November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 AM PST. Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. November 17, 2018 November 17, 2018 09:00 AM PST 11:00 AM PST Join the Quiz Saturday November 17th, 9 AM PST. The Quiz will last approximately 2 hours. Make sure you are on time or you will be at a disadvantage.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Aug 2009
Posts: 7035

How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such
[#permalink]
Show Tags
21 Jul 2018, 03:58
Question Stats:
23% (01:54) correct 77% (01:32) wrong based on 90 sessions
HideShow timer Statistics
How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such that the 3digit number formed is a multiple of 3? (A) 6 (B) 24 (C) 27 (D) 28 (E) 64 New question !!!..
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Ask GMAT Experts Forum Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 983
Location: India
GPA: 3.64

Re: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such
[#permalink]
Show Tags
21 Jul 2018, 04:18
chetan2u wrote: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such that the 3digit number formed is a multiple of 3? (A) 6 (B) 24 (C) 27 (D) 28 (E) 64
New question !!!.. Multiple of 3 means the sum of the digits of the 3digit number must be divisible by 3. We observe that if the no. contains 8, it cannot form a no. divisible by 3 except when all the digits are 8 i.e. 888. (Check 3+6+8=17, 6+9+8=23 etc...) Nos. that can be formed by digits 3,6,9 are 3x3x3=27, since each digit can be formed by these 3 digits to obtain a no. divisible by 3. But we have to count the possibility of 888, so total nos. = 27+1=28. Answer D.
_________________
Please give kudos, if you like my post
When the going gets tough, the tough gets going...



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)

Re: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such
[#permalink]
Show Tags
21 Jul 2018, 04:32
chetan2u wrote: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such that the 3digit number formed is a multiple of 3? (A) 6 (B) 24 (C) 27 (D) 28 (E) 64
New question !!!.. Here we have two sets of numbers viz, {3,6,9} and {8}; those form 3digit numbers a multiple of 3. 1. Considering the set {3,6,9}, We have \(3^3\) nos of 3digit numbers a multiple of 3. (Since it's not explicitly mentioned; We have to treat that repetition is allowed) 2. Considering the set {8}, We have only 1 three digit number(888) multiple of 3. (8+8+8=24 is a multiple of 3) So, total no of 3digit number=27+1=28 Ans. (D)
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine



VP
Joined: 09 Mar 2016
Posts: 1076

Re: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such
[#permalink]
Show Tags
23 Jul 2018, 06:22
souvonik2k wrote: chetan2u wrote: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such that the 3digit number formed is a multiple of 3? (A) 6 (B) 24 (C) 27 (D) 28 (E) 64
New question !!!.. Multiple of 3 means the sum of the digits of the 3digit number must be divisible by 3. We observe that if the no. contains 8, it cannot form a no. divisible by 3 except when all the digits are 8 i.e. 888. (Check 3+6+8=17, 6+9+8=23 etc...) Nos. that can be formed by digits 3,6,9 are 3x3x3=27, since each digit can be formed by these 3 digits to obtain a no. divisible by 3. But we have to count the possibility of 888, so total nos. = 27+1=28. Answer D. souvonik2k Hi there Why do you say "Multiple of 3 means the sum of the digits of the 3digit number must be divisible by 3. Where is it mentoned 'the sum of the digits" it could be PRODUCT OF THREE DIGITS as well please explain thanks, D.



Math Expert
Joined: 02 Aug 2009
Posts: 7035

Re: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such
[#permalink]
Show Tags
23 Jul 2018, 06:51
dave13 wrote: souvonik2k wrote: chetan2u wrote: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such that the 3digit number formed is a multiple of 3? (A) 6 (B) 24 (C) 27 (D) 28 (E) 64
New question !!!.. Multiple of 3 means the sum of the digits of the 3digit number must be divisible by 3. We observe that if the no. contains 8, it cannot form a no. divisible by 3 except when all the digits are 8 i.e. 888. (Check 3+6+8=17, 6+9+8=23 etc...) Nos. that can be formed by digits 3,6,9 are 3x3x3=27, since each digit can be formed by these 3 digits to obtain a no. divisible by 3. But we have to count the possibility of 888, so total nos. = 27+1=28. Answer D. souvonik2k Hi there Why do you say "Multiple of 3 means the sum of the digits of the 3digit number must be divisible by 3. Where is it mentoned 'the sum of the digits" it could be PRODUCT OF THREE DIGITS as well please explain thanks, D. Hi.. There are certain divisibility rules .. For 3 and 9, it is that if sum of the digit is div by 3 or 9, the numy is divisible by 3 or 9.. Example.. 363...3+6+3=12 div by 3, do 363 is div by 3 but not by 9 as 12 is not div by 9... 999999999999 will be div by both 3 and 9 Some more rules can be seen in the following post. https://gmatclub.com/forum/divisibilitymultiplesfactorstipsandhints174998.html?hilit=Divisibility%20by%209
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



