The remainder when 7^84 is divided by 342 is :

Question

The remainder when 7^84 is divided by 342 is:

A. 0
B. 1
C. 49
D. 51
E. 341

mikemcgarry · Accepted Answer

Dear ankur1901 , First, let me make perfectly clear: this is NOT a GMAT question. This is far too advanced for anything on the GMAT. This is getting into mathematical hot-shot territory. Step one is to notice that 342 = 343 -1, and of course, 343 = 7^3, so 342 = (7^3) - 1. Step two is to remember that (a^n - 1) is divisible by (a^m - 1) if n is divisible by m. Obviously, 84 is divisible by 3. Therefore: must be divisible by = 342 If 342 goes evenly into , then it must divide into (7^84) leaving a remainder of 1. Does all this make sense? Mike :-)

gayam · Answer

Hi Ankur,

For this kind of problems, the best approach is to find the power of the dividend which is closest to divisor(or the multiple of the divisor)

7 cube = 343
Divisor = 342

343/342 => reminder =1
as 7^84 can be written as (7^3)^28 = the result is 1^28 =>1

Loser94 · Answer

7^84/ 342
(7*7*7)^21/342
343^21/342
 Acc to remainder theorem n^x/z if n/z gives remainder r then n^x/z gives remainder r

Ans B 1 or 1^21=1

Thanks

Abhishek009 · Answer

\frac{7^3}{342} = \frac{343}{342}  , Remainder 1

Now,  \frac{7^{84}}{342} = \frac{7^{3*28}}{342}  , Remainder 1 , Answer must be (B) 1

The remainder when 7^84 is divided by 342 is :

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The remainder when 7^84 is divided by 342 is :

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