ChenggongMAS wrote:
If a is a positive integer, and if 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?
A) 1
B) 3
C) 5
D) 6
C) 14
I guess I am just not reading this properly. I don't understand what they mean by units digit...
1234.567
1 - THOUSANDS
2 - HUNDREDS
3 - TENS
4 - UNITS
. - decimal point
5 - TENTHS
6 - HUNDREDTHS
7 - THOUSANDTHS
So th units digit is the digit to the left of the decimal point or in integer it's the rightmost digit. For example: the units digit of 1.2 is 1 and the units digit of 13 is 3.
Back to the original question.
If a is a positive integer, and if 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 units digit of a^2 is 9 --> the units digit of a itself is either 3 or 7 (3^2=
9 and 7^2=4
9);
The units digit of (a+1)^2 is 4 --> the units digit of a+1 is either 2 or 8 (2^2=
4 and 8^2=6
4), so the the units digit of a itself is either 2-1=1 or 8-1=7;
To satisfy both conditions the units digit of a must be 7. Now, a+2 will have the units digit equal to 7+2=9, thus the units digit of (a+2)^2, will be 1 (9^2=8
1).
Answer: A.
Check Number Theory chapter of Math Book for more:
math-number-theory-88376.html
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