Latest Elitmus Aptitude Question SOLUTION: A set S has all 3-digit numbers which is divisible by 11. Mr. A picks one numbers out from the set which when divided by 3 and 7, remainder is same. How many numbers is possible to

• Placement Papers
• /
• Elitmus
• /
• Numerical Ability
• /
• Number System

Elitmus Question Papers:

(#M40035325) ELITMUS Numerical Ability question Number System Keep an EYE

A set S has all 3-digit numbers which is divisible by 11. Mr. A picks one numbers out from the set which when divided by 3 and 7, remainder is same. How many numbers is possible to pick out by Mr. A?
a) 12
b) 21
c) 24
d) 36

Asked In Elitmus jitendra kumar (10 years ago)

Unsolved Read Solution (7)

Is this Puzzle helpful?   (10)   (5) Submit Your Solution Number System

Read Solution (7) :

RAKESH  (10 years ago)

A) 12

remainder is same when divided by 3 and 7, LCM of 3,7 = 21
so number can be of form 21k, (21k+1),(21k+2)
also no. is divisible by 11 so, no. will be of form 11*21k,11*(21k+1),11*(21k+2)

i.e 231k, (231k+11) & (231k+22)
k=1,2,3,4

231,462,693,924 => rem=0
242,473,704,935 => rem=2
253,484,716,946 => rem=1

total = 12 numbers

Is this solution Helpfull? Yes (76) | No (12)  

ANKIT JAISWAL  (9 years ago)

rakesh 242 when divided by 3 and 7 will give remainder 2 and 4 which is not equal.

Is this solution Helpfull? Yes (13) | No   

PARVY GOVIL  (10 years ago)

all the 3- digit nos that are of the form 11k are
12,132,143,......209,220,...308,319,....407,418,...506,517,...606,616,...704,715,...803,814,...920,913,..990)
out of these the nos that are (7k and 3k')..or leave rem 1 or 2 are :
231,253,275,462,484,506,693,715,737,924,946,968 respectively
thus 12 such nis. exist .

Is this solution Helpfull? Yes (5) | No (2)  

arijit roy  (10 years ago)

12

remainder is same when divided by 3 and 7, LCM of 3,7 = 21
so number can be of form 21k, (21k+1),(21k+2)
also no. is divisible by 11 so, no. will be of form 11*21k,11*(21k+1),11*(21k+2)

i.e 231k, (231k+11) & (231k+22)
k=1,2,3,4

231,462,693,924 => rem=0
242,473,704,935 => rem=2
253,484,716,946 => rem=1
:) :)

Is this solution Helpfull? Yes (2) | No (14)  

Hari  (9 years ago)

remainder is same when divided by 3 and 7, LCM of 3,7 = 21
so number can be of form 21k, (21k+1),(21k+2)
also no. is divisible by 11 so, no. will be of form 11*21k,11*(21k+2),11*(21k+4)
here we didnt use 11*(21k+1) & 11*(21k+3) since it gives diffrnt remnder.
i.e 231k, (231k+22)&(231k+44)
k=1,2,3,4
solving we get 12 different nos

total = 12 numbers

Is this solution Helpfull? Yes (2) | No (1)  

murthy  (10 years ago)

Answer is 12 or 21?

Is this solution Helpfull? Yes | No (2)  

murthy  (10 years ago)

S = { 121, 132, ........ , 990 }

set devided by 3 and 7 ={ 231, 462, 693, 924 } reamining ??????????

Is this solution Helpfull? Yes | No (2)  

Please Login to Read Solution.