It is currently 21 Sep 2017, 19:58

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# Is rst = 1 ?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 06 Aug 2006
Posts: 21

Kudos [?]: 46 [1], given: 2

Is rst = 1 ? [#permalink]

### Show Tags

10 Feb 2010, 12:43
1
KUDOS
19
This post was
BOOKMARKED
00:00

Difficulty:

25% (medium)

Question Stats:

66% (00:52) correct 34% (00:45) wrong based on 1363 sessions

### HideShow timer Statistics

Is rst = 1 ?

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

Last edited by Bunuel on 07 Dec 2012, 09:01, edited 1 time in total.
Renamed the topic and edited the question.

Kudos [?]: 46 [1], given: 2

Math Expert
Joined: 02 Sep 2009
Posts: 41666

Kudos [?]: 124373 [6], given: 12077

Re: GMAT Paper test - Test Code 14 [#permalink]

### Show Tags

10 Feb 2010, 13:56
6
KUDOS
Expert's post
4
This post was
BOOKMARKED
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.

_________________

Kudos [?]: 124373 [6], given: 12077

Senior Manager
Joined: 22 Dec 2009
Posts: 356

Kudos [?]: 409 [5], given: 47

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

### Show Tags

14 Feb 2010, 11:34
5
KUDOS
2
This post was
BOOKMARKED
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.

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.

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!!

|For CR refer Powerscore CR Bible|For SC refer Manhattan SC Guide|

~~Better Burn Out... Than Fade Away~~

Kudos [?]: 409 [5], given: 47

Manager
Joined: 26 Feb 2015
Posts: 125

Kudos [?]: 23 [2], given: 43

Re: Is rst = 1 ? [#permalink]

### Show Tags

04 May 2015, 04:56
2
KUDOS
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

Kudos [?]: 23 [2], given: 43

e-GMAT Representative
Joined: 04 Jan 2015
Posts: 746

Kudos [?]: 2006 [2], given: 123

Is rst = 1 ? [#permalink]

### Show Tags

04 May 2015, 22:26
2
KUDOS
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

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
_________________

| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Kudos [?]: 2006 [2], given: 123

Manager
Joined: 26 Nov 2009
Posts: 163

Kudos [?]: 60 [1], given: 5

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

### Show Tags

15 Feb 2010, 06:32
1
KUDOS
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

Kudos [?]: 60 [1], given: 5

Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 1414

Kudos [?]: 759 [1], given: 5

Re: Is rst = 1 ? [#permalink]

### Show Tags

14 May 2016, 06:15
1
KUDOS
Expert's post
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.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Kudos [?]: 759 [1], given: 5

Senior Manager
Joined: 28 Jun 2009
Posts: 442

Kudos [?]: 189 [0], given: 46

Location: United States (MA)
Re: GMAT Paper test - Test Code 14 [#permalink]

### Show Tags

10 Feb 2010, 12:56
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.

Kudos [?]: 189 [0], given: 46

Intern
Joined: 06 Aug 2006
Posts: 21

Kudos [?]: 46 [0], given: 2

Re: GMAT Paper test - Test Code 14 [#permalink]

### Show Tags

10 Feb 2010, 13:21
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'

Kudos [?]: 46 [0], given: 2

Senior Manager
Joined: 28 Jun 2009
Posts: 442

Kudos [?]: 189 [0], given: 46

Location: United States (MA)
Re: GMAT Paper test - Test Code 14 [#permalink]

### Show Tags

10 Feb 2010, 13:51
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.

Kudos [?]: 189 [0], given: 46

Intern
Joined: 06 Aug 2006
Posts: 21

Kudos [?]: 46 [0], given: 2

Re: GMAT Paper test - Test Code 14 [#permalink]

### Show Tags

10 Feb 2010, 14:04
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.

OA is E. I get it now! Thank you!

Kudos [?]: 46 [0], given: 2

Manager
Joined: 09 Dec 2009
Posts: 120

Kudos [?]: 54 [0], given: 19

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

### Show Tags

14 Feb 2010, 11:19
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.

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 2: 07/10/10 - This time it's personal.

Kudos [?]: 54 [0], given: 19

Director
Joined: 27 Jun 2008
Posts: 541

Kudos [?]: 68 [0], given: 92

WE 1: Investment Banking - 6yrs
Re: OG DS 95, explain how my logic is wrong [#permalink]

### Show Tags

14 Feb 2010, 11:36
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.

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.

Kudos [?]: 68 [0], given: 92

Manager
Joined: 09 Dec 2009
Posts: 120

Kudos [?]: 54 [0], given: 19

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

### Show Tags

14 Feb 2010, 11:41
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!
_________________

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

Round 2: 07/10/10 - This time it's personal.

Kudos [?]: 54 [0], given: 19

Manager
Joined: 05 Oct 2011
Posts: 170

Kudos [?]: 54 [0], given: 62

Re: Is rst=1? Statement 1: rs=1 Statement 2: st=1 [#permalink]

### Show Tags

29 Nov 2011, 12:31
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

Kudos [?]: 54 [0], given: 62

Intern
Joined: 15 Nov 2012
Posts: 3

Kudos [?]: [0], given: 1

Re: Is rst = 1 ? [#permalink]

### Show Tags

29 Dec 2012, 12:27
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?

Kudos [?]: [0], given: 1

Math Expert
Joined: 02 Sep 2009
Posts: 41666

Kudos [?]: 124373 [0], given: 12077

Re: Is rst = 1 ? [#permalink]

### Show Tags

30 Dec 2012, 07:34
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.
_________________

Kudos [?]: 124373 [0], given: 12077

Manager
Joined: 18 Oct 2011
Posts: 90

Kudos [?]: 87 [0], given: 0

Location: United States
Concentration: Entrepreneurship, Marketing
GMAT Date: 01-30-2013
GPA: 3.3
Re: Is rst = 1 ? [#permalink]

### Show Tags

03 Jan 2013, 15:21
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

Kudos [?]: 87 [0], given: 0

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 17588

Kudos [?]: 270 [0], given: 0

Re: Is rst = 1 ? [#permalink]

### Show Tags

22 Apr 2014, 08:43
Hello from the GMAT Club BumpBot!

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.
_________________

Kudos [?]: 270 [0], given: 0

Intern
Joined: 15 Aug 2015
Posts: 3

Kudos [?]: 5 [0], given: 2

Location: United States
WE: Analyst (Consumer Products)
Re: Is rst = 1 ? [#permalink]

### Show Tags

30 Aug 2015, 16:18
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

Kudos [?]: 5 [0], given: 2

Re: Is rst = 1 ?   [#permalink] 30 Aug 2015, 16:18

Go to page    1   2    Next  [ 23 posts ]

Similar topics Replies Last post
Similar
Topics:
7 If r > s + t , is r positive? (1) s > t (2) r/(s+t) > 1 10 02 Apr 2016, 03:28
12 Is rst > rs/t? 9 24 Jun 2017, 05:01
Does rst = 1? (1) rs = –1 (2) rt = –1 6 29 Aug 2017, 01:45
2 Is rst > 1? 7 06 Jul 2017, 18:30
10 Is rst <= 1? 8 13 Mar 2016, 07:27
Display posts from previous: Sort by