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Is rst = 1 ?

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Is rst = 1 ? [#permalink] New post 10 Feb 2010, 11:43
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Is rst = 1 ?

(1) rs = 1
(2) st = 1
[Reveal] Spoiler: OA

Last edited by Bunuel on 07 Dec 2012, 08:01, edited 1 time in total.
Renamed the topic and edited the question.
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Re: GMAT Paper test - Test Code 14 [#permalink] New post 10 Feb 2010, 11:56
Answer: "E" : Both statements not sufficient

Reason:
(plugging in method)

Statement 1: Say r = 1/3 and s = 3

satisfies statement 1 i.e. rs = 1 but cant comment about value of rst as t is still unknown.

Statement 2: Say t = 1/3 and s = 3

satisfies statement 1 i.e. st = 1 but cant comment about value of rst as t is still unknown.

Now if both statements are taken together, r=1/3 s=3 and t=1/3 => rst not equal to 1.

hence both the statements are not sufficient.
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Re: GMAT Paper test - Test Code 14 [#permalink] New post 10 Feb 2010, 12:21
piyatiwari wrote:
Answer: "E" : Both statements not sufficient


Now if both statements are taken together, r=1/3 s=3 and t=1/3 => rst not equal to 1.

hence both the statements are not sufficient.


But from your response above combining the two statements tells us conclusively that rst not eqaul to 1. Therefore combining the two statements is sufficient to answer the question as a 'NO'. So shouldn't the answer be 'C'
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Re: GMAT Paper test - Test Code 14 [#permalink] New post 10 Feb 2010, 12:51
loki wrote:
piyatiwari wrote:
Answer: "E" : Both statements not sufficient


Now if both statements are taken together, r=1/3 s=3 and t=1/3 => rst not equal to 1.

hence both the statements are not sufficient.


But from your response above combining the two statements tells us conclusively that rst not eqaul to 1. Therefore combining the two statements is sufficient to answer the question as a 'NO'. So shouldn't the answer be 'C'



Oh yes. My usual mistake :). Thanks so much Loki. This goes directly to my error log.

So the answer is "C"
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Re: GMAT Paper test - Test Code 14 [#permalink] New post 10 Feb 2010, 12:56
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loki wrote:
piyatiwari wrote:
Answer: "E" : Both statements not sufficient


Now if both statements are taken together, r=1/3 s=3 and t=1/3 => rst not equal to 1.

hence both the statements are not sufficient.


But from your response above combining the two statements tells us conclusively that rst not eqaul to 1. Therefore combining the two statements is sufficient to answer the question as a 'NO'. So shouldn't the answer be 'C'


Is rst = 1 ?

(1) rs = 1
(2) st = 1

Try r=s=t=1, both statements hold true and rst=1.
Try r=s=t=-1, both statements hold true and rst=-1.

Two different answers. Not sufficient.

Answer: E.
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Re: GMAT Paper test - Test Code 14 [#permalink] New post 10 Feb 2010, 13:04
Bunuel wrote:
loki wrote:
piyatiwari wrote:
Answer: "E" : Both statements not sufficient


Now if both statements are taken together, r=1/3 s=3 and t=1/3 => rst not equal to 1.

hence both the statements are not sufficient.


But from your response above combining the two statements tells us conclusively that rst not eqaul to 1. Therefore combining the two statements is sufficient to answer the question as a 'NO'. So shouldn't the answer be 'C'


Try r=s=t=1, both statement hold true and rst=1.
Try r=s=t=-1, both statement hold true and rst=-1.

Two different answers. Not sufficient.

Answer: E.


OA is E. I get it now! Thank you!
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OG DS 95, explain how my logic is wrong [#permalink] New post 14 Feb 2010, 10:19
Ok, without a doubt my number property skills are my achillies heel when is comes to GMAT quant.

I was reviewing my error log today. Tell me why my logic is wrong.

