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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

Check the Answer


But try the problem first…

Answer: 419

Source
Suggested Reading

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.

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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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