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10 Feb 2011, 15:56
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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
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...
10 Feb 2011, 16:12
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ChenggongMAS
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...
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 thE 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=49);
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=64), 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=81).
Answer: A.
Check Number Theory chapter of Math Book for more: math-number-theory-88376.html
09 Aug 2011, 12:35
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The units' digit is the first digit to the left of the decimal point.
For example, in 123.4567, the units digit is 3.
Similarly, in 234, the units digit is 4.
In the given question, if the units digit of a^2 is 9, it means the units digit of a can be 3 or 7 (because both 3^2 and 7^2 end in a units digit of 9). Now, the units digit of (a+1)^2 is given to be 4. This means the units digit of a must be 7 because the units digit of (7+1)^2 = 4, but the units digit of (3+1)^2 is not 4 (it is 6).
This means the units digit of a is 7, and therefore the units digit of a+2 is 9. So the units digit of (a+2)^2 = units digit of 9^2 = 1
The answer is therefore (A).
For example, in 123.4567, the units digit is 3.
Similarly, in 234, the units digit is 4.
In the given question, if the units digit of a^2 is 9, it means the units digit of a can be 3 or 7 (because both 3^2 and 7^2 end in a units digit of 9). Now, the units digit of (a+1)^2 is given to be 4. This means the units digit of a must be 7 because the units digit of (7+1)^2 = 4, but the units digit of (3+1)^2 is not 4 (it is 6).
This means the units digit of a is 7, and therefore the units digit of a+2 is 9. So the units digit of (a+2)^2 = units digit of 9^2 = 1
The answer is therefore (A).
