In the decimal notation of number (2/23)^3. What is the thir

Question

In the decimal notation of the number  (\frac{2}{23})^3 , what is the third digit after the decimal point?

A. 0
B. 1
C. 2
D. 4
E. 8

Bunuel · Accepted Answer

In the decimal notation of the number  (\frac{2}{23})^3 , what is the third digit after the decimal point?

A. 0
B. 1
C. 2
D. 4
E. 8

Observe that  (\frac{2}{23})^3 < (\frac{2}{20})^3 .
 
Now,  (\frac{2}{20})^3 = (\frac{1}{10})^3 = 0.001 .
 
Finally, since  (\frac{2}{23})^3 < 0.001 , the third digit after the decimal point of  (\frac{2}{23})^3  must be less than 1, which is the third digit after the decimal point of 0.001. Therefore, it must be 0.

Answer: A

dileeprk · Answer

Simple and quickest approach:

(2/23) - > (0.0x..) no need to calculate after x

(0.0x..)^3 -> (0.000z....) (one 0 will multiply 3 times when cubed)

Therefore the third digit after the decimal point is 0.

IvanW · Answer

Is there a recommended spot to conceptually study how to approach problems like this?

How to notice these situations and to approximate as Bunuel did, ya know? Is Bunuel's approach the preferred method or is there a "book" approach to these styles of questions?

nitin6305 · Answer

There can be numerous ways to solve such questions. IMO, Bunuel approach is the best and you should follow that. But, end of the day what strikes you under timed conditions is the what matters. I suggest, to develop acumen for such questions, follow Bunuel and understand his approach for every question he responds to. 90% of times you will find that he has solved the questions in a much easier way. Initially, you will find his approach too hard to digest, but when you keep on seeing his methods, you will probably start thinking on the same lines.

Hope it helps!

OutOfTheHills · Answer

I got stuck and just couldn't find the shortcut to this question so I just tried the dumb method of doing long division. 23^3 took me 10 seconds, 2^3 was memorized. As soon as I tried long division of 8/12167, I figured out the trick. There were a lot of zeros before I could reach a number large enough to be divided by 12167 even once.

For anyone who still don't get it, just try solving the problem the dumb way by finding the numerator, denominator, and then doing long division. This question is one of those questions that you just have to start doing to understand what the "trick" is.

Akshit03 · Answer

Didn't get this at all:
"since  (\frac{2}{23})^3<0.001 , then the third digit to the right of the decimal point of  (\frac{2}{23})^3  is 0.
"

How can you say that just because it is 1 in another case, it will be 0 in another number which is shorter? I am missing something.
Can you please explain in detail? Thanks.

Bunuel · Answer

Check any positive number less than 0.001. You'll see that the third digit to the right of the decimal point will be 0.

gmatchile1 · Answer

Explanation by Claudio Hurtado, GMAT QUANT Tutor:
We must devise a strategy that allows us, through bounding or another method, to draw a conclusion in order to choose the correct alternative.

Do you have any ideas? Take 3 minutes to come up with something, don’t be afraid, it doesn’t matter if you’re wrong, dare to try.

Alright, we can compare the given expression with a similar but more manageable one.

Do you see it? Take 2 more minutes and try to identify it.
Excellent, if we compare (2/23)^3 with (2/20)^3, what do you notice?

Yes, the second expression (2/20)^3 is greater than the first (2/23)^3.
Now, calculate (2/20)^3 and tell me the decimal it yields.

Notice that (2/20)^3=(1/20)^3, (2/20)^3=(1/10)3 why is that?
Very good, (2/20)^3=(1/10)^3= 0.001.

With what you have discovered so far, are you able to give an answer to the question? Take 2 minutes.
Alright, given that (2/23)^3<0.001, the third digit of (2/23)^3 must be less than 1 (and thus, there is only one possibility; the third digit of (2/23)^3 must be zero).

If you arrived at the answer, CONGRATULATIONS! If not, keep practising.

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

In the decimal notation of number (2/23)^3. What is the thir

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

In the decimal notation of number (2/23)^3. What is the thir

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards