Properties of Number

[chitrasrid]

Can someone, please help me out with this question?

If a is a positive integer, and the units digit of a^2 is 9 and the units digit of (a+1) ^ 2 is 4, what is the units digit of (a+2) ^2?

The answer choices are:

(a)1
(b)3
(c)5
(d)6
(e)14

The correct answer is (a)

Here is my thought process:

Only numbers ending in 3 or 7 would yield a units digit of 9 when squared.

If 9 is the units digit of a^2, then either 3 or 7 must be the units digit of a

I am not too sure how to proceed from here.

Thanks for your help!

Chitra Sridhar[*][*]

[jnelson0612]

Can someone, please help me out with this question?

If a is a positive integer, and the units digit of a^2 is 9 and the units digit of (a+1) ^ 2 is 4, what is the units digit of (a+2) ^2?

The answer choices are:

(a)1
(b)3
(c)5
(d)6
(e)14

The correct answer is (a)

Here is my thought process:

Only numbers ending in 3 or 7 would yield a units digit of 9 when squared.

If 9 is the units digit of a^2, then either 3 or 7 must be the units digit of a

I am not too sure how to proceed from here.

Thanks for your help!

Chitra Sridhar[*][*]

You've done a nice job so far! You are correct: only a number ending in 3 or 7 would yield a units digit of 9 when squared. So let's consider 3 or 7 for a.

The next thing that the problem tells us is that (a+1)^2 has a units digit of 4. Let's test out our two possibilities:

If a=3, then (3+1)^2 is 16, units digit of 6. Doesn't work.
If a=7, then (7+1)^2 is 64, units digit of 4. This works!

Thus, a must be 7 or some number ending in 7. Let's just say a=7 to make our lives easier. The question is what is the units digit of (a+2)^2? Let's just plug in a=7 and find that (7+2)^2 = 81. Thus, the units digit is 1. Answer A.