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

It is currently 24 May 2019, 10:17

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel

If r and s are positive numbers and θ is one of the operations, +, −,

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

Hide Tags

 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55271
If r and s are positive numbers and θ is one of the operations, +, −,  [#permalink]

Show Tags

New post 26 Apr 2019, 02:30
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

85% (01:19) correct 15% (01:23) wrong based on 89 sessions

HideShow timer Statistics

Director
Director
User avatar
D
Joined: 18 Jul 2018
Posts: 906
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
Premium Member Reviews Badge
Re: If r and s are positive numbers and θ is one of the operations, +, −,  [#permalink]

Show Tags

New post 26 Apr 2019, 04:32
From S1:

r = s (both positive numbers)
r θ s = 0, then θ can only be subtraction.
Sufficient.

From S2:

r ≠ s, then r θ s ≠ s θ r
Let r = 3
s = 4
addition and multiplication will be the same.
but, 3-4 ≠ 4-3
also, 3/4 ≠ 4/3
Hence θ can be - or /
Insufficient.

A is the answer.
_________________
Press +1 Kudo If my post helps!
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3529
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: If r and s are positive numbers and θ is one of the operations, +, −,  [#permalink]

Show Tags

New post 27 Apr 2019, 07:04
Bunuel wrote:
If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?

(1) If r = s, then r θ s = 0.
(2) If r ≠ s, then r θ s ≠ s θ r.



DS37502.01
OG2020 NEW QUESTION


#1
If r = s, then r θ s = 0
only subtraction possible ; sufficeint
#2
f r ≠ s, then r θ s ≠ s θ r.
then addition , multiplication possible
insufficient
IMO A
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Intern
Intern
User avatar
S
Joined: 14 Apr 2017
Posts: 44
Location: Hungary
GMAT 1: 690 Q50 V34
GMAT 2: 760 Q50 V42
GMAT 3: 700 Q50 V33
WE: Education (Education)
CAT Tests
Re: If r and s are positive numbers and θ is one of the operations, +, −,  [#permalink]

Show Tags

New post 27 Apr 2019, 07:35
Bunuel wrote:
If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?

(1) If r = s, then r θ s = 0.
(2) If r ≠ s, then r θ s ≠ s θ r.


DS37502.01
OG2020 NEW QUESTION


We know that \(r\) and \(s\) are positive numbers and θ is one of the 4 basic operations. The original question: Which operation is θ ?

1) If \(r=s\), then

\(r+s=r+r>0\)

\(r-s=r-r=0\)

\(r\cdot s=r\cdot r>0\)

\(\frac{r}{s}=\frac{r}{r}=1\neq 0\)

θ must be subtraction. Thus, we can get a definite answer to the original question. \(\implies\) Sufficient

2) If \(r\neq s\), then

\(r+s=s+r\)

\(r-s\neq s-r\) since the two sides have different signs.

\(r\cdot s=s\cdot r\)

\(\frac{r}{s}\neq \frac{s}{r}\) since one of the sides has a value greater than 1, while the other side has a value less than 1.

θ can be either subtraction or division. Thus, we can't get a definite answer to the original question. \(\implies\) Insufficient

Answer: A
_________________
CEO
CEO
User avatar
V
Joined: 12 Sep 2015
Posts: 3727
Location: Canada
Re: If r and s are positive numbers and θ is one of the operations, +, −,  [#permalink]

Show Tags

New post 30 Apr 2019, 08:06
Top Contributor
Bunuel wrote:
If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?

(1) If r = s, then r θ s = 0.
(2) If r ≠ s, then r θ s ≠ s θ r.



DS37502.01
OG2020 NEW QUESTION


Given: r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷

Target question: Which operation is θ ?

Statement 1: If r = s, then r θ s = 0
Keep in mind that r and s are POSITIVE
So, we have POSITIVE θ POSITIVE = 0

POSITIVE + POSITIVE ≠ 0 So, θ cannot represent addition
POSITIVE - POSITIVE = 0 So, θ COULD represent subtraction
POSITIVE × POSITIVE ≠ 0 So, θ cannot represent multiplication
POSITIVE ÷ POSITIVE ≠ 0 So, θ cannot represent division
The answer to the target question is θ represents subtraction
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: If r ≠ s, then r θ s ≠ s θ r
Let's test some values for each possible operation.
1 ≠ 2, yet 1 + 2 = 2 + 1. So, θ cannot be addition
1 ≠ 2, yet 1 x 2 = 2 x 1. So, θ cannot be multiplication

If r and s are DIFFERENT positive numbers, then r - s will never equal s - r. So, θ COULD represent subtraction
If r and s are DIFFERENT positive numbers, then r ÷ s will never equal s ÷ r. So, θ COULD represent division
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6231
Location: United States (CA)
Re: If r and s are positive numbers and θ is one of the operations, +, −,  [#permalink]

Show Tags

New post 06 May 2019, 20:19
Bunuel wrote:
If r and s are positive numbers and θ is one of the operations, +, −, ×, or ÷, which operation is θ ?

(1) If r = s, then r θ s = 0.
(2) If r ≠ s, then r θ s ≠ s θ r.



DS37502.01
OG2020 NEW QUESTION


Statement One Alone:

If r = s, then r θ s = 0.

If r = s, then the only way for r θ s = 0 is for θ to represent subtraction.

Statement one alone is sufficient to answer the question.

Statement Two Alone:

If r ≠ s, then r θ s ≠ s θ r.

We can let r = 2 and s = 3.

We see that 2 - 3 does not equal 3 - 2 and 2/3 does not equal 3/2, thus θ could represent subtraction or division.

Statement two alone is not sufficient to answer the question.

Answer: A
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

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.

EMPOWERgmat Instructor
User avatar
V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14198
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: If r and s are positive numbers and θ is one of the operations, +, −,  [#permalink]

Show Tags

New post 21 May 2019, 15:58
Hi All,

We're told that R and S are POSITIVE NUMBERS and θ is one of the operations add, subtract, multiply or divide. We're asked which operation is θ. This question comes down to some basic Arithmetic and TESTing VALUES.

(1) If R =S, then R θ S = 0.

With the information in Fact 1, we have to check the 4 possible operations to see which one(s) fit the given equation.
IF....
R=S=1....
1 + 1 = 2 this is NOT a match
1 - 1 = 0 this IS a match
(1)(1) = 1 this is NOT a match
1/1 = 1 this is NOT a match

The ONLY operation that fits is SUBTRACTION, so that is the answer to the question.
Fact 1 is SUFFICIENT

(2) If R ≠ S, then R θ S ≠ S θ R

Just as we did with Fact 1, we have to check the 4 possible operations to see which one(s) fit the given equation (meaning that the two calculations do NOT equal one another).
IF....
R=1 and S=2....
1 + 2 = 3 IS equal to 2 + 1 = 3 this is NOT a match
1 - 2 = - 1 DOES NOT equal 2 - 1 = 1 this IS a match for the given information
(1)(2) = 2 IS equal to (2)(1) = 2 this is NOT a match
1/2 = 1/2 DOES NOT equal 2/1 = 2 this IS a match for the given information.

Thus, the operation could be either SUBTRACTION OR DIVISION.
Fact 2 is INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save $75 + GMAT Club Tests Free
  Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
GMAT Club Bot
Re: If r and s are positive numbers and θ is one of the operations, +, −,   [#permalink] 21 May 2019, 15:58
Display posts from previous: Sort by

If r and s are positive numbers and θ is one of the operations, +, −,

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.