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

It is currently 20 Nov 2018, 23:57

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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • All GMAT Club Tests are Free and open on November 22nd in celebration of Thanksgiving Day!

     November 22, 2018

     November 22, 2018

     10:00 PM PST

     11:00 PM PST

    Mark your calendars - All GMAT Club Tests are free and open November 22nd to celebrate Thanksgiving Day! Access will be available from 0:01 AM to 11:59 PM, Pacific Time (USA)
  • Free lesson on number properties

     November 23, 2018

     November 23, 2018

     10:00 PM PST

     11:00 PM PST

    Practice the one most important Quant section - Integer properties, and rapidly improve your skills.

A set of numbers is defined such that if x and y are in the

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

Hide Tags

Intern
Intern
avatar
Joined: 01 May 2013
Posts: 10
A set of numbers is defined such that if x and y are in the  [#permalink]

Show Tags

New post Updated on: 15 Oct 2017, 08:42
5
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

61% (00:56) correct 39% (01:11) wrong based on 173 sessions

HideShow timer Statistics

A set of numbers is defined such that if x and y are in the set, xy is also in the set. If 2 and 6 are in the set, which of the following must also be in the set?

I. 3
II. 12
III. 24

A. None
B. I only
C. II only
D. I and II only
E. II and III only


Hey Guys,

I am confused here. Please help. According to me the following is the logic:

2, 6 are in the set, then 2*6 = 12 is also in the set
if 6 and 2 are in the set then 2*3=6 ==> 3 must be also in the set
if 12 and 2 are in the set then 2*12 = 24 should also be in the set

So according to me all 3 options are possible in the set. However such an option does not exist. Please clarify.

Thanks.

Originally posted by kalravaibhav on 03 Oct 2013, 11:21.
Last edited by Bunuel on 15 Oct 2017, 08:42, edited 2 times in total.
Renamed the topic and edited the question.
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4488
Re: A set of numbers is defined such that if x and y are in the  [#permalink]

Show Tags

New post 03 Oct 2013, 12:44
4
kalravaibhav wrote:
A set of numbers is defined such that if x and y are in the set, xy is also in the set. If 2 and 6 are in the set, which of the following must also be in the set?
I. 3
II. 12
III. 24

a) None
b) I only
c) II only
d) I and II only
e) II and III only

Hey Guys,

I am confused here. Please help. According to me the following is the logic:

2, 6 are in the set, then 2*6 = 12 is also in the set
if 6 and 2 are in the set then 2*3=6 ==> 3 must be also in the set
if 12 and 2 are in the set then 2*12 = 24 should also be in the set

So according to me all 3 options are possible in the set. However such an option does not exist. Please clarify.

Thanks.

Dear kalravaibhav,
Be careful about switching parts of the premise and conclusion in an IF-THEN statement. The statement If P, then Q does not imply If Q, then P. Similarly, the statement If P and Q, then T does not implies If P and T, then Q. That's the transformation you did.
TRUE: if x and y are in the set, the xy is also in the set
FALSE: if x and xy are in the set, then y is also in the set
That's precisely the logic you followed in the line of yours that I marked in red. That's not true ---- in fact, that was precisely the trap of the question, inducing folks to make this incorrect logical deduction.

Does all this make sense?
Mike :-)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Manager
Manager
avatar
Joined: 26 Sep 2013
Posts: 196
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: A set of numbers is defined such that if x and y are in the  [#permalink]

Show Tags

New post 03 Oct 2013, 17:54
got it correct, but honestly I guessed.

You don't know if 2 or 6 are x or y. There could be 30 numbers in this set, and who knows what X and Y will be. All you know is two of the numbers in the set, so you can't know what other numbers have to be in it. Poorly worded question IMO
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50712
Re: A set of numbers is defined such that if x and y are in the  [#permalink]

Show Tags

New post 03 Oct 2013, 23:32
kalravaibhav wrote:
A set of numbers is defined such that if x and y are in the set, xy is also in the set. If 2 and 6 are in the set, which of the following must also be in the set?

I. 3
II. 12
III. 24

A. None
B. I only
C. II only
D. I and II only
E. II and III only


Hey Guys,

I am confused here. Please help. According to me the following is the logic:

2, 6 are in the set, then 2*6 = 12 is also in the set
if 6 and 2 are in the set then 2*3=6 ==> 3 must be also in the set
if 12 and 2 are in the set then 2*12 = 24 should also be in the set

So according to me all 3 options are possible in the set. However such an option does not exist. Please clarify.

Thanks.


Similar questions to practice:
a-set-of-numbers-has-the-property-that-for-any-number-t-in-t-98829.html
for-a-certain-set-of-numbers-if-x-is-in-the-set-then-x-136580.html
if-p-is-a-set-of-integers-and-3-is-in-p-is-every-positive-96630.html
k-is-a-set-of-integers-such-that-if-the-integer-r-is-in-k-103005.html
k-is-a-set-of-numbers-such-that-i-if-x-is-in-k-then-x-96907.html

Hope this helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4488
Re: A set of numbers is defined such that if x and y are in the  [#permalink]

Show Tags

New post 04 Oct 2013, 12:10
2
AccipiterQ wrote:
got it correct, but honestly I guessed.

You don't know if 2 or 6 are x or y. There could be 30 numbers in this set, and who knows what X and Y will be. All you know is two of the numbers in the set, so you can't know what other numbers have to be in it. Poorly worded question IMO

Dear AccipiterQ,
First of all, I am just going to recommend a grammar correction in what you have written:
"You don't know whether 2 or 6 are x or y."
That's a very typical GMAT SC trap. See:
http://magoosh.com/gmat/2012/gmat-sente ... s-whether/

I would say --- the wording of this question is very clear. I would call this a high quality, well-written question.

The issue you raise ---- we don't know whether the numbers given equal x or y --- this betrays a subtle misunderstanding. In some algebra problems, the "solve for x" variety of problems, x or y or any variable will have one definite value, or perhaps two possible values, and the point is to find those individual values. In many other algebraic situations, the variables are general variables that don't have specific values. For example, when we have the equation of the graph of a line in the x-y plane, such as y = 2x - 3, the x & y don't have individual specific values --- rather, the x & y coordinates of every point on the line, the whole continuous infinity of them, satisfy the equation. Thus, the x & y could be any one of a whole infinity of values, and yet it's very precise and clear which x' & y's could or couldn't fit the pattern.

In this set, it is unambiguous from context --- x and y are general variables that could equal any member of the set. If we know a number is in the set, that number could equal x or y. At the outset, the only known members of the set are 2 & 6, so either could be x, and either could be y. That's how we know 12 must be in the set. There's nothing saying that x and y have to be different, so if we pick x = y = 2, then 4 has to be in the set, and if we pick x = y = 6, then 36 has to be in the set. With just this analysis, we see the members of the set must include {2, 4, 6, 12, 36}. Now, any of those five numbers could be x, and any of the five could be y. Thus, if we pick x = 2 and y = 12, we see that 24 must be in the set. In fact, for what it's worth, here is the full set of all numbers less than 100 that must be in the set
{2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96}
Many other numbers could be in the set, but those are the ones that absolutely have to be in the set, no question.

It's true --- many other element could be in the set, but that's not the question. The question is unambiguously clear: "which of the following must also be in the set?" From the analysis above, we see that 12 and 24 absolutely must be in the set, no doubt. It's true, 3 could be in the set, but that's strictly irrelevant to this particular question.

My friend, it is crucially important for you to understand: any ambiguity you experience in this question does not lie in the wording of the question itself, but in subtle gaps in your own understanding. I want you to understand this, so you resolve these issues and don't have this same ambiguous experience on test day.

