It is currently 21 Oct 2017, 18:26

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

Events & Promotions in June
Open Detailed Calendar

M26-17

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129173 [0], given: 12194

M26-17 [#permalink]

Show Tags

New post 16 Sep 2014, 01:25
Expert's post
8
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

75% (01:40) correct 25% (01:09) wrong based on 71 sessions

HideShow timer Statistics

The numbers {1, 3, 6, 7, 7, 7} are used to form three 2-digit numbers. If the sum of these three numbers is a prime number \(p\), what is the largest possible value of \(p\)?

A. 97
B. 151
C. 209
D. 211
E. 219
[Reveal] Spoiler: OA

_________________

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

Kudos [?]: 129173 [0], given: 12194

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129173 [1], given: 12194

Re M26-17 [#permalink]

Show Tags

New post 16 Sep 2014, 01:25
1
This post received
KUDOS
Expert's post
Official Solution:

The numbers {1, 3, 6, 7, 7, 7} are used to form three 2-digit numbers. If the sum of these three numbers is a prime number \(p\), what is the largest possible value of \(p\)?

A. 97
B. 151
C. 209
D. 211
E. 219


What is the largest possible sum of these three numbers that we can form? Maximize the first digit: \(76+73+71=220=even\), so not a prime. Let's try next largest sum, switch digits in 76 and we'll get: \(67+73+71=211=prime\).


Answer: D
_________________

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

Kudos [?]: 129173 [1], given: 12194

Manager
Manager
User avatar
Joined: 11 Sep 2013
Posts: 149

Kudos [?]: 144 [0], given: 156

Concentration: Finance, Finance
Re: M26-17 [#permalink]

Show Tags

New post 18 Mar 2015, 10:20
When we say that we will make three 2 digit numbers from (1,3,6,7,7,7), it is clear that we have to use these numbers. Besides, notice carefully that 7 is already repeating. So, it is clear that we have to make three numbers by using each and every given number once because there are 6 numbers.

Actually we are not doing hit and trial. Our target is to make highest possible numbers. So we are carefully picking digits to make largest possible numbers.

Kudos [?]: 144 [0], given: 156

Manager
Manager
avatar
B
Joined: 02 Sep 2014
Posts: 90

Kudos [?]: 237 [0], given: 32

Location: United States
Schools: Haas EWMBA '20
GMAT 1: 770 Q50 V44
GPA: 3.97
GMAT ToolKit User Reviews Badge
Re: M26-17 [#permalink]

Show Tags

New post 27 Jun 2015, 14:08
Is there a better way to find out how 3 numbers will add to a prime? Obviously 1 of 3 or 3 of 3 have to be odd, but anything else?

Kudos [?]: 237 [0], given: 32

Intern
Intern
avatar
Joined: 06 Jul 2014
Posts: 20

Kudos [?]: 12 [0], given: 5

WE: Supply Chain Management (Manufacturing)
Re M26-17 [#permalink]

Show Tags

New post 09 Mar 2016, 11:13
why can't any no be used repetitively?

Kudos [?]: 12 [0], given: 5

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129173 [0], given: 12194

Re: M26-17 [#permalink]

Show Tags

New post 09 Mar 2016, 11:29

Kudos [?]: 129173 [0], given: 12194

Intern
Intern
avatar
Joined: 20 Jan 2016
Posts: 12

Kudos [?]: 3 [0], given: 16

Re: M26-17 [#permalink]

Show Tags

New post 11 Apr 2016, 13:11
How are you supposed to know 211 is prime is 2 min? I have no idea. Yes you can check numbers up to 20, but how do we know?

Kudos [?]: 3 [0], given: 16

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129173 [1], given: 12194

Re: M26-17 [#permalink]

Show Tags

New post 12 Apr 2016, 06:57
1
This post received
KUDOS
Expert's post

Kudos [?]: 129173 [1], given: 12194

Intern
Intern
avatar
Joined: 20 Jan 2016
Posts: 12

Kudos [?]: 3 [0], given: 16

Re: M26-17 [#permalink]

Show Tags

New post 12 Apr 2016, 07:04
Thank you so much for your reply. I want to start off by thanking you for the incredible content you have posted here for eveyone to use. Your solutions are simple and witty. I really appreciate your style and I will you all the best!!

I did take a look at the post that you referred to. I do understand how we typically carry out prime factorizations, but in this case, the factor could 29 or 57 for example, in that case, it is extremely difficult to know if it is a prime number or not. My question really is: prime number don't have a formula, so how do we know if such a large number is a prime without checking if it's divisible by a bunch of numbers, which makes the questions impossible.

Thank you in advance and keep rocking!!

