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

It is currently 20 Aug 2014, 18:31

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

The sum of two number is 588 and their HCF is 49. How many

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 09 Feb 2012
Posts: 48
Followers: 0

Kudos [?]: 10 [0], given: 14

The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 07 Jun 2012, 11:44
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

36% (02:08) correct 64% (01:23) wrong based on 111 sessions
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

A. 6
B. 5
C. 4
D. 3
E. 2
[Reveal] Spoiler: OA

Last edited by Bunuel on 08 Jun 2012, 05:34, edited 2 times in total.
Edited the question and added the OA
Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24407 [2] , given: 2677

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 07 Jun 2012, 12:14
2
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
NYC5648 wrote:
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

A 6
B. 5
C. 4
D. 3
E. 2


The question should read:

The sum of two positive integers is 588 and their greatest common factor is 49. How many such pairs of numbers can be formed?

We are told that the greatest common factor of two integers is 49. So, these integers are 49x and 49y, for some positive integers x and y. Notice that x and y must not share any common factor but 1, because if they do then GCF of 49x and 49y will be more that 49.

Next, we know that 49x+49y=588 --> x+y=12 --> since x and y don't share any common factor but 1 then (x, y) can be only (1, 11) and (5, 7) (all other pairs (2, 10), (3, 9), (4, 8), (6, 6) do share common factor greater than 1). So, there are only two pairs of such numbers possible: 49*1=49 and 49*11=539 AND 49*5=245 and 49*7=343.

Answer: E.

P.S. Please read and follow: 11-rules-for-posting-133935.html (points 3 and 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

Senior Manager
Senior Manager
User avatar
Joined: 13 Jan 2012
Posts: 304
Weight: 170lbs
GMAT 1: 730 Q48 V42
GMAT 2: 740 Q48 V42
WE: Analyst (Other)
Followers: 9

Kudos [?]: 64 [0], given: 36

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 07 Jun 2012, 13:05
Bunuel wrote:
NYC5648 wrote:
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

A 6
B. 5
C. 4
D. 3
E. 2


The question should read:

The sum of two positive integers is 588 and their greatest common factor is 49. How many such pairs of numbers can be formed?

We are told that the greatest common factor of two integers is 49. So, these integers are 49x and 49y, for some positive integers x and y. Notice that x and y must not share any common factor but 1, because if they do then GCF of 49x and 49y will be more that 49.

Next, we know that 49x+49y=588 --> x+y=12 --> since x and y don't share any common factor but 1 then (x, y) can be only (1, 11) and (5, 7) (all other pairs (2, 10), (3, 9), (4, 8), (6, 6) do share common factor greater than 1). So, there are only two pairs of such numbers possible: 49*1=49 and 49*11=539 AND 49*5=245 and 49*7=343.

Answer: E.

P.S. Please read and follow: 11-rules-for-posting-133935.html (points 3 and 8).


Awesome explanation! I was wondering what difficulty level you found this question? This seems pretty complicated to me.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24407 [0], given: 2677

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 07 Jun 2012, 13:11
Expert's post
vandygrad11 wrote:
Bunuel wrote:
NYC5648 wrote:
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

A 6
B. 5
C. 4
D. 3
E. 2


The question should read:

The sum of two positive integers is 588 and their greatest common factor is 49. How many such pairs of numbers can be formed?

We are told that the greatest common factor of two integers is 49. So, these integers are 49x and 49y, for some positive integers x and y. Notice that x and y must not share any common factor but 1, because if they do then GCF of 49x and 49y will be more that 49.

Next, we know that 49x+49y=588 --> x+y=12 --> since x and y don't share any common factor but 1 then (x, y) can be only (1, 11) and (5, 7) (all other pairs (2, 10), (3, 9), (4, 8), (6, 6) do share common factor greater than 1). So, there are only two pairs of such numbers possible: 49*1=49 and 49*11=539 AND 49*5=245 and 49*7=343.

Answer: E.

P.S. Please read and follow: 11-rules-for-posting-133935.html (points 3 and 8).


