39a very old and well known question...
answer is 7072=499849
Sally is thinking of a 6-digit number. The sum of the digits is 43. And only two of the following three statements about the number are true: (1) it's a square number. (2) it's a cube number, and (3) the number is under 500000. What number was Sally thinking of?
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12 Answers
1with congruency this will be easy....
congruency is not in jee but it was discussed sometime back in this forum....so thought to post this one
1i am not old([3][3][3][3][3]) so i didnt come upon this question...................................................sooner
full solution anyone???
1if the number is a cube, it should be of the form 9n-1 or 9n or 9n+1
but 43 is not of the above mentioned forms, the number is not a cube
so now we know the number is a perfect square, <500000 and of the form 9n+7 (as 43 is of this form) and the sum of its digits is 43
so its root is of the form 9n+4 or 9n+5
now how do i continue from here
1Plz someone post the solution...I'm still not easy with congruency.
39sorry , see this instead:
http://www.mathlinks.ro/viewtopic.php?search_id=216714598&t=37726
1thats exactly what i have done(as in the link provided by b555). Arshad can you give us an elegant method to single out 707 from the 90 possible numbers.