Kudos [?]: 3 [0], given: 16

Expert Post
1 KUDOS received
Math Forum Moderator
avatar
B
Joined: 20 Mar 2014
Posts: 2675

Kudos [?]: 1728 [1], given: 792

Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
GMAT ToolKit User Premium Member Reviews Badge
M26-17 [#permalink]

Show Tags

New post 12 Apr 2016, 07:07
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
NothingComes3asy wrote:
How are you supposed to know 211 is prime is 2 min? I have no idea. Yes you can check numbers up to 20, but how do we know?


For primality, all you need to do is to check for divisibility of the number in question by prime numbers from 2 to \(\sqrt{number}\)

Example, for checking primality of 211 ---> \(\sqrt {211}\) \(\approx\) 15 (but less than 15, you need to remember square of numbers 1 to 20 and cubes of 1 to 10 for GMAT). Thus you need to check divisibility of 211 by prime numbers from 2 to 14 (=2,3,5,7,11,13)

For this, remember the divisibility tests --->

211 is NOT even ---> eliminate 2,4,6,8,10,12,14
211 by 3 ---> sum of the digits \(\neq\) divisible by 3 ---> eliminate 3,6,9,12
211 by 5---> does not end in 5 or 0 ---> eliminate 5 and 10
211 by 7 ---> 210 is clearly divisible by 7 --> 211 can not be divisible by 7 ---> eliminate 7 and 14.
211 by 11 ---> |sum of odd place digits - sum of even place digits| = |2+1-1| = 2 = NOT a multiple of 11 ---> eliminate 11
211 by 13 ---> regular division is the only way ---> 130 is a multiple of 13 and 211 is 81 more than 13 ---> as 81 is NOT a multiple of 13 ---> eliminate 13.

Thus, 211 IS a prime number.

Hope this helps.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Inequalities tips: http://gmatclub.com/forum/inequalities-tips-and-hints-175001.html
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Kudos [?]: 1728 [1], given: 792

Expert Post
1 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129173 [1], given: 12194

Re: M26-17 [#permalink]

Show Tags

New post 12 Apr 2016, 07:09
1
This post received
KUDOS
Expert's post
NothingComes3asy wrote:
Thank you so much for your reply. I want to start off by thanking you for the incredible content you have posted here for eveyone to use. Your solutions are simple and witty. I really appreciate your style and I will you all the best!!

I did take a look at the post that you referred to. I do understand how we typically carry out prime factorizations, but in this case, the factor could 29 or 57 for example, in that case, it is extremely difficult to know if it is a prime number or not. My question really is: prime number don't have a formula, so how do we know if such a large number is a prime without checking if it's divisible by a bunch of numbers, which makes the questions impossible.

Thank you in advance and keep rocking!!


To check whether 211 is prime you should try dividing by prime numbers up to \(\sqrt{211}\approx{14.5}\), so you should try dividing 211 by 2, 3, 5, 7, 11 and 13.
_________________

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

Kudos [?]: 129173 [1], given: 12194

Intern
Intern
User avatar
Joined: 08 Feb 2016
Posts: 46

Kudos [?]: 21 [0], given: 14

Premium Member
Re: M26-17 [#permalink]

Show Tags

New post 27 Jul 2016, 00:37
An alternate way to solve
The numbers {1, 3, 6, 7, 7, 7} are to be used to form three 2-digit numbers.

Let the numbers be AB, CD, EF so their sum can be expressed as (A+C+E)*10 + (B+D+F).
In the sum (A+C+E)*10 + (B+D+F), the first term ends with zero (multiplying by "0"), so the units digit is not impacted by the first term.

As we want to maximize the number, we should maximize the total for (A+C+E). So we can use the numbers {7, 7, 7}. This leaves out {1, 3, 6}. The total of units digits {1, 3, 6} ends in zero, hence cannot be a prime [A number > 10, ending with 0, 5, or even cannot be prime].

So lets switch a 7 from 10's with the next largest number i.e., 6. The sets are {6, 7, 7} and {1, 3, 7}. The units digit are now {1, 3, 7} = 11, ends with 1. So can be prime.
The total now is {6 + 7 + 7} *10 + {1 + 3 + 7} = 20*10 + 11 = 211, which is prime.

Thanks
_________________

Once you know the answer, it is easy to justify.

Kudos [?]: 21 [0], given: 14

Manager
Manager
avatar
B
Joined: 23 Apr 2014
Posts: 67

Kudos [?]: 6 [0], given: 82

Location: United States
GMAT 1: 680 Q50 V31
GPA: 2.75
Reviews Badge
Re: M26-17 [#permalink]

Show Tags

New post 01 Aug 2016, 15:05
In case of prime number with number of digits > 1, I think unit digit of number will have to be 1,3,7 or 9. It cannot end with 5 and (no chance for 2 as well).
We can use this point as well while selecting the numbers.

Please correct me if we cannot use this point.

