Can someone please explain why the answer is C.?

Question

If x is a positive integer, which of the following CANNOT be the units digit of 7^x?

A. 1
B. 3
C. 5
D. 7
E. 9

(what is units digit?)

Answer 1

to answer that, we experiment on 7^x by having different values of x. when x=1, 7^1=7, units digit = 7
x=2, 7^2=49 = 9
x=3, 7^3=343 = 3
x=4, 7^4=2401 = 1
x=5, 7^5=16,807 = 7
x=6, 7^6=117649 =9
this pattern goes on and follows: 7-9-3-1-7-9-3-1....in intervals of 4. thus, among the choices, C)5 cant be the last digit. there you go :D

Answer 2

Unit's digit is the last digit of a whole number.2 is the units digit of 12.6 is the units digiy of 236 and so on
if x is a positive integer
7^1=7
7^2=49
7^3=49*7=343
7^4=343*7=2401
7^5=2401*7=16807
7^6=16807*7=117649
7^7=117649*7=823543
7^8=823543*7=5764801
From the above table you may notice that the units digit will go on repeating 7,9,3 and 1 and no other digit excepting these 4 digits is possible as units digit.hence 5 is the odd digit out.

Answer 3

The units digit is also known as the ones digit (the digit to the left of the decimal when the number is written with one).

To solve this problem simply multiply like normal, but only keeping the units digit (that's the only part that's relevant):

7^1 >>> 7
7^2 >>> 9
7^3 >>> 3
7^4 >>> 1
7^5 >>> 7

As you can see the pattern starts to repeat, so looking at your options 5 (C) is the only number that isn't in the pattern.

Answer 4

"Units digit" is the one's place or the last digit
of the number.
Let's rule out the other answers by a counterexample:
7² = 49, so E is out
7³ = 343, so B is out
7^4 = 2401, so A is out
finally,
7^1 = 7 so D is out.
So, by elimination, C is the answer.
Another solution:
If 7^x ended in 5, then 5 would have to
be a divisor of 7^x, which is impossible.
So again, C is the answer.

Answer 5

7^1 = 7 so answer is not D
7^2 = 49 so answer cannot be E
7^3 = 343 so answer cannot be B
7^4 =2401 so answer cannot be A
After this the sequence repeats with the last digits being 7,9,3,1 over and over. So answer is C = 5
But it is also true that the units digit cannot be 2,4,5,6,8,or 0.

Answer 6

The "units digit" is a different term for "ones digit".

In the number 354, 3 is the hundreds digit, 5 the tens digit, and 4 the ones digit or units digit.

Answer 7

The units digit is the 1's place (right-most in a non-decimal number).

Think of multiples of 7. 7, 14, 21, 28, 35, 42, 49, 56, 63, 70, 77 (they begin to repeat the units digit). The only number missing is C. 5.

Answer 8

Successive powers of 7 end in 7, 9, 3, 1 endlessly. There is never a 5 on the end.

Answer 9

The answer is 4 Let's try to make this easier for you: Lets call the "c" "cats" and instead of the "4", you write "something" So your equation will read: 4 cats = 3 cats + something. Can you see that the "something"(4) is actually the 1 missing cat? But how did we actually get there? Back to the actual sum 4c = 3c + 4 We need to get rid of as many c's as possible to simplify things, so you take the lowest number of c's (3c) and deduct it from both sides like this: (4c - 3c) = (3c - 3c) + 4 = 1c = 4 Does that make sense to you?