since 2^a=3^b, that means a=b=0,
line A, B are parallel

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Re: DS-slope [#permalink]  24 Aug 2009, 20:08
1
KUDOS
suppose
f(a)=2^a
g(b)=3^b,

the graphs of these two functions have one and only one intersection.
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Re: DS-slope [#permalink]  24 Aug 2009, 22:37
I would like to know the answer because my answer is C and not E as a majority...

Statement 1: 2^{2a}=2^{b}
2a=b => if a=0 and b= 0, the lines can be parallel.

Statement 2:
2^a=3^b
1 solution: a=b=0, line are parallel
2 solution: any pair (a,b) such that \frac{a}{b}=\frac{log3}{log2}.Since \frac{log3}{log2}\neq1, lines are not parallel.
It is possible they are parallel and it is possible they are not parallel.

Combined, the solution should a=b=0. Therefore, lines are parallel. Answer C.
Re: DS-slope   [#permalink] 24 Aug 2009, 22:37
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