Awesome explanation! I was wondering what difficulty level you found this question? This seems pretty complicated to me.


I'd say it's about 650+ level question.
_________________

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
avatar
Joined: 12 May 2012
Posts: 85
Location: India
Concentration: General Management, Operations
GMAT 1: 650 Q51 V25
GMAT 2: 730 Q50 V38
GMAT 3: Q V
GPA: 4
WE: General Management (Transportation)
Followers: 2

Kudos [?]: 40 [0], given: 14

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 08 Jun 2012, 05:33
I choose the wrong option A. :oops:

The moment I clicked and saw the correct as E, I realised my mistake.

I hope to not do it in my test.

A simple and nice explanation Bunuel.
Manager
Manager
avatar
Joined: 15 Apr 2012
Posts: 95
Location: Bangladesh
Concentration: Technology, Entrepreneurship
GMAT 1: 460 Q38 V17
GMAT 2: Q V
GPA: 3.56
Followers: 0

Kudos [?]: 9 [0], given: 134

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 08 Jun 2012, 07:49
Bunuel wrote:
NYC5648 wrote:
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

A 6
B. 5
C. 4
D. 3
E. 2


The question should read:

The sum of two positive integers is 588 and their greatest common factor is 49. How many such pairs of numbers can be formed?

We are told that the greatest common factor of two integers is 49. So, these integers are 49x and 49y, for some positive integers x and y. Notice that x and y must not share any common factor but 1, because if they do then GCF of 49x and 49y will be more that 49.

Next, we know that 49x+49y=588 --> x+y=12 --> since x and y don't share any common factor but 1 then (x, y) can be only (1, 11) and (5, 7) (all other pairs (2, 10), (3, 9), (4, 8), (6, 6) do share common factor greater than 1). So, there are only two pairs of such numbers possible: 49*1=49 and 49*11=539 AND 49*5=245 and 49*7=343.

Answer: E.

P.S. Please read and follow: 11-rules-for-posting-133935.html (points 3 and 8).


Hi,Can you please explain how you got the value 49x and 49y?if you give me an example that will be great...Thanks
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24407 [1] , given: 2677

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 08 Jun 2012, 07:53
1
This post received
KUDOS
Expert's post
farukqmul wrote:
Bunuel wrote:
NYC5648 wrote:
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

A 6
B. 5
C. 4
D. 3
E. 2


The question should read:

The sum of two positive integers is 588 and their greatest common factor is 49. How many such pairs of numbers can be formed?

We are told that the greatest common factor of two integers is 49. So, these integers are 49x and 49y, for some positive integers x and y. Notice that x and y must not share any common factor but 1, because if they do then GCF of 49x and 49y will be more that 49.

Next, we know that 49x+49y=588 --> x+y=12 --> since x and y don't share any common factor but 1 then (x, y) can be only (1, 11) and (5, 7) (all other pairs (2, 10), (3, 9), (4, 8), (6, 6) do share common factor greater than 1). So, there are only two pairs of such numbers possible: 49*1=49 and 49*11=539 AND 49*5=245 and 49*7=343.

Answer: E.

P.S. Please read and follow: 11-rules-for-posting-133935.html (points 3 and 8).


Hi,Can you please explain how you got the value 49x and 49y?if you give me an example that will be great...Thanks


Since 49 is the greatest common factor of two integers, then 49 is a factor of both, so we can express one of them as 49x and another as 49y. For example one of them can be 49x=49*1=49 or 49*x=49*5=245.

Hope it's clear.
_________________

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
avatar
Joined: 26 Dec 2011
Posts: 117
Followers: 1

Kudos [?]: 9 [0], given: 17

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 14 Jun 2012, 23:15
@ farukqmul: To answer your question, 49x+49y: We know that the GCF of the two number x and y is 49, which means that these number definitely have 49 common in both, thus, it translates to that they are definitely multiples of 49. Thus, x+y=588 can be rewritten as 49x + 49y = 588, I hope I have answered your question.
Intern
Intern
avatar
Joined: 09 Feb 2012
Posts: 48
Followers: 0

Kudos [?]: 10 [0], given: 14

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 28 Jul 2012, 04:53
Hi Bunuel,

could you please explain why (1,11) and (5,7) are the only possible pairs.

