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by [email protected] » Tue Sep 15, 2015 8:09 am
Hi nahid078,

Since the GMAT will NEVER require that you actually work through that entire calculation, there MUST be a pattern that you can take advantage of. I'm going to give you a hint as to how to figure out the patterns involved, so that you can attempt this question again:

The 'key' is the Units Digit of each calculation.

eg.
7^1 = 7
7^2 = 49
7^3 = _ _ 3
7^4 = _ _ _ 1
-----------
7^5 = _ _ _ _ 7

Notice the pattern here with the Units Digit: every 4 'powers', the cycle repeats: 7, 9, 3, 1. You can now determine the Units Digit of the first part of the calculation.

Using the same method, can you determine the pattern when dealing with a Units Digit of 3? Once you have that digit, you can subject it from the other Units Digit to get the correct answer.

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by nahid078 » Tue Sep 15, 2015 8:23 am
Yes, but actually I can't simplify the other portion. Can you please explain it.
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by MartyMurray » Tue Sep 15, 2015 11:57 pm
When integers are multiplied, the only digits that affect the units digit of a product are the units digits of the numbers being multiplied.

For instance, the units digit of 9 x 9 is the same as the units digit of 209 x 139. The units digits of both are 1.

So in this case, the only digits that matter are the 7 from 17 and the 3 from 1973.

So essentially the problem becomes this. What is the units digit of (7³)�, or 7¹², and what is the units digit of 3^3², or 3�?

The other thing you need to realize to do this problem is that when an integer is raised to consecutive powers, the resulting units digits repeat in a cyclical pattern.

So to get the answer here, we need the cyclical pattern for 7 and the cyclical pattern for 3.

7¹ = 7 (units digit 7)
7² = 49 (units digit 9)
7³ = _ _ 3 (units digit 3 - I am not going to bother multiplying out 7 x 49 since I only need the units digit. Since 7 x 9 = 63, I know the units digit of 7 x 49 is 3.)
7� = _ _ 1 units digit of 1. (Since 7 x 3 = 21 I know that the units digit of 7 x _ _ 3 is 1.)

Now that I am back to 1 as the units digit, when I multiply by 7 again, I will get a units digit of 7 and the pattern will repeat.

7 9 3 1 7 9 3 1 7 9 3 1

So 7¹² has a units digit of 1.

The pattern for 3 is the following.

3¹ = 3 (units digit 3)
3² = 9 (units digit 9)
3³ = 27 (units digit 7)
3� = 81 (units digit 1)

Then, since the last digit of 81 is 1, the pattern starts over, and so the pattern for 3 is the following.

3 9 7 1 3 9 7 1 3 9 7 1

Now since the units digit of 17¹² is 1 and the units digit of 1973� is 3, I was tempted to subtract 3 from 11 and get 8.

Then I figured out that 1973� > 17¹². So the answer is going to be a negative number and we have to reverse the subtraction to get the last digit.

So 3 - 1 = 2 and the correct answer is B.
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by Brent@GMATPrepNow » Wed Sep 16, 2015 7:06 am
If anyone is interested, we have a free video on finding the units digit of large powers: https://www.gmatprepnow.com/module/gmat- ... video/1031

Afterwards, you can practice with this question: https://www.gmatprepnow.com/module/gmat- ... video/1032

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by sandipgumtya » Thu Sep 17, 2015 6:03 am
where is the qus? Can u pl pl repost?
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by MartyMurray » Thu Sep 17, 2015 6:05 am
Sandip, the question is at the top.
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by sandipgumtya » Thu Sep 17, 2015 7:03 am
Ya.got it sir.
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by sandipgumtya » Thu Sep 17, 2015 7:06 am
Hi Marty,
Got the ans 8 at first instance.later saw ur post and realised where i went wrong.Can u pl suggest how can i avoid such silly mistakes.thanks.
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by DavidG@VeritasPrep » Thu Sep 17, 2015 7:17 am
Got the ans 8 at first instance.later saw ur post and realised where i went wrong.Can u pl suggest how can i avoid such silly mistakes.thanks.
There's no magic pill that will allow you to avoid these kinds of mistakes, but it is worth internalizing the idea, as Marty explained earlier, that when we're trying to determine the units digit of the result of the difference of two numbers, we cannot look at the units digits in isolation. I find it helpful to remind myself of this principle by using simple numbers. If x has a units digit of '6,' and y has a units digit of '2,' for example, then the units digit of x - y isn't necessarily 6-2 = 4, because if x = 16 and y = 22, then x - y = -6. Generally speaking, using simple numbers to confirm our intuition is a helpful strategy when dealing with larger values.
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by Brent@GMATPrepNow » Thu Sep 17, 2015 9:18 am
sandipgumtya wrote:Hi Marty,
Got the ans 8 at first instance.later saw ur post and realised where i went wrong.Can u pl suggest how can i avoid such silly mistakes.thanks.
Finally, if silly mistakes are hurting your score, then it's important that you identify and categorize these mistakes so that, during tests, you can easily spot situations in which you're prone to making errors. I write about this and other strategies in the following article: https://www.gmatprepnow.com/articles/avo ... teaks-gmat

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by MartyMurray » Thu Sep 17, 2015 6:35 pm
sandipgumtya wrote:Got the ans 8 at first instance.later saw ur post and realised where i went wrong.Can u pl suggest how can i avoid such silly mistakes.thanks.
For me much of what helps with avoiding such errors is being aware of the little uneasiness I feel at times when looking at a question.

In this case, I was ready to do the same thing you did, but there was some little uneasiness I was feeling; on some level I was wondering whether the second number were greater than the first.

So one thing you can do is to seek to be aware of what's going through your mind as you work on answering a question and to be sure to pay attention to any questions you have about what you are doing.

Another thing that helps is, as Brent mentioned, being aware of the types of things you do. Then you can seek to catch yourself in the act, and not do them, before you choose answers.

In my case I had a tendency to make silly calculation errors, doing things like adding 26 and 26 and getting 56. I learned to say to myself, "There you go. DOOOOON'T do that." before I did it.

Overall, you can work to develop an accuracy mindset. There is a whole psychology to doing things accurately and precisely, and even as I am typing this I am noticing the typing errors I have to correct as I go along. Why am I making those totally avoidable errors? In order to type more accurately the first time, I have to develop more of an accuracy mindset. The more one develops an accuracy mindset, the more one will be accurate and precise in everything one does.
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