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# If a is a positive integer, and if the units digit of a^2 is 9 and the

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CEO
Joined: 15 Aug 2003
Posts: 3322
If a is a positive integer, and if the units digit of a^2 is 9 and the  [#permalink]

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Updated on: 23 Nov 2014, 06:45
6
00:00

Difficulty:

5% (low)

Question Stats:

86% (01:08) correct 14% (00:55) wrong based on 187 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-is-a-positive-integer-and-if-the-units-digit-of-a-2-is-109036.html

Originally posted by Praetorian on 12 Sep 2003, 23:30.
Last edited by Bunuel on 23 Nov 2014, 06:45, edited 1 time in total.
Renamed the topic, edited the question and added the OA.
Senior Manager
Joined: 22 May 2003
Posts: 301
Location: Uruguay
Re: If a is a positive integer, and if the units digit of a^2 is 9 and the  [#permalink]

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13 Sep 2003, 19:52
I also got A. By punching in numers:

...7^2=...9
...8^2=...4
...9^2=...1
Senior Manager
Joined: 17 Mar 2014
Posts: 441
Re: If a is a positive integer, and if the units digit of a^2 is 9 and the  [#permalink]

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23 Nov 2014, 06:18
Praetorian 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. 7
E. 9

For Quant problems, some of us just provide the answer...The new members cant help but feel lost and left behind.

please make an effort to explain ...it could be just a few lines.

Thanks
Praetorian

I got A(1) by using number 7, 7+1, 7+2.
Is there any other way to do it ?

Regards,
Ammu
Math Expert
Joined: 02 Sep 2009
Posts: 56300
Re: If a is a positive integer, and if the units digit of a^2 is 9 and the  [#permalink]

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23 Nov 2014, 06:46
1
1
ammuseeru wrote:
Praetorian 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. 7
E. 9

For Quant problems, some of us just provide the answer...The new members cant help but feel lost and left behind.

please make an effort to explain ...it could be just a few lines.

Thanks
Praetorian

I got A(1) by using number 7, 7+1, 7+2.
Is there any other way to do it ?

Regards,
Ammu

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).

Check Number Theory chapter of Math Book for more: math-number-theory-88376.html

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-a-is-a-positive-integer-and-if-the-units-digit-of-a-2-is-109036.html
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Joined: 09 Sep 2013
Posts: 11709
Re: If a is a positive integer, and if the units digit of a^2 is 9 and the  [#permalink]

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06 Sep 2018, 10:19
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Re: If a is a positive integer, and if the units digit of a^2 is 9 and the   [#permalink] 06 Sep 2018, 10:19
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# If a is a positive integer, and if the units digit of a^2 is 9 and the

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