Latest Elitmus Aptitude Question SOLUTION: A maximum number of 3 digit such that when expressedin base 2 or base 3 or base 7 has 1 as the rightmost(last) digit. If a,b,c are the first digits(leftmost) of the base 2, base 3

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

Elitmus Question Papers:

(#M40033158) ELITMUS Numerical Ability question Elitmus 23rd feb14 Keep an EYE

A maximum number of 3 digit such that when expressedin base 2 or base 3 or base 7 has 1 as the rightmost(last) digit. If a,b,c are the first digits(leftmost) of the base 2, base 3 and base 7 representation of that number. Then sum of a,b,c

Asked In Elitmus Vivek Jain (10 years ago)

Unsolved Read Solution (9)

Is this Puzzle helpful?   (1)   (3) Submit Your Solution Number System

Read Solution (9) :

RAKESH KUMAR RANJAN  (9 years ago)

given that right most digit is 1.
means in base system 1 is remainder in each case.
we have to find greatest 3 digit number, so first we have
to find the greatest 3 digit number which is divisible by 2,3
and 7.
so take lcm of 2,3 and 7.
LCM(2,3,7)=42.
Now
42)999(23
84
-----
159
126
-------
33

so greatest 3 digit number which is divisible by 2,3 and 7 is
999-33=966

Number which have right most digit is 1 is equal to 966+1=967.
now express this number in base 2, base 3 and base 7 system
and find a,b and c.

Is this solution Helpfull? Yes (9) | No   

Naveen Agarwal  (10 years ago)

a=1 , b=1 , c=2 ans is 4
number is 967

Is this solution Helpfull? Yes (4) | No   

Mani kandan  (10 years ago)

The number is 967, 2*3*7 = 42, highest 3 digit number = 42*23 = 966 , 966 +1 = 967

Leftmost digit = 2+1+1 = 4

Is this solution Helpfull? Yes (3) | No   

BIMPY KUMARI  (9 years ago)

2a+1 = 3b+1 = 7c +1

2a=3b

a=3, b=2 : 7

a=6, b=4 : 13

6p + 7

6p + 7 = 7c + 1

6p + 6 = 7c

6 (p+1) / 7 = c

p=6 : 43

p=13 : 85

42d + 43

42(22) + 43 = 967

967 in base 2 = 1111000111

967 in base 3 = 1022211

967 is base 7 = 2551

answer = 1+1+2 = 4

Is this solution Helpfull? Yes (3) | No   

Yash karan   (9 years ago)

The answer is 4
The question says that the number has last digit as 1 in base 2,3,and 7.
You will see that this true for only those numbers which when divided by 2,3,and 7 leaves remainder 1.
So the number will be of format (L.C.M of 2,3,7)*n+1.=42n+1
The highest 3 digit number is 42*23+1=967.
When you will convert it into base 2,3,and 7 the sum of first digit ie a+b+c will be 4
Thanks

Is this solution Helpfull? Yes (3) | No   

mounika  (10 years ago)

pls explain in detail

Is this solution Helpfull? Yes (2) | No   

priya saxena  (10 years ago)

plzz explain not got the correct answer???????? urgently

Is this solution Helpfull? Yes (2) | No   

hitesh gupta  (10 years ago)

It must be 5

Is this solution Helpfull? Yes | No (1)  

anujnandwana  (10 years ago)

naveen how did you find that no. ??

Is this solution Helpfull? Yes | No (1)  

Please Login to Read Solution.