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Re: OG DS 95, explain how my logic is wrong [#permalink]

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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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|Do not post questions with OA|Please underline your SC questions while posting|Try posting the explanation along with your answer choice| |For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

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.

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

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'

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.

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.

OG DS 95, explain how my logic is wrong [#permalink]

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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.

Re: OG DS 95, explain how my logic is wrong [#permalink]

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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

Re: OG DS 95, explain how my logic is wrong [#permalink]

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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!
_________________

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?

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.

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
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