GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 14 Oct 2019, 03:40 GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  Is rst = 1 ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

Hide Tags

Intern  Joined: 06 Aug 2006
Posts: 17
Is rst = 1 ?  [#permalink]

Show Tags

4
39 00:00

Difficulty:   25% (medium)

Question Stats: 68% (01:08) correct 32% (01:02) wrong based on 1357 sessions

HideShow timer Statistics

Is rst = 1 ?

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

Originally posted by loki on 10 Feb 2010, 12:43.
Last edited by Bunuel on 07 Dec 2012, 09:01, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert V
Joined: 02 Sep 2009
Posts: 58312
Re: GMAT Paper test - Test Code 14  [#permalink]

Show Tags

10
4
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.

_________________
Senior Manager  Joined: 22 Dec 2009
Posts: 253
Re: OG DS 95, explain how my logic is wrong  [#permalink]

Show Tags

6
3
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!
_________________
Cheers!
JT...........
If u like my post..... payback in Kudos!! |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|

~~Better Burn Out... Than Fade Away~~
General Discussion
Senior Manager  Joined: 28 Jun 2009
Posts: 354
Location: United States (MA)
Re: GMAT Paper test - Test Code 14  [#permalink]

Show Tags

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.
Intern  Joined: 06 Aug 2006
Posts: 17
Re: GMAT Paper test - Test Code 14  [#permalink]

Show Tags

1
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'
Senior Manager  Joined: 28 Jun 2009
Posts: 354
Location: United States (MA)
Re: GMAT Paper test - Test Code 14  [#permalink]

Show Tags

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"
Manager  Joined: 09 Dec 2009
Posts: 117
OG DS 95, explain how my logic is wrong  [#permalink]

Show Tags

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
_________________
G.T.L. - GMAT, Tanning, Laundry

Round 1: 05/12/10 http://gmatclub.com/forum/handling-a-grenade-thesituation-s-official-debrief-94181.html

Round 2: 07/10/10 - This time it's personal.
Senior Manager  Joined: 27 Jun 2008
Posts: 442
WE 1: Investment Banking - 6yrs
Re: OG DS 95, explain how my logic is wrong  [#permalink]

Show Tags

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.
Manager  Joined: 09 Dec 2009
Posts: 117
Re: OG DS 95, explain how my logic is wrong  [#permalink]

Show Tags

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!
_________________
G.T.L. - GMAT, Tanning, Laundry

Round 1: 05/12/10 http://gmatclub.com/forum/handling-a-grenade-thesituation-s-official-debrief-94181.html

Round 2: 07/10/10 - This time it's personal.
Manager  Joined: 26 Nov 2009
Posts: 110
Re: OG DS 95, explain how my logic is wrong  [#permalink]

Show Tags

1
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
Manager  Joined: 05 Oct 2011
Posts: 150
Re: Is rst=1? Statement 1: rs=1 Statement 2: st=1  [#permalink]

Show Tags

1
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
Intern  Joined: 15 Nov 2012
Posts: 1
Re: Is rst = 1 ?  [#permalink]

Show Tags

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?
Math Expert V
Joined: 02 Sep 2009
Posts: 58312
Re: Is rst = 1 ?  [#permalink]

Show Tags

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.
_________________
Manager  Joined: 18 Oct 2011
Posts: 78
Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Re: Is rst = 1 ?  [#permalink]

Show Tags

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

Manager  Joined: 26 Feb 2015
Posts: 110
Re: Is rst = 1 ?  [#permalink]

Show Tags

2
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
e-GMAT Representative V
Joined: 04 Jan 2015
Posts: 3074
Is rst = 1 ?  [#permalink]

Show Tags

6
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.

