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

It is currently 18 Nov 2018, 19:06

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
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

If each of the two digits X and Y is distinct

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

Hide Tags

Senior Manager
Senior Manager
User avatar
Joined: 28 Apr 2012
Posts: 284
Location: India
Concentration: Finance, Technology
GMAT 1: 650 Q48 V31
GMAT 2: 770 Q50 V47
WE: Information Technology (Computer Software)
If each of the two digits X and Y is distinct  [#permalink]

Show Tags

New post 28 Aug 2012, 05:56
3
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

49% (02:17) correct 51% (02:17) wrong based on 100 sessions

HideShow timer Statistics

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.

_________________

"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!

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: If each of the two digits X and Y is distinct  [#permalink]

Show Tags

New post 28 Aug 2012, 06:15
2
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.


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 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

Senior Manager
Senior Manager
avatar
Joined: 14 May 2011
Posts: 254
Location: Costa Rica
Concentration: Healthcare, International Business
GMAT 1: 710 Q42 V45
GMAT 2: 740 Q48 V42
GPA: 3.3
WE: Research (Consulting)
Re: If each of the two digits X and Y is distinct  [#permalink]

Show Tags

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)

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: If each of the two digits X and Y is distinct  [#permalink]

Show Tags

New post 31 Aug 2012, 07:39
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 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

Manager
Manager
User avatar
Status: GMATting
Joined: 21 Mar 2011
Posts: 105
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
GMAT ToolKit User
Re: If each of the two digits X and Y is distinct  [#permalink]

Show Tags

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?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50627
Re: If each of the two digits X and Y is distinct  [#permalink]

Show Tags

New post 03 Sep 2012, 01:50
1
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 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

Manager
Manager
User avatar
Status: GMATting
Joined: 21 Mar 2011
Posts: 105
Concentration: Strategy, Technology
GMAT 1: 590 Q45 V27
GMAT ToolKit User
Re: If each of the two digits X and Y is distinct  [#permalink]

Show Tags

New post 03 Sep 2012, 01:59
Hi Bunuel,

Thanks for the quick reply. I misunderstood the statement in the first read. :(
CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3122
Location: Canada
Re: If each of the two digits X and Y is distinct  [#permalink]

Show Tags

New post 25 Aug 2018, 05:47
Top Contributor
ConnectTheDots 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.


Target question: Is the two-digit integer xy prime?

Given: Each of the two digits x and y is distinct

Statement 1: Each of the digits x and y is the sum of 2 distinct single digit prime numbers.
Let's TEST some values.
There are several values of x and y that satisfy statement 1. Here are two:
Case a: x = 3 + 5 = 8 and y = 2 + 7 = 9. So, xy = 89. In this case, the answer to the target question is YES, xy IS prime
Case b: x = 2 + 7 = 9 and y = 3 + 5 = 8. So, xy = 98. In this case, the answer to the target question is NO, xy is NOT prime
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The sum of digits x and y is 16
Since x and y are DISTINCT, there are only 2 possible ways to get a sum of 16. Let's examine each possible case:
Case a: x = 7 and y = 9. So, xy = 79. In this case, the answer to the target question is YES, xy IS prime
Case b: x = 9 and y = 7. So, xy = 97. In this case, the answer to the target question is YES, xy IS prime
Since each possible case yields the SAME answer to the target question, it MUST be the case that xy IS prime
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

GMAT Club Bot
Re: If each of the two digits X and Y is distinct &nbs [#permalink] 25 Aug 2018, 05:47
Display posts from previous: Sort by

If each of the two digits X and Y is distinct

  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®.