Kudos [?]: 6 [0], given: 82

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129173 [0], given: 12194

Re: M26-17 [#permalink]

Show Tags

New post 02 Aug 2016, 00:23
PerseveranceWins wrote:
In case of prime number with number of digits > 1, I think unit digit of number will have to be 1,3,7 or 9. It cannot end with 5 and (no chance for 2 as well).
We can use this point as well while selecting the numbers.

Please correct me if we cannot use this point.

______________
Yes, that's correct.
_________________

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

Kudos [?]: 129173 [0], given: 12194

Manager
Manager
avatar
B
Joined: 23 Apr 2014
Posts: 67

Kudos [?]: 6 [0], given: 82

Location: United States
GMAT 1: 680 Q50 V31
GPA: 2.75
Reviews Badge
Re: M26-17 [#permalink]

Show Tags

New post 02 Aug 2016, 11:18
Bunuel wrote:
PerseveranceWins wrote:
In case of prime number with number of digits > 1, I think unit digit of number will have to be 1,3,7 or 9. It cannot end with 5 and (no chance for 2 as well).
We can use this point as well while selecting the numbers.

Please correct me if we cannot use this point.

______________
Yes, that's correct.


Thanks for confirming.

Kudos [?]: 6 [0], given: 82

Intern
Intern
avatar
Joined: 27 Oct 2015
Posts: 20

Kudos [?]: [0], given: 8

Re: M26-17 [#permalink]

Show Tags

New post 14 Dec 2016, 03:37
Hi Buenel,

The numbers {1, 3, 6, 7, 7, 7} are used to form three 2-digit numbers. If the sum of these three numbers is a prime number pp, what is the largest possible value of pp?

Do such type of questions mean that we have to use all the numbers given?

I know this is not prime, but if 77+77+77 =prime, could not that be the correct answer?

Many Thanks.

Kudos [?]: [0], given: 8

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 41892

Kudos [?]: 129173 [0], given: 12194

Re: M26-17 [#permalink]

Show Tags

New post 14 Dec 2016, 04:18
dsheth7 wrote:
Hi Buenel,

The numbers {1, 3, 6, 7, 7, 7} are used to form three 2-digit numbers. If the sum of these three numbers is a prime number pp, what is the largest possible value of pp?

Do such type of questions mean that we have to use all the numbers given?

I know this is not prime, but if 77+77+77 =prime, could not that be the correct answer?

Many Thanks.


I understand what you mean. The answer is no, you have only three 7's, so that's the maximum number of 7's you can use to form a number.
_________________

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

Kudos [?]: 129173 [0], given: 12194

Intern
Intern
avatar
B
Joined: 02 Oct 2016
Posts: 36

Kudos [?]: 11 [0], given: 20

Schools: HEC Dec '17
Re: M26-17 [#permalink]

Show Tags

New post 02 Feb 2017, 22:23
I'm not sure if this approach is correct but I will explain my reasoning.

The sum of all the number in the set add up to 31. Now 3+1=4 (sum of digits)
For every possible combination of different 2 digit numbers using the numbers from the given set, the sum of digits when reduced to a single digit must be 4.

A; 97 -> 9+7 = 16 -> 1+6=7
B: 151 -> 1+5+1 = 7
C: 209 -> 2+0+9 = 11 -> 1+1 = 2
D: 211 - > 2+1+1 = 4 (matches)
E: 219 -> 2+1+9 = 12 -> 1+2

Of course, if there were two options which summed up to 4, you'd have to make a guess. But I suppose an educated guess is better than a random one.

Kudos [?]: 11 [0], given: 20

Intern
Intern
avatar
Joined: 15 Feb 2015
Posts: 2

Kudos [?]: [0], given: 1

Re: M26-17 [#permalink]

Show Tags

New post 27 Mar 2017, 10:50
My alternative approach:

{1, 3, 6, 7, 7, 7} -> we need a prime number -> each of the 3 numbers has to be odd (as there is only one even digit in the set), thus, the biggest odd numbers are:

77
73
61
=====
= 211 (prime)

Kudos [?]: [0], given: 1

Intern
Intern
avatar
Joined: 20 Mar 2017
Posts: 1

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

Re: M26-17 [#permalink]

Show Tags

New post 01 May 2017, 20:50
The Unit digit has to be 1,7, or 9 (from the answer choice) the only combo that will give you one of them is 7,3,1 . Just take it from there. so you have
-7
-3
-1

only make sense to put 7 with 7
7 with 3
and 6 with 1
in order to get the max.

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

Re: M26-17   [#permalink] 01 May 2017, 20:50

Go to page    1   2    Next  [ 24 posts ] 

Display posts from previous: Sort by

M26-17

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

Moderators: Bunuel, Vyshak



GMAT Club MBA Forum Home| About| Terms and Conditions| 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®.