I still don't get it.

Many thanks!

Great weekend!
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24407 [1] , given: 2677

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 28 Jul 2012, 05:05
1
This post received
KUDOS
Expert's post
NYC5648 wrote:
Hi Bunuel,

could you please explain why (1,11) and (5,7) are the only possible pairs.

I still don't get it.

Many thanks!

Great weekend!


Because if x and y are for example 2 and 10, respectively, the greatest common factor of 49x=98 and 49y=490 will be 98, so more than 49. That's because x and y, in this case, share a common factor greater than 1. Only if x and y are 1 and 11 OR 5 and 7 (so only when x and y do not share any common factor more than 1) the greatest common factor of 49x and 49y will be 49.

Hope it's clear.
_________________

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
avatar
Joined: 26 Dec 2011
Posts: 117
Followers: 1

Kudos [?]: 9 [0], given: 17

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 28 Jul 2012, 05:10
To answer your question why only these two pairs are possible:

we know that 49 is the GCF of two numbers and their sum is 588, so let it be x+y = 588. Further, given that their GCF is 49, they can be written as 49x + 49y = 588.

In other words, x+y = 12. Now the important thing is that x and y must be selected in such a way that their should be no additional factor, otherwise, the GCF will not remain 49. For example, let x and y be 4 and 8..sum being 12 but the GCF of the numbers (49*4 and 49*8) will be more than 49, hence you cannot take this pair. and if you write down the pairs then only 1,11 and 5,7 satisfy as they do not have any factor in common.

I hope this helps.

NYC5648 wrote:
Hi Bunuel,

could you please explain why (1,11) and (5,7) are the only possible pairs.

I still don't get it.

Many thanks!

Great weekend!
Intern
Intern
avatar
Joined: 09 Feb 2012
Posts: 48
Followers: 0

Kudos [?]: 10 [0], given: 14

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 28 Jul 2012, 06:25
I got it!! Thanks you Bunuel!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24407 [0], given: 2677

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 26 Jun 2013, 01:25
Expert's post
Bumping for review and further discussion*. Get a kudos point for an alternative solution!

*New project from GMAT Club!!! Check HERE

All DS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=354
All PS Divisibility/Multiples/Factors questions to practice: search.php?search_id=tag&tag_id=185

_________________

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

Intern
Intern
avatar
Joined: 28 Jan 2011
Posts: 24
Followers: 1

Kudos [?]: 3 [0], given: 15

The sum of two numbers is 588 and their HCF is 49. How many [#permalink] New post 06 Sep 2013, 13:11
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

(a) 1
(b) 2
(c) 3
(d) 4
(e) 5


[Reveal] Spoiler:
My approach:

49 = 7^2 is the greatest common factor, thus both numbers must contain 7^2.

So, one pair would be: 49 and 539 (from 588-49). Both contain 7^2 if you prime factor them. The prime factorization of 539 is 7^2 x 11.

Another pair would be: 7^3 = 343 and 245 (from 588-343). The prime factorization of 245 is 7^2 x 5 and thus contains 7^2.

Since 7^4 exceeds 588, we can stop looking for further pairs.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24407 [0], given: 2677

Re: The sum of two numbers is 588 and their HCF is 49. How many [#permalink] New post 06 Sep 2013, 13:28
Expert's post
salsal wrote:
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

(a) 1
(b) 2
(c) 3
(d) 4
(e) 5


[Reveal] Spoiler:
My approach:

49 = 7^2 is the greatest common factor, thus both numbers must contain 7^2.

So, one pair would be: 49 and 539 (from 588-49). Both contain 7^2 if you prime factor them. The prime factorization of 539 is 7^2 x 11.

