* Reminder related problem

[nithyanandhasubramanya]

1 . if x= (21^3+22^3+23^3+24^3) Then what is the reminder when x is divided by 90 ?

2. Find the reminder when (3^14+7^14) is divided by 13 ?

Kindly help me find the answers for these 2 questions

[rohan.dd.bhatia]

if x= (21^3+22^3+23^3+24^3) Then what is the reminder when x is divided by 90 ?
IMO - Did not calculate a lot -- but broke the division into two steps...
-> If we quickly add the unit digits
-> 21^3 = 1;22^3= 8;23^3 = 7;24^3 = 4;1+7+8+4 = 20
-> Above exp. will end with 0, thus is divisible by 10
-> To check divisibilty by 9 --
-> (21^3+22^3+23^3+24^3) = (21+22+23+24)^3 - (all other terms from expanding (a+b+c+d)^3) -- Lets call this X
-> 90-(X)
-> thus remainder will be "X/9 "
-> If we expand (a+b+c+----)^3 = we get multiples of 3 - with pair of each term - ex. 3a^2b+3ab^2+3a^2c+3ac^2 .....
-> Since 21 & 24 each are divisible by 3 -- all terms in X with 21 or 24 will be divisible by 9
-> Leaving .....+3*22*22*23+3*23*23*22+.....
-> ....+3*22*23(22+23)....
-> ...+3*22*23*45...
-> Even this term is divisible by 9
-> Thus X or 90-X must be divisble by 9
Therefore remainder would be 0

[RonPurewal]

hi,
please read the forum rules (first thread in this folder).
to post a problem here, you must cite the original source of the problem. (that's the original source -- not another forum or aggregator site.)
in addition, the source must be something that's directly related to the gmat exam. (this problem is MUCH too arithmetically intense to represent anything you'd ever see on the official gmat.)

please cite the original source, or else we'll have to delete the thread in a few days.
thanks.

[nithyanandhasubramanya]

hi,
please read the forum rules (first thread in this folder).
to post a problem here, you must cite the original source of the problem. (that's the original source -- not another forum or aggregator site.)
in addition, the source must be something that's directly related to the gmat exam. (this problem is MUCH too arithmetically intense to represent anything you'd ever see on the official gmat.)

please cite the original source, or else we'll have to delete the thread in a few days.
thanks.

Hi Ron

These problems were given by my friend , i asked him about the source but he said his mentor gave him and was not sure about it , even i was not able to trace the source .Kindly let them be there for a couple of days , i will put the source if found or will delete the thread myself.

Thanks

[tim]

These questions are NOT GMAT-related at all. They test concepts that are FAR too advanced for the GMAT. If a friend gave you these as problems to study for the GMAT, he either has no clue what the GMAT is about or is a terrible friend! :)