Latest CAT Aptitude Question SOLUTION: the least number which when divided by 5,6,7 and 8 leaves a remainder 3,but when divided by 9 leaves no remainder is:

• Placement Papers
• /
• CAT

CAT Question Papers:

(#M40018392) CAT question Keep an EYE

the least number which when divided by 5,6,7 and 8 leaves a remainder 3,but when divided by 9 leaves no remainder is:

Asked In CAT MohanRaj (11 years ago)

Unsolved Read Solution (3)

Is this Puzzle helpful?   (4)   (0) Submit Your Solution

Read Solution (3) :

PARAG KAMRA  (11 years ago)

devided by 5 6 7 8 it leaves 3

so it is 3 more than multiples ot LCM of 5 6 7 8

now LCM of 5 6 7 8
factorisee
5 = 5
6 = 2*3
7 = 7
8 = 2* 2* 2 = 2^3
LCM = 5*2^3*3*7 = 840
now it has to be of the form 840n + 3

this is divisible by 9

840n + 3 = 9m

3 = 9m - 840n

now using extended euler algorithm

we need to find GCD of 840 and 9

840 = 9*93 + 3
3= 840*1 - 9*93
so n = -1 or 2 as it is mod 3

so 840*n +3 = 1683 divisible by 9

hence ans is 1683

Is this solution Helpfull? Yes (1) | No   

Vinay Sipani   (11 years ago)

1683

5*6*7*8 + 3 = 1683

Is this solution Helpfull? Yes | No (1)  

PARAG KAMRA  (11 years ago)

the least number which when divided by 5,6,7&8 leaves a remainder 3 is = (LCM of 5, 6, 7 and 8 + 3)
LCM of 6 and 8 is 24
LCM of 5, 7, 24 is = 5 × 7 × 24 = 840
so the least number = 840 + 3 = 843
sum of digits 8 + 4 + 3 = 15 not divisible by 9
Next number is 840 × 2 + 3 = 1680 + 3 = 1683
sum of digits = 1 + 6 + 8 + 3 = 18 divisible by 9
so the required no. 1683

Is this solution Helpfull? Yes | No   

Please Login to Read Solution.