adymehta29 wrote:
Check this first:
218-if-x-and-y-are-positive-integers-what-is-the-remainder-109636.html#p875157If you divide 7^131 by 5, which remainder do you get?A. 0
B. 1
C. 2
D. 3
E. 4
Last digit of 7^(positive integer) repeats in blocks of 4: {7, 9, 3, 1} - {7, 9, 3, 1} - ... (cyclicity of 7 in power is 4).
As the remainder upon division 131 by 4 (cyclicity) is 3 then the last digit of 7^131 is the same as that of 7^3 so 3 (the third digit from the pattern {7, 9, 3, 1}). Now, any positive integer ending with 3 upon division by 5 yields the remainder of 3.
Answer: D.
Hope it's clear.
bunuel, as per the theory in gmat club math book "When a smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller
integer." i tried solving the above sum and got the correct answer just want to know whether the method is correct or not , as 3 is smaller than 5 so the remainder would be 3
thanks
Hey Bunuel,
If you don't mind, I think I see the problem Ady is facing so I will take it up.
Note that the gmat club math book says "When a
smaller integer is divided by a larger integer, the quotient is 0 and the remainder is the smaller
integer."
So when 3 is divided by 5, remainder is 3. When 10 is divided by 39, remainder is 10 and so on...
But in this question, you have \(7^{131}\) divided by 5. You find that \(7^{131}\) ends in 3. This means it is a number which looks something like this:
\(7^{131} = 510320.....75683\) (a huge number that ends in 3. Other than 3, I have used some random digits.)
So the remainder is 3 not because 3 is smaller than 5. The actual number is much much bigger than 5. For example, if you have 276543 divided by 5, will you say that the number is smaller than 5 and hence the remainder is 3? No. The remainder is 3 because the number ends in 3 and when you divide such a number by 5, you know that the number which is 3 steps before it i.e. 276540 in this case, is a multiple of 5 (every number ending in 0 or 5 is a multiple of 5). That is the reason that you will be left with 3 when you divide this number by 5.
Similarly, 4367 divided by 5 leaves remainder 2 because 4365 is divisible by 5 and so on...
The first part of this post discusses remainders in case of division by 5:
http://www.veritasprep.com/blog/2014/03 ... emainders/ _________________
Karishma
Veritas Prep GMAT Instructor
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