Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Sep 2014, 04:33

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If each of the two digits X and Y is distinct

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
User avatar
Joined: 28 Apr 2012
Posts: 310
Location: India
GMAT 1: 610 Q49 V23
GMAT 2: 650 Q48 V31
GMAT 3: 770 Q50 V47
WE: Information Technology (Computer Software)
Followers: 13

Kudos [?]: 190 [0], given: 142

If each of the two digits X and Y is distinct [#permalink] New post 28 Aug 2012, 05:56
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

28% (02:02) correct 72% (01:59) wrong based on 32 sessions
If each of the two digits X and Y is distinct, is the two digit integer XY prime?

(1) Each of the digits X and Y is the sum of 2 distinct single digit prime numbers.

(2) The sum of digits X and Y is 16.
[Reveal] Spoiler: OA

_________________

"Appreciation is a wonderful thing. It makes what is excellent in others belong to us as well."
― Voltaire


Press Kudos, if I have helped.
Thanks!

shit-happens-my-journey-to-172475.html#p1372807

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23500
Followers: 3508

Kudos [?]: 26578 [1] , given: 2713

Re: If each of the two digits X and Y is distinct [#permalink] New post 28 Aug 2012, 06:15
1
This post received
KUDOS
Expert's post
ahmed2502 wrote:
If each of the two digits X and Y is distinct, is the two digit integer XY prime?

(1) Each of the digits X and Y is the sum of 2 distinct single digit prime numbers.

(2) The sum of digits X and Y is 16.


[Reveal] Spoiler:
OA. C
OE:
Statement (1) means that X or Y can take on the values 5, 7, 8, 9 each of which can be made by adding two distinct single digit prime numbers. Now, plug in to evaluate the statement. If XY = 75, then the answer to the question is no. However, if XY = 59, then the answer to the question is yes. The correct answer must be B, C or E. Statement (2) is also insufficient. If XY = 88, the answer is no but if XY = 79, the answer is yes. Cross off B. If the statements are combined, then only two numbers, 79 and 97, satisfy both conditions and both are prime.
The correct answer is C.

I choose B. It is given X and Y are different, so XY=88 in second case is not possible.


You are right, answer must be B:

(2) The sum of digits X and Y is 16. There are only three such two-digit numbers possible: 79, 97 and 88, but since we are told that X and Y are distinct then 88 is out and we are left with two prime numbers - 79 and 97.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Current Student
avatar
Joined: 14 May 2011
Posts: 277
Location: Costa Rica
Concentration: Healthcare, International Business
GMAT 1: 640 Q V0
GMAT 2: 710 Q42 V45
GMAT 3: 740 Q48 V42
GMAT 4: Q V0
GMAT 5: Q V0
GPA: 3.3
WE: Research (Consulting)
Followers: 11

Kudos [?]: 68 [0], given: 134

GMAT Tests User
Re: If each of the two digits X and Y is distinct [#permalink] New post 31 Aug 2012, 07:23
Bunuel wrote:
OE:
Statement (1) means that X or Y can take on the values 5, 7, 8, 9 each of which can be made by adding two distinct single digit prime numbers. Now, plug in to evaluate the statement. If XY = 75, then the answer to the question is no. However, if XY = 59, then the answer to the question is yes. The correct answer must be B, C or E. Statement (2) is also insufficient. If XY = 88, the answer is no but if XY = 79, the answer is yes. Cross off B. If the statements are combined, then only two numbers, 79 and 97, satisfy both conditions and both are prime.
The correct answer is C.

I choose B. It is given X and Y are different, so XY=88 in second case is not possible.[/spoiler]



Hi Bunuel/Ahmed, could you please explain again as I'm getting a definite "no" from (1) and a "yes" from (2), which is not possible of course:
(1)The option XY = 75 can not exist, note it says that X & Y are both the sum of distinct prime numbers, so X and Y must each be one of the following options -> 4 (1+3), 6 (1+5), 8 (1+7 OR 5+3). So that gives only even XY options which can not be prime.

Thus (1) is a definite "NO", so its either A or D
(2) X+Y=16, so as you mentioned its 88, 79, 97 - 88 goes out as its not distinct for X & Y, so YES as they're both prime.

