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# GMATPrep Units Digit Question

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Intern
Joined: 09 Aug 2011
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09 Aug 2011, 12:12
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Difficulty:

25% (medium)

Question Stats:

89% (02:47) correct 11% (01:57) wrong based on 9 sessions

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I've taken the same GMATPrep problem solving test twice. Despite the fact that I guessed the answer, I don't really understand the explanation behind this particular problem. What is the UNITS DIGIT!? Could anyone care to explain why the answer is what it is? Attached is the print screen shot of the problem.

[Reveal] Spoiler: OA

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Joined: 24 Jul 2011
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Re: GMATPrep Units Digit Question [#permalink]

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09 Aug 2011, 12:35
1
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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

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Intern
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Re: GMATPrep Units Digit Question [#permalink]

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09 Aug 2011, 12:48
thank you! this helped so much!
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Re: GMATPrep Units Digit Question [#permalink]

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09 Aug 2011, 15:29
Hi aks1985,
Consider the no 1234
Here
4 - units digit
3 - tens
2 - hundreds
1 - thousands
You might need that for other problems.
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Re: GMATPrep Units Digit Question [#permalink]

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21 Aug 2011, 20:05
units digit of a^2 is 9

=> units digit of a is either 3 or 7

also given units digit of (a+1)^2 is 4. so units digit of a can be only be 7 ( 3 is ruled out)

=> units digit of (a+2)^2 is 1 (as (7+2)^2 = 81)

Re: GMATPrep Units Digit Question   [#permalink] 21 Aug 2011, 20:05
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