VP
Joined: 09 Mar 2016
Posts: 1076

Re: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such
[#permalink]
Show Tags
23 Jul 2018, 07:54
PKN wrote: chetan2u wrote: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such that the 3digit number formed is a multiple of 3? (A) 6 (B) 24 (C) 27 (D) 28 (E) 64
New question !!!.. Here we have two sets of numbers viz, {3,6,9} and {8}; those form 3digit numbers a multiple of 3. 1. Considering the set {3,6,9}, We have \(3^3\) nos of 3digit numbers a multiple of 3. (Since it's not explicitly mentioned; We have to treat that repetition is allowed) 2. Considering the set {8}, We have only 1 three digit number(888) multiple of 3. (8+8+8=24 is a multiple of 3) So, total no of 3digit number=27+1=28 Ans. (D) hey there PKN if repetition is allowed (and you wrote 888) then how about number 333 3+3+3 =9 is a multtiple of 3 and how about 9+9+9 = 27 is multiple of 3 so whats wrong then with my reasoning now



Math Expert
Joined: 02 Aug 2009
Posts: 7035

Re: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such
[#permalink]
Show Tags
23 Jul 2018, 08:07
dave13 wrote: PKN wrote: chetan2u wrote: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such that the 3digit number formed is a multiple of 3? (A) 6 (B) 24 (C) 27 (D) 28 (E) 64
New question !!!.. Here we have two sets of numbers viz, {3,6,9} and {8}; those form 3digit numbers a multiple of 3. 1. Considering the set {3,6,9}, We have \(3^3\) nos of 3digit numbers a multiple of 3. (Since it's not explicitly mentioned; We have to treat that repetition is allowed) 2. Considering the set {8}, We have only 1 three digit number(888) multiple of 3. (8+8+8=24 is a multiple of 3) So, total no of 3digit number=27+1=28 Ans. (D) hey there PKN if repetition is allowed (and you wrote 888) then how about number 333 3+3+3 =9 is a multtiple of 3 and how about 9+9+9 = 27 is multiple of 3 so whats wrong then with my reasoning now Dave.. When you write 3*3*3, it includes all possibilities.. Each 3 in 3*3*3 means that any of the three digits 3,6,9 can be used.. So it includes 333,336,339,369,396,366 and so on
_________________
1) Absolute modulus : http://gmatclub.com/forum/absolutemodulusabetterunderstanding210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effectsofarithmeticoperationsonfractions269413.html
GMAT online Tutor



Ask GMAT Experts Forum Moderator
Status: Preparing for GMAT
Joined: 25 Nov 2015
Posts: 983
Location: India
GPA: 3.64

Re: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such
[#permalink]
Show Tags
23 Jul 2018, 08:08
dave13 wrote: PKN wrote: chetan2u wrote: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such that the 3digit number formed is a multiple of 3? (A) 6 (B) 24 (C) 27 (D) 28 (E) 64
New question !!!.. Here we have two sets of numbers viz, {3,6,9} and {8}; those form 3digit numbers a multiple of 3. 1. Considering the set {3,6,9}, We have \(3^3\) nos of 3digit numbers a multiple of 3. (Since it's not explicitly mentioned; We have to treat that repetition is allowed) 2. Considering the set {8}, We have only 1 three digit number(888) multiple of 3. (8+8+8=24 is a multiple of 3) So, total no of 3digit number=27+1=28 Ans. (D) hey there PKN if repetition is allowed (and you wrote 888) then how about number 333 3+3+3 =9 is a multtiple of 3 and how about 9+9+9 = 27 is multiple of 3 so whats wrong then with my reasoning now Hi 333, 999 and 666 are already covered in 3^3=27, but 888 is not covered. So it is added and answer is 27+1=28. Hope it is clear.
_________________
Please give kudos, if you like my post
When the going gets tough, the tough gets going...



Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 930
WE: Supply Chain Management (Energy and Utilities)

Re: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such
[#permalink]
Show Tags
23 Jul 2018, 08:18
dave13 wrote: PKN wrote: chetan2u wrote: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such that the 3digit number formed is a multiple of 3? (A) 6 (B) 24 (C) 27 (D) 28 (E) 64
New question !!!.. Here we have two sets of numbers viz, {3,6,9} and {8}; those form 3digit numbers a multiple of 3. 1. Considering the set {3,6,9}, We have \(3^3\) nos of 3digit numbers a multiple of 3. (Since it's not explicitly mentioned; We have to treat that repetition is allowed) 2. Considering the set {8}, We have only 1 three digit number(888) multiple of 3. (8+8+8=24 is a multiple of 3) So, total no of 3digit number=27+1=28 Ans. (D) hey there PKN if repetition is allowed (and you wrote 888) then how about number 333 3+3+3 =9 is a multiple of 3 and how about 9+9+9 = 27 is multiple of 3 so whats wrong then with my reasoning now Hi dave13, 333, 999,666 these are already included in 3^3 nos of 3digit numbers ,a multiple of 3. Had it been a case of "repetition is not allowed" then we had to exclude 333,666,999,888,336,363,663 etc.....so on... Thanking You. P.S: 1. The number of permutations of 'n' different things taken 'r' at a time , when each is allowed to repeat any number of times in each arrangement is \(n^r\). Here 3 different digits{3,6,9} are to be taken 3 at a time(since we have to form a 3digit number), hence no of permutations/arrangements=\(3^3\) 2. If repetition of digits is not allowed then the number of possible 3digits arrangements =nPn=3P3=3!
_________________
Regards,
PKN
Rise above the storm, you will find the sunshine




Re: How many 3digit numbers can be formed from digits 3, 6, 8 and 9 such &nbs
[#permalink]
23 Jul 2018, 08:18