Let me know if you have any further questions.

Mike :-)
_________________

Mike McGarry
Magoosh Test Prep


Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Manager
Manager
avatar
Joined: 26 Sep 2013
Posts: 196
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Re: A set of numbers is defined such that if x and y are in the  [#permalink]

Show Tags

New post 04 Oct 2013, 16:31
mikemcgarry wrote:
AccipiterQ wrote:
got it correct, but honestly I guessed.

You don't know if 2 or 6 are x or y. There could be 30 numbers in this set, and who knows what X and Y will be. All you know is two of the numbers in the set, so you can't know what other numbers have to be in it. Poorly worded question IMO

Dear AccipiterQ,
First of all, I am just going to recommend a grammar correction in what you have written:
"You don't know whether 2 or 6 are x or y."
That's a very typical GMAT SC trap. See:
http://magoosh.com/gmat/2012/gmat-sente ... s-whether/

I would say --- the wording of this question is very clear. I would call this a high quality, well-written question.

The issue you raise ---- we don't know whether the numbers given equal x or y --- this betrays a subtle misunderstanding. In some algebra problems, the "solve for x" variety of problems, x or y or any variable will have one definite value, or perhaps two possible values, and the point is to find those individual values. In many other algebraic situations, the variables are general variables that don't have specific values. For example, when we have the equation of the graph of a line in the x-y plane, such as y = 2x - 3, the x & y don't have individual specific values --- rather, the x & y coordinates of every point on the line, the whole continuous infinity of them, satisfy the equation. Thus, the x & y could be any one of a whole infinity of values, and yet it's very precise and clear which x' & y's could or couldn't fit the pattern.

In this set, it is unambiguous from context --- x and y are general variables that could equal any member of the set. If we know a number is in the set, that number could equal x or y. At the outset, the only known members of the set are 2 & 6, so either could be x, and either could be y. That's how we know 12 must be in the set. There's nothing saying that x and y have to be different, so if we pick x = y = 2, then 4 has to be in the set, and if we pick x = y = 6, then 36 has to be in the set. With just this analysis, we see the members of the set must include {2, 4, 6, 12, 36}. Now, any of those five numbers could be x, and any of the five could be y. Thus, if we pick x = 2 and y = 12, we see that 24 must be in the set. In fact, for what it's worth, here is the full set of all numbers less than 100 that must be in the set
{2, 4, 6, 8, 12, 16, 24, 32, 36, 48, 64, 72, 96}
Many other numbers could be in the set, but those are the ones that absolutely have to be in the set, no question.

It's true --- many other element could be in the set, but that's not the question. The question is unambiguously clear: "which of the following must also be in the set?" From the analysis above, we see that 12 and 24 absolutely must be in the set, no doubt. It's true, 3 could be in the set, but that's strictly irrelevant to this particular question.

My friend, it is crucially important for you to understand: any ambiguity you experience in this question does not lie in the wording of the question itself, but in subtle gaps in your own understanding. I want you to understand this, so you resolve these issues and don't have this same ambiguous experience on test day.

Let me know if you have any further questions.

Mike :-)



Oh my goodness....you probably just added 30 points onto my GMAT score with this post alone. Seriously, on practice tests I have gotten EVERY one of these questions wrong. Wow....that is so clear now...I just had a 'light bulb' go off over my head. So based on being given 2 and 6, you could come up with an infinite number of numbers that have to be in the set then, yes?


P.S. Thank you for the SC tip, I've managed to go from getting about 20% of them right to about 90% right by picking up tips like that, every one helps.
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8869
Premium Member
Re: A set of numbers is defined such that if x and y are in the  [#permalink]

Show Tags

New post 15 Sep 2018, 22:39
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: A set of numbers is defined such that if x and y are in the &nbs [#permalink] 15 Sep 2018, 22:39
Display posts from previous: Sort by

A set of numbers is defined such that if x and y are in the

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


cron
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®.