Not sure what I'm doing wrong here. Would appreciate your clarification!
_________________


How to improve your RC score, pls Kudo if helpful! http://gmatclub.com/forum/how-to-improve-my-rc-accuracy-117195.html
Work experience (as of June 2012)
2.5 yrs (Currently employed) - Mckinsey & Co. (US Healthcare Analyst)
2 yrs - Advertising industry (client servicing)

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23500
Followers: 3508

Kudos [?]: 26578 [0], given: 2713

Re: If each of the two digits X and Y is distinct [#permalink] New post 31 Aug 2012, 07:39
Expert's post
Aximili85 wrote:
Bunuel wrote:
OE:
Statement (1) means that X or Y can take on the values 5, 7, 8, 9 each of which can be made by adding two distinct single digit prime numbers. Now, plug in to evaluate the statement. If XY = 75, then the answer to the question is no. However, if XY = 59, then the answer to the question is yes. The correct answer must be B, C or E. Statement (2) is also insufficient. If XY = 88, the answer is no but if XY = 79, the answer is yes. Cross off B. If the statements are combined, then only two numbers, 79 and 97, satisfy both conditions and both are prime.
The correct answer is C.

I choose B. It is given X and Y are different, so XY=88 in second case is not possible.[/spoiler]



Hi Bunuel/Ahmed, could you please explain again as I'm getting a definite "no" from (1) and a "yes" from (2), which is not possible of course:
(1)The option XY = 75 can not exist, note it says that X & Y are both the sum of distinct prime numbers, so X and Y must each be one of the following options -> 4 (1+3), 6 (1+5), 8 (1+7 OR 5+3). So that gives only even XY options which can not be prime.

Thus (1) is a definite "NO", so its either A or D
(2) X+Y=16, so as you mentioned its 88, 79, 97 - 88 goes out as its not distinct for X & Y, so YES as they're both prime.

Not sure what I'm doing wrong here. Would appreciate your clarification!


1 is not a prime number. Single digit primes are:
2, 3, 5, and 7. So, x and y could be: 2+3=5, 2+5=7, 2+7=9, 3+5=8 --> xy could be: 57, 75, 58, 85, 59, 95, 78, 87, 79, 97, 89 and 98. Some numbers are prime (for example 79) and some are not (for example 75).

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Status: GMATting
Joined: 21 Mar 2011
Posts: 108
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Followers: 1

Kudos [?]: 59 [0], given: 104

GMAT ToolKit User
Re: If each of the two digits X and Y is distinct [#permalink] New post 03 Sep 2012, 01:45
Hi Bunuel,

I have a question here: I agree that the 2nd statement leads to 79, 97 and 88. While the 1st statement states that each of the digits in X and Y need to be single digit prime numbers, can we definitively conclude, using the 2nd statement, that 79 or 97 is a prime number? Since 9 is not a prime number, can both statements contradict or am I missing something here?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23500
Followers: 3508

Kudos [?]: 26578 [1] , given: 2713

Re: If each of the two digits X and Y is distinct [#permalink] New post 03 Sep 2012, 01:50
1
This post received
KUDOS
Expert's post
nutshell wrote:
Hi Bunuel,

I have a question here: I agree that the 2nd statement leads to 79, 97 and 88. While the 1st statement states that each of the digits in X and Y need to be single digit prime numbers, can we definitively conclude, using the 2nd statement, that 79 or 97 is a prime number? Since 9 is not a prime number, can both statements contradict or am I missing something here?


(1) doesn't say that X and Y must be primes, it says that "each of the digits X and Y is the sum of 2 distinct single digit prime numbers". So, x and y could be: 2+3=5, 2+5=7, 2+7=9, or 3+5=8.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
User avatar
Status: GMATting
Joined: 21 Mar 2011
Posts: 108
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
Followers: 1

Kudos [?]: 59 [0], given: 104

GMAT ToolKit User
Re: If each of the two digits X and Y is distinct [#permalink] New post 03 Sep 2012, 01:59
Hi Bunuel,

Thanks for the quick reply. I misunderstood the statement in the first read. :(
Re: If each of the two digits X and Y is distinct   [#permalink] 03 Sep 2012, 01:59
    Similar topics Author Replies Last post
Similar
Topics:
If x and y are two distinct prime numbers, which of the following cann PareshGmat 0 09 Sep 2014, 20:37
2 Experts publish their posts in the topic If x and y are two distinct positive integers, is x/y an int alphonsa 9 18 Aug 2014, 08:00
1 Experts publish their posts in the topic If x and y are distinct prime numbers, each greater than 2, nades09 4 13 Nov 2010, 10:09
If points X and Y are two distinct points in the coordinate HVD1975 1 09 Sep 2008, 08:48
If points X and Y are two distinct points in the coordinate nupurgupt 3 24 Mar 2007, 10:30
Display posts from previous: Sort by

If each of the two digits X and Y is distinct

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.