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# If a is a positive integer, and if the units digit of a^2 is

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Manager
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Re: If a is a positive integer, and if the units digit of a^2 is  [#permalink]

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26 Jan 2017, 08:27
a = Positive Integer
a^2 = _9
Here , 2 cases
a = 3 or a = 7
Since, Units digit of (a+1)^2 = 64 ; a should be 7
(a+2)^2 = (7+2)^2 = 9^2 = 81
A
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Re: If a is a positive integer, and if the units digit of a^2 is  [#permalink]

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03 Apr 2017, 09:27
a^2 ends in 9
Possible cases:
3^2= 9
7^2=49

(a+1)^2 ends in 4
Possible cases:
(7+1)^2= 8^2=64

7 is the value of a because there is no need to consider any other value for a as from the first condition a^2, we know that a can either be 3 or 7. Information in second case confirms that the value of a is 7.

Thus (a+2)^2 will end in 1.
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Re: If a is a positive integer, and if the units digit of a^2 is  [#permalink]

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06 Apr 2017, 09:05
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

Since the units digit of a^2 is 9, the units digit of a is either 3 or 7. However, since the units digit of (a+1)^2 is 4, we see that the units digit of a must equal 7, since then the units digit of a + 1 is 8 and 8^2 = 64 (had the units digit of a been 3, then the units digit of a + 1 would have been 4, but 4^2 = 16). Thus, the units digit of a + 2 is 9, and since 9^2 = 81, the units digit of (a + 2)^2 is 1.

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Re: If a is a positive integer, and if the units digit of a^2 is  [#permalink]

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06 Apr 2017, 10:06
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...

Since, units digit of $$a^2$$ is $$9$$ : a can be 3 or 7

Since, units digit of $$(a+1)^2$$ is $$4$$ : a must be 7

Thus, $$(a+2)^2 = (7+2)^2 = 81$$ , so units digit is 1

Answer must be (A) 1
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Re: If a is a positive integer, and if the units digit of a^2 is  [#permalink]

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02 Jul 2017, 17:05
Another possible solution without the substitution based on a logical equation:
a^2= x9 (where x - other place values, tenths, hundredths and so on)
(a + 1)^2 = a^2 + 2a + 1 = x4 ,so x9 + 1 + 2a = x0 + 2a = x4
(a + 2)^2 = a^2 + 4a + 4 = x9 +4 + 4а = x3 + 8 = x1 (result of logical equation compared to the above one, with 2а)
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Re: If a is a positive integer, and if the units digit of a^2 is  [#permalink]

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06 Sep 2018, 09:35
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Re: If a is a positive integer, and if the units digit of a^2 is   [#permalink] 06 Sep 2018, 09:35

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# If a is a positive integer, and if the units digit of a^2 is

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