# A stamp collector has the habit to arrange or rearrange the stamps accordingly. whiledoing this he some times keeps the stamps in pairs, or in group of 3 or in 4 or in or in 6 andrealises that in any case he is left with 1 stamp and when he arranges them in groups of 7 nostamps remain. what is the number of stamps he has?

• Oct 6th, 2006

Total number of stamps = 49

if grouped by 3,6,4 then 1 stamp will be left

#### Archana.G Profile

• Oct 6th, 2006

He keeps stamps in pairs,3's,4's ,5's and in 6's then 1 is left. when he aranges them in 7's then nothing is left so the number of stamps must be multiple of 7 so,(2*3*4*5*6)=720 therefore number of stamps are (720+1)=721 which is divisible by 7.

#### zakirhussain

• Oct 20th, 2006

The total no of stamps is 49, if he arrange the stamps in order of 2,3.4.6 there will be remining one but when he arrange it by 7 there will be none.

• Oct 25th, 2006

721 is correct, but, least possible no. is 427.49 is wrong b'coz, It has to give 1 as remainder when divided by 5. (not printed in the problem).Correct me if I'm wrong.....

#### prakash267 Profile Answers by prakash267

• Oct 31st, 2006

what u mean least possible is 427 if u divide that number with 4 or 5 it will give remainder other than one plse explain me that one.

#### sovan

• Nov 13th, 2006

427 also gives reminder 2 not 1.................so 721 is absolutely correct and the least value

#### swarna

• Dec 1st, 2006

the answer should be a multiple of 7 bt not of 2, 3,4 or 6 and the number should always be one more than yhe multiples  of 2, 3, 4and 6... so 7 -ruled out. 14 ruled out 21- ruled out.so on ... 49 is right... (2*24+1),(3*16+1),(4*12+1),(6*8+1).. so v can conclude that the lest possible number is  49.

#### ravi setti

• Dec 20th, 2006

There can multiple answers for the question.... Mathematically, (n-1)=LCM(2,3,4,5,6)*k1 => (n-1)=60*k1 ---->(1) and n=7*k2 ----->(2) solve (1) & (2) we have n= 30*k1 + (7*k2+1)/2 where k1=(7*k2-1)%60few solutions:with k1=5 and k2=43 n= 301 ... least possible solution... with k1=12 and k2=103n=721and etc....Noticible: number k2 has 3 as last digit.

#### chanducoolboy Profile Answers by chanducoolboy

• Jan 15th, 2007

u r wrong bcoz when we divide 49 by 5 the remainder will be 4 not 1............

#### marian.chandan Profile Answers by marian.chandan

• Mar 4th, 2007

answer can also b 121, it is the least no. of stamps possible........

if one stamp is left if he makes groups of 2,3,4,6 then we have to find LCM of 2,3,4,6  which is 12 now since we get a remainder of 1 ... it shud b 12+1 ie 13

now we now tht the no. of stamps is exactly divisible by 7 therefore   no. of stamps = 13*7=121

#### Musturu Thippareddy

• Nov 11th, 2007

721 are also correct but the least posible answer is 121. Here the number should be multople of 2,3,4,5,6, so multiply 2*3*4*5 but not with 6 because if you multiply with 2 and 3 then that number must and should divisible by 6

#### meera_987 Profile Answers by meera_987

• Apr 21st, 2008

how is 121 divicible by 7 ??

#### johnjps Profile Answers by johnjps

• Jun 2nd, 2008

The answer is 301 or 601 or 901

#### praneet143 Profile Answers by praneet143

• Jun 19th, 2008

14 stamps if we pair 3's,4's,6's each pair we are left with one stamp but if we pair with 7's no stamp is left

#### subbu_4450 Profile Answers by subbu_4450

• Dec 7th, 2009

49 is the answer because for 2 3 4 and 6 49 gives remainder 1 and with 7 it is exactly divisible

#### neo.seekr Profile Answers by neo.seekr

• Dec 7th, 2009

Stamp collector make groups of 2,3,4,5,6

Therefore we shud take LCM of all these nos. which will be 60
Then according to question we will get eq.
60x+1=7n  (since in above gps 1 stamp is always left out but in gp of 7 it fits)

From the eq we can infer that no. of stamps must be of form _ _ 1
therefore n must be of type 3,13,23,..etc (so that on multiplying it by 7 we get 1 in LSD)
multiplying by these we get n=43 & x=5

ie No. of stamps will be 301 (and not 721 bcoz its min)

#### subutheboss Profile Answers by subutheboss

• Dec 18th, 2009

LCM of 2,3,4,6 is 12,
if grouped in 2,3,4,6 one is left therefore 12+1=13 not divisible by 7
(since no reminder wen groupd in 7),

(12*2)+1=25 (not divisble),
(12*3)+1=37 (not divisible),
(12*4)+1=49 (divisilble),
Thus ans is 49

#### utk186 Profile Answers by utk186

• Mar 30th, 2010

Let x be the No. of groups of 7 stamps
Total no. of stamps=7*x
Let a be the No. groups of pair of stamps
Let b be the No. of groups of 3 stamps
Let c be the No of groups of 4 stamps
Let d be the No. of groups of 6 stamps

Total no. of stamps=7*x=2*a+1      & a=7x-1/2
=7x=3*b+1        & b=7x-1/3
=7x=4*c+1        & c=7x-1/4
=7x=6*d+1        & d=7x-1/6
Solving the above eqs we get x=7 which satisfies the above eqs.
Hence total no of stamps=7*x=7*7=49

• Mar 24th, 2021

here most of us get mistaken because the question does not say we have to make a group of 5 stamps, we only have to make a group of 2 3 4, or 6 and that is why 49 is the correct answer.
if they would say that to also include a group of 5 stamps then I think 721 will be the correct answer.
correct me if I am wrong ......
thanks for the question