If the units digit of n^33 is 7, which of the following could be the

Question

If the units digit of n^33 is 7, which of the following could be the value of n?

I. n = 41
II. n = 43
III. n = 47

(A) Only I
(B) Only II
(C) Only III
(D) I and II
(E) II and III

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Rabab36 · Answer

n=47

since last digit is 7 
it has cycle of
7,9,3,1

therefore 33/4=1

7 will be only unit digit of 47^33

option C

wadhwakaran · Answer

options are 
41 (1 has a cyclicity of 1 meaning thereby that any power of 1 will get 1)

43 (3 has a cyclicity of 4 meaning that after every four powers of 3, the unit digit will be same)
The unit digit of powers of 3 are 3,9,7,1,3 
since, third power of 3 will get a unit digit of 7 
n^33 has a unit digit of 7
33/4 Remainder comes out to be 1 meaning that the unit digit will be 3.

47 (7 has a cyclicity of 4 meaning that after every four powers of 7, the unit digit will be same)
The unit digit of powers of 7 are 7,9,3,1,7 
since, first power of 7 will get a unit digit of 7 
n^33 has a unit digit of 7
33/4 Remainder comes out to be 1 meaning that the unit digit will be 7.

Therefore option C i.e. Only III

harshittahuja · Answer

If the units digit of n^33 is 7, which of the following could be the value of n?
Solution
When N=41 then 41^33=1
When N=43 then 43^33=43^32*43=1*3=3
When N=47 then 47^33=7^33=7^32*7=1*7=7
Answer is III

SaquibHGMATWhiz · Answer

Solution:

Unit digit of n^33 is 7 or we can say  (n^{33})_U=7

Let us pick each number one by one and see which of them CAN be the value of n

I. n = 41

If  n=41 , then  (n^{33})_U=(41^{33})_U=(1^{33})_U=1

Therefore, the  value of n cannot be 41

II. n = 43

If  n=43 , then  (n^{33})_U=(43^{33})_U=(3^{33})_U

Since the cyclicity of 3 is 4, we will break it in the following way:

(3^{33})_U=(3^{32})_U	imes (3^{1})_U=(3^{4	imes 8})_U	imes (3^{1})_U=1	imes 3=3

Therefore, the  value of n cannot be 43

III. n = 47

If  n=47 , then  (n^{33})_U=(47^{33})_U=(7^{33})_U

Since the cyclicity of 7 is 4, we will break it in the following way:

(7^{33})_U=(7^{32})_U	imes (7^{1})_U=(7^{4	imes 8})_U	imes (7^{1})_U=1	imes 7=7

Therefore, the  value of n can be 47

Hence the right answer is    Option C

Abhishek009 · Answer

7^3 =  xx 3

Now,  7^{3*11} =  xx 3  , Hence Answer must be (C) III.

If the units digit of n^33 is 7, which of the following could be the

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If the units digit of n^33 is 7, which of the following could be the

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