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

It is currently 22 Aug 2018, 00:53

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

A number is said to be a “digifac” if each of its digits is a factor

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48119
A number is said to be a “digifac” if each of its digits is a factor  [#permalink]

Show Tags

New post 10 Sep 2015, 00:32
1
12
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

68% (01:25) correct 32% (01:44) wrong based on 197 sessions

HideShow timer Statistics

A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?

(A) 5
(B) 7
(C) 9
(D) 10
(E) 14

Kudos for a correct solution.

_________________

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

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6047
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
A number is said to be a “digifac” if each of its digits is a factor  [#permalink]

Show Tags

New post 10 Sep 2015, 01:23
1
3
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?

(A) 5
(B) 7
(C) 9
(D) 10
(E) 14



Let the missing digits be A, B. Then we should find five-digit digifac 9, 5, 3, A, B. First of all, it should be a multiple of 5. Since a multiple of 5 should have unit digit 0 or 5, B should be 5(since 0 cannot be a factor of an integer). Furthermore the sum of all digits of a multiple of 3 or 9 is also a multiple of 3 or 9. So 9+5+3+A+5 should be a multiple of 9(it’s enough to consider only 9, since a multiple of 9 is also a multiple of 3). Therefore 13+A should be multiple of 9. So A is 5. The answer is 5+5=10 --> D.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Manager
Manager
avatar
Joined: 10 Aug 2015
Posts: 103
GMAT ToolKit User
Re: A number is said to be a “digifac” if each of its digits is a factor  [#permalink]

Show Tags

New post 10 Sep 2015, 05:07
1
Bunuel wrote:
A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?

(A) 5
(B) 7
(C) 9
(D) 10
(E) 14

Kudos for a correct solution.


Solution: The number should be multiple of 5. So, the last digit is 5 or 0. But 0 cant be a factor. So, Last digit is 5. The sum of all digits should be a multiple of 9. Now the sum is 22. So, 4th digit should be 5. Therefore, required sum = 10

Option D
Manager
Manager
avatar
Joined: 29 Jul 2015
Posts: 159
GMAT ToolKit User
Re: A number is said to be a “digifac” if each of its digits is a factor  [#permalink]

Show Tags

New post 10 Sep 2015, 06:37
1
1
Bunuel wrote:
A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?

(A) 5
(B) 7
(C) 9
(D) 10
(E) 14

Kudos for a correct solution.


For the number to be divisible by 9, its sum should be a multiple of 9. This number will also be divisible by 3.
The sum of digits we have now is 9+5+3 = 17
For number to be divisible by 5, it's unit digit should be 0 or 5. But 0 cannot be a factor of any number as 0 multiplied with any number will be 0.
So, the unit's digit will be 5. The sum now becomes, 17+5 = 22
We need a multiple of 9 greater than 22 i.e 27.
so, the ten's digit will be 27-22 = 5.
and the sum of missing digits will be 5+5=10

Answer:- D
Director
Director
avatar
G
Joined: 21 May 2013
Posts: 649
Re: A number is said to be a “digifac” if each of its digits is a factor  [#permalink]

Show Tags

New post 10 Sep 2015, 07:06
1
Bunuel wrote:
A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?

(A) 5
(B) 7
(C) 9
(D) 10
(E) 14

Kudos for a correct solution.


For the number to be divisible by 3 and 9, the sum of the digits should be divisible by 3 and 9. Only D=10 satisfies. The sum is 27
Answer D
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48119
Re: A number is said to be a “digifac” if each of its digits is a factor  [#permalink]

Show Tags

New post 13 Sep 2015, 08:31
Bunuel wrote:
A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?

(A) 5
(B) 7
(C) 9
(D) 10
(E) 14

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works: the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.
_________________

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 48119
Re: A number is said to be a “digifac” if each of its digits is a factor  [#permalink]

Show Tags

New post 13 Sep 2015, 08:35
Bunuel wrote:
Bunuel wrote:
A number is said to be a “digifac” if each of its digits is a factor of the number itself. What is the sum of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ?

(A) 5
(B) 7
(C) 9
(D) 10
(E) 14

Kudos for a correct solution.


VERITAS PREP OFFICIAL SOLUTION:

Here, the term “digifac” should look intimidating. You probably haven’t studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs aren’t being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, too…) will see the unfamiliar term “digifac” and lose faith immediately. “I don’t know what that is!” She who finds the challenge in the GMAT fun, however, will read the definition and think “got it – I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factors”. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isn’t an option. Why not? That would require 0 to be one of the digits…and 0 isn’t a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works: the correct answer is D, and more importantly this fun challenge required no “trivial” information about digifacs…that term only existed to obscure the link between the given information and the path to the answer.


Check other Special Numbers and Sequences questions in our Special Questions Directory.
_________________

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
avatar
S
Joined: 29 Sep 2017
Posts: 113
Location: United States
Concentration: Strategy, Leadership
GMAT 1: 720 Q49 V39
GPA: 3.3
WE: Consulting (Consulting)
GMAT ToolKit User Reviews Badge
Re: A number is said to be a “digifac” if each of its digits is a factor  [#permalink]

Show Tags

New post 27 Jul 2018, 13:41
Hmm good question, got me thinking a bit. It's just recognizing divisibility rules. If each digit is a factor, then the number must be divisible by 3, 5, 9 (all provided). Everything divisible by 9 is divisible by 3 so ignore 3. If we take 9 + 5 + 3, we get 17. The only way to get a number divisible by 9 and 5 is to have it be a multiple of 9 and end in 5 or 0. Only adding 10 (D) gives a choice that is divisible by 9 and ends in 0.
_________________

If this helped, please give kudos!

Re: A number is said to be a “digifac” if each of its digits is a factor &nbs [#permalink] 27 Jul 2018, 13:41
Display posts from previous: Sort by

A number is said to be a “digifac” if each of its digits is a factor

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

Events & Promotions

PREV
NEXT


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®.