powers

[joanjgonzalez]

can anybody help on this one?

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

Imo is c

[iamcste]

C

Pattern of powers of 7 are 7 ,9,3,1 and then this pattern repeats further...

( 7^1, 7^2,7^3,7^4 and pattern repeats........)

Patters of powers of 3 are 3 ,9,7,1 and then this pattern repeats

so both 7 ^n or 3 ^n can have unit digit as 7 depending on the value of power

here we need power of 33

( pattern repeats every 4 th power ,(8*4+1) and hence we need to check the first position in power pattern where the first position is 7

this is in the power pattern of 7)

C

[brb588]

Wow, you're good.

[niraj_a]

brb,

pick up an mgmat number properties book, this units digit with exponents rule is in there.