CAT Exam

For what value of 'n' will the remainder of 351n and 352n be the same when divided by 7?

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The official answer is n=3.

For what value of 'n' will the remainder of 351^n and 352^n be the same when divided by 7?

When 351 is divided by 7, the remainder is 1.
When 352 is divided by 7, the remainder is 2.

Let us look at answer choice (1), n = 2

When 351^2 is divided by 7, the remainder will be 1^2 = 1.
When 352^2 is divided by 7, the remainder will be 2^2 = 4.

So when n = 2, the remainders are different.

When n = 3,

When 351^3 is divided by 7, the remainder will be 1^3 = 1.
When 352^3 is divided by 7, the remainder will be 2^3 = 8.

As 8 is greater than 7, divide 8 again by 7, the new remainder is 1.
So when n = 3, both 351^n and 352^n will have the same remainder when divided by 7.
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CAT Other Question

Ram and Shyam take a vacation at their grandparents' house. During the vacation, they do any activity together. They either played tennis in the evening or practiced Yoga in the morning, ensuring that they do not undertake both the activities on any single day. There were some days when they did nothing. Out of the days that they stayed at their grandparents' house, they involved in one of the two activities on 22 days. However, their grandmother while sending an end of vacation report to their parents stated that they did not do anything on 24 mornings and they did nothing on 12 evenings. How long was their vacation? A person starts multiplying consecutive positive integers from 20. How many numbers should he multiply before the will have result that will end with 3 zeroes?