Question 25, Chapter 11, GRE 5 lb. Book of GRE Practice Prob

[franalej]

Hello there,

Please I have a concern about problem 25, Chapter 11, GRE 5 lb. Book of GRE Practice, page 457.

The question stem is:

"x is a digit in the decimal 12.15x9, which, if rounded to the nearest hundredth, would equal 12.16.

Question A:

x

Question B:

4

Your answer on page 470 says that the answer is A, because the decimal would round to 12.16, since the thousandths digit x must be 5 or greater (6, 7, 8, or 9), and all of these possibilities are greater than 4.

However, your answer does not include the possibilty that x could be below 5. Since the position of the number 9 is to the right of x, x could be 4 and then because of the number 9 to its right, it would become 5, which would again render an answer of 12.16. However, in this case the answer for x could be 4, 5, 6, 7, 8 or 9, which would render an answer of D.

Is this latter logic wrong, and if so why?

Thanks for the help. I'm learning a lot with you.

-F

[tommywallach]

Hi F,

Indeed, you are falling for the trap here. Here's the thing about rounding:

Whenever you round to a given digit, you only pay attention to the digit directly to the right of that digit. Never round twice.

x is a digit in the decimal 12.15x9, which, if rounded to the nearest hundredth, would equal 12.16.

If you want to round this to the nearest hundredth, you only look at the thousandth digit. If we want a digit that will round UP to 6, x needs to be 5 or greater.

Your logic would require rounding twice:

12.1549

If we round to the nearest thousandth: 12.155

THEN, round to the nearest hundredth: 12.16

We'd get the number we want. But you can't round twice like this. If you're rounding to the nearest hundredth, you only look to the thousandth digit and round once.

Hope that helps!

-t

[franalej]

Thanks a lot for the clarification. Very important concept, I did not know this!

Please, just one more clarification regarding this concept. Does the same concept that you mentioned in bold apply to non-decimal numbers?

Thanks,

-F

Hi F,

Indeed, you are falling for the trap