I hope this alternate solution was helpful for you Best Regards

Japinder
_________________
Intern  Joined: 15 Aug 2015
Posts: 3
Location: United States
WE: Analyst (Consumer Products)
Re: Is rst = 1 ?  [#permalink]

Show Tags

1.) Tells us nothing about t - INS (eliminate A/D from grid)
2.) Tells us nothing about r - INS (eliminate B from grid)

Combined (left with C or E)
r*s = 1
s*t = 1

a.) 1*1*1 = 1 True
b.) 1/4 * 4 * 1/4 = 1 False

Therefore answer is E
Target Test Prep Representative G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2817
Re: Is rst = 1 ?  [#permalink]

Show Tags

1
loki wrote:
Is rst = 1 ?

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

Solution:

We need to determine whether RST = 1.

Statement One Alone:

RS = 1

Since we don’t know the value of T, knowing only that RS = 1 is not sufficient to determine whether RST = 1. We can eliminate answer choices A and D.

Statement Two Alone:

ST = 1

Since we don’t know the value of R, knowing only that ST = 1, is not sufficient to determine whether RST = 1. We can eliminate answer choice B.

Statements One and Two Together:

From statements one and two we know that RS = 1 and that ST = 1. Thus, we can say that:

RS = ST

RS – ST = 0

S(R – T) = 0

S = 0 or R = T

Because RS and ST both equal 1, S cannot be 0. Thus, R = T.

However, knowing that R = T is not enough information to determine whether RST = 1.

For example, if R = T = 1, then S = 1 (since RS = 1 and ST = 1), RST = 1.

However, if R = T = 2, then S = ½ (since RS = 1 and ST = 1), RST = 2  1.

The answer is E.
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

CEO  V
Joined: 12 Sep 2015
Posts: 3990
Re: Is rst = 1 ?  [#permalink]

Show Tags

2
Top Contributor
loki wrote:
Is rst = 1 ?

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

Target question: Is rst=1?

Statement 1: rs = 1
No information about t
INSUFFICIENT

Statement 2: st = 1
No information about r
INSUFFICIENT

Statements 1 and 2 combined
So, rs = 1 and st = 1
This means that rs/st = 1/1
Simplify to get r/t = 1
This tells us that r = t, so this is all that we can conclude one we combine the statements.

If r = t, there are still several values of r, s and t that satisfy the both statements. Here are two:
Case a: r = 1, s = 1 and t = 1, in which case rst = 1
Case b: r = 0.5, s = 2 and t = 0.5, in which case rst = 0.5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent
_________________
Manager  B
Joined: 02 Jan 2017
Posts: 68
Location: Pakistan
Concentration: Finance, Technology
GMAT 1: 650 Q47 V34 GPA: 3.41
WE: Business Development (Accounting)
Re: Is rst = 1 ?  [#permalink]

Show Tags

GMATPrepNow wrote:
loki wrote:
Is rst = 1 ?

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

Target question: Is rst=1?

Statement 1: rs = 1
No information about t
INSUFFICIENT

Statement 2: st = 1
No information about r
INSUFFICIENT

Statements 1 and 2 combined
So, rs = 1 and st = 1
This means that rs/st = 1/1
Simplify to get r/t = 1
This tells us that r = t, so this is all that we can conclude one we combine the statements.

If r = t, there are still several values of r, s and t that satisfy the both statements. Here are two:
Case a: r = 1, s = 1 and t = 1, in which case rst = 1
Case b: r = 0.5, s = 2 and t = 0.5, in which case rst = 0.5
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Cheers,
Brent

I would urge all experts on forums to provide solutions like this one, we are learning and often experts forget we need layman basic terminology to really grip the concepts. I have read all the solutions and at the end, i understood from this post.

I have great respect for Bunnel, but man sometimes you forget that all do not share your level of expertise on this content. Using words helps us students a lot. Thank you for the post Re: Is rst = 1 ?   [#permalink] 07 Dec 2017, 02:07

Go to page    1   2    Next  [ 23 posts ]

Display posts from previous: Sort by

Is rst = 1 ?

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne  