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

A. 0

B. 1

C. 2

D. 4

E. 8

Answer A

Explanation by Claudio Hurtado, GMAT QUANT Tutor +56 937780070

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. If you want to learn these techniques to tackle GMAT QUANT questions, take classes with Claudio Hurtado (+56 937780070), a specialist teacher in developing tailored GMAT QUANT preparation programmes for students.