Another pair would be: 7^3 = 343 and 245 (from 588-343). The prime factorization of 245 is 7^2 x 5 and thus contains 7^2.

Since 7^4 exceeds 588, we can stop looking for further pairs.


Merging similar topics. Please refer to the solutions above.
_________________

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
avatar
Joined: 11 Jul 2012
Posts: 51
GMAT 1: 650 Q49 V29
Followers: 0

Kudos [?]: 5 [0], given: 19

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 07 Sep 2013, 23:24
Bunuel wrote:
NYC5648 wrote:
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

A 6
B. 5
C. 4
D. 3
E. 2


The question should read:

The sum of two positive integers is 588 and their greatest common factor is 49. How many such pairs of numbers can be formed?

We are told that the greatest common factor of two integers is 49. So, these integers are 49x and 49y, for some positive integers x and y. Notice that x and y must not share any common factor but 1, because if they do then GCF of 49x and 49y will be more that 49.

Next, we know that 49x+49y=588 --> x+y=12 --> since x and y don't share any common factor but 1 then (x, y) can be only (1, 11) and (5, 7) (all other pairs (2, 10), (3, 9), (4, 8), (6, 6) do share common factor greater than 1). So, there are only two pairs of such numbers possible: 49*1=49 and 49*11=539 AND 49*5=245 and 49*7=343.

Answer: E.

P.S. Please read and follow: 11-rules-for-posting-133935.html (points 3 and 8).



Hi Bunuel.... aren't we supposed to count the two pairs (1,11) and (5,7) twice? "unique pair" is not mentioned in the question. Aren't we supposed to mark C(4 pairs) as the right choice?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19030
Followers: 3361

Kudos [?]: 24407 [0], given: 2677

Re: The sum of two number is 588 and their HCF is 49. How many [#permalink] New post 08 Sep 2013, 05:20
Expert's post
avaneeshvyas wrote:
Bunuel wrote:
NYC5648 wrote:
The sum of two numbers is 588 and their HCF is 49. How many such pairs of numbers can be formed?

A 6
B. 5
C. 4
D. 3
E. 2


The question should read:

The sum of two positive integers is 588 and their greatest common factor is 49. How many such pairs of numbers can be formed?

We are told that the greatest common factor of two integers is 49. So, these integers are 49x and 49y, for some positive integers x and y. Notice that x and y must not share any common factor but 1, because if they do then GCF of 49x and 49y will be more that 49.

Next, we know that 49x+49y=588 --> x+y=12 --> since x and y don't share any common factor but 1 then (x, y) can be only (1, 11) and (5, 7) (all other pairs (2, 10), (3, 9), (4, 8), (6, 6) do share common factor greater than 1). So, there are only two pairs of such numbers possible: 49*1=49 and 49*11=539 AND 49*5=245 and 49*7=343.

Answer: E.

P.S. Please read and follow: 11-rules-for-posting-133935.html (points 3 and 8).



Hi Bunuel.... aren't we supposed to count the two pairs (1,11) and (5,7) twice? "unique pair" is not mentioned in the question. Aren't we supposed to mark C(4 pairs) as the right choice?


How is (49, 539) different from (539, 49)?
_________________

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

Re: The sum of two number is 588 and their HCF is 49. How many   [#permalink] 08 Sep 2013, 05:20
    Similar topics Author Replies Last post
Similar
Topics:
HCF of two numbers is 23. Find the smaller of the two number cumulonimbus 4 07 May 2014, 21:28
7 Experts publish their posts in the topic If the LCM of two numbers a and b is 1104 and their HCF is 4 ricsingh 5 09 Apr 2014, 09:24
The sum of two numbers is 588 and their HCF is 49. How many salsal 0 06 Sep 2013, 13:11
1 Sum of two numbers mdfrahim 2 12 Jun 2009, 11:37
The sum of two numbers is 216 and thier HCF or GCD is 27 rxs0005 2 28 Dec 2004, 18:18
Display posts from previous: Sort by

The sum of two number is 588 and their HCF is 49. How many

  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®.