95. Is rst=1

(1) rs=1
(2) st=1

I attacked it by rearranging the original equations, dividing both sides by t.

so, rs=1/t
then sub in rs=1
so, 1=1/t
then cross multiply t=1
Combined with what we already know (rs=1) we have 1*1=1
Therefore, sufficient.

Same logic can be applied to statment 2.
Therefore my answer was D.

OA is actually E and I understand how they got it, but I also fail to see why my strategy was wrong. I feel like I'm probably overlooking some basic rule that governs all equations here but if someone could help me out that'd be great.

Thanks
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Re: OG DS 95, explain how my logic is wrong [#permalink] New post 14 Feb 2010, 10:34
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Currency wrote:
Ok, without a doubt my number property skills are my achillies heel when is comes to GMAT quant.

I was reviewing my error log today. Tell me why my logic is wrong.

95. Is rst=1

(1) rs=1
(2) st=1

I attacked it by rearranging the original equations, dividing both sides by t.

so, rs=1/t
then sub in rs=1
so, 1=1/t
then cross multiply t=1
Combined with what we already know (rs=1) we have 1*1=1
Therefore, sufficient.

Same logic can be applied to statment 2.
Therefore my answer was D.

OA is actually E and I understand how they got it, but I also fail to see why my strategy was wrong. I feel like I'm probably overlooking some basic rule that governs all equations here but if someone could help me out that'd be great.

Thanks


The highlighted part is the mistake.

The question is asking u to prove that... and you are considering the same as True. This isnt the correct approach.

The Answer E is correct...

Is rst = 1?
S1: rs = 1,
t can be 2 ... then rst is not equal to 1...
t can be 1... then rst is equal to 1...
Hence IN SUFF

S2: st =1 ,
r can be 2 ... then rst is not equal to 1..
r can be 1 .. then rst is equal to 1...
Hence IN SUFF...

combining I and 2...
we can have .. r = 2, s = 1/2, t = 2
Then rst = 2
but we can also have r = 1, s = 1, t =1
Then rst = 1..

Hence E...

Hope this helps!
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Re: OG DS 95, explain how my logic is wrong [#permalink] New post 14 Feb 2010, 10:36
Currency wrote:
Ok, without a doubt my number property skills are my achillies heel when is comes to GMAT quant.

I was reviewing my error log today. Tell me why my logic is wrong.

95. Is rst=1

(1) rs=1
(2) st=1

I attacked it by rearranging the original equations, dividing both sides by t.

so, rs=1/t
then sub in rs=1
so, 1=1/t
then cross multiply t=1
Combined with what we already know (rs=1) we have 1*1=1
Therefore, sufficient.

Same logic can be applied to statment 2.
Therefore my answer was D.

OA is actually E and I understand how they got it, but I also fail to see why my strategy was wrong. I feel like I'm probably overlooking some basic rule that governs all equations here but if someone could help me out that'd be great.

Thanks

Okay, you can really deal with this much simpler. But, let's review what you've done.

I attacked it by rearranging the original equations, dividing both sides by t.
so, rs=1/t


your question then changes to -- Is rs=1/t?
1. Does this give the vale of t? No. Even if you use (1), you get -- 1=1/t -> t=1. Does this answer your question. No. A/D out
2. Similarly, does the value of st=1, help us in answering the question? No. B out

Hope this helps.
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Re: OG DS 95, explain how my logic is wrong [#permalink] New post 14 Feb 2010, 10:41
Quote:
"The question is asking u to prove that... and you are considering the same as True. This isnt the correct approach."


This is what I was missing. Normally I'd instinctively follow that, but I think cause it was in my error log I over-thought it and got fancy - effectively confusing myself. Ha!

Thanks for the quick repsonses guys, much appreciated!
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Re: OG DS 95, explain how my logic is wrong [#permalink] New post 15 Feb 2010, 05:32
i) rs=1
r=1/3 s=3 and t=7 so ans is no
r=1/3 s=3 and t=1 so ans is yes
not suff.

ii) st=1
s=1/3 and t=3 and r=7 so ans is no
r=1/3 s=3 and t=1 so ans is yes

not sufficient

combining both 1 and 2

s=1/3 r=3 and t=3 still it satisfies both eq but rst is not 1

if s=1 r=1 and t=1 it satisifies both eq. and rst is 1

so ans is E
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Re: Is rst=1? Statement 1: rs=1 Statement 2: st=1 [#permalink] New post 29 Nov 2011, 11:31
i) rs=1
As we don't know anything about value of t so we cant answer if rst = 1. Insufficient.

ii) st=1
As we don't know anything about value of r so we cant answer if rst = 1. Insufficient.

Combining both 1 and 2

(rs)(st) = 1
(rst)s = 1
rst = 1/s

As we don't know the value of s. rst can be anything (1 or something else). we cannot answer "Is rst = 1?"

Insufficient
Ans: E
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Re: Is rst = 1 ? [#permalink] New post 29 Dec 2012, 11:27
Its clear that 1 and 2 do not lead to a solution. then, Cant this be solved by observing that we have 2 equations and 3 unknown variables. hence not sufficient and hence E?
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Re: Is rst = 1 ? [#permalink] New post 30 Dec 2012, 06:34
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4sguy wrote:
Its clear that 1 and 2 do not lead to a solution. then, Cant this be solved by observing that we have 2 equations and 3 unknown variables. hence not sufficient and hence E?


That's not entirely correct. Notice that we are asked to find whether rst = 1, not the values of the unknowns.

For example if the question were:

Is rst = 1 ?

(1) rs = 0
(2) st = 1

The answer would be A not E.
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Re: Is rst = 1 ? [#permalink] New post 03 Jan 2013, 14:21
statement 1: don't know anything about t. not sufficient
statement 2: don't know anything about r. not sufficient

put them together: rst could equal (1)(1)(1) in which case would be 1. or rst could equal (1/2)(2)(1/2) in which case rst = 1/2. Not sufficient

Answer: E
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Re: Is rst = 1 ? [#permalink] New post 22 Apr 2014, 07:43
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Re: Is rst = 1 ? [#permalink] New post 04 May 2015, 03:56
I found that the easiest way to tackle this problem was as following:

(A) rs = 1 means r and s have same sign. Make a chart:


r s
+ +
- -

Clearly not sufficient

(B)

st = 1 means s and t have same sign. Make a chart:

s t
+ +
- -

Clearly not sufficient


combined:

r s t
+ + +
- - -

two different solutions: -1 or 1, hence (E)

Incredibly fast solution, took less than 15 seconds
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Is rst = 1 ? [#permalink] New post 04 May 2015, 21:26
Expert's post
Going through the solutions posted by students in this thread, I realized that this question is a good illustration of the perils of 'solve by substituting numbers' approach. A student considered one set of possible values of r, s and t and thought that since he was able to get a tangible value of the product rst that was not equal to 1, this meant the 2 statements together were sufficient. It didn't occur to him at that time (later he did realize this oversight) that other values of r, s and t were also possible that did lead to rst = 1.

To eliminate all this uncertainty about whether you've considered all possible sets of values for the different unknowns, I would like to suggest the algebraic way of thinking through this question. Here's how I would solve it:

The question asks if rst = 1 (Note to self: it's not mentioned that r, s and t are integers. So, they might very well be fractions)

1. rs = 1
But t = ? Don't know :(

Insufficient

2. st = 1
But r = ? Don't know :(

Insufficient.

1 + 2

The question asks about the product rst.
This product can be written as \(\frac{(rs)(st)}{s}\). Substituting the values of rs and st from St. 1 and 2, we get:

rst = \(\frac{(1)(1)}{s}\) = \(\frac{1}{s}\)

But s = ? Don't know :(

If s = 1, rst = 1
But if s = some other value, rst is not equal to 1.

So, clearly insufficient.

Answer: Option E


I hope this alternate solution was helpful for you :)

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