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April 19, 2020

Integers and remainders | TOMATO B.Stat Objective 85

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


Answer: 419

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 comment on “Integers and remainders | TOMATO B.Stat Objective 85”

  1. 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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