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# Integers and remainders | TOMATO B.Stat Objective 85

Try this TOMATO problem from I.S.I. B.Stat Entrance Objective Problem based on Integers and remainders. You may use sequential hints to solve the problem.

Try this problem from I.S.I. B.Stat Entrance Objective Problem based on Integers and remainders.

## Integers and remainders( B.Stat Objective Question )

The smallest integer that produces remainder of 2,4,6 and 1 when divided by 3,5,7,11 is

• 104
• 419
• 1154
• none of these

### Key Concepts

Integers

Remainders

Smallest integer

But try the problem first…

Source

B.Stat Objective Problem 85

Challenges and Thrills of Pre-College Mathematics by University Press

## Try with Hints

First hint

here 419=3(139)+2 and 419=7(59)+6

Second Hint

419=5(83)+4 and 419=11(38)+1

Final Step

then required number=419.

## One reply on “Integers and remainders | TOMATO B.Stat Objective 85”

The smallest integer that produces remainder of 2,4,6 and 1 when divided by 3,5,7,11 is:
N=3*q1+2=3*(q1+1)-1=5*q2+4=5*(q2+1)-1=7*q3+6=7*(q3+1)-1=11*q4+1=
Considering only First Three N=3*q1+2=3*(q1+1)-1=5*q2+4=5*(q2+1)-1=7*q3+6=7*(q3+1)-1, we get N=105* Q-1
So ,N=105* Q-1=11*q4+1;
OR Q= (N+1)/105=4; q4= (N-1)/11=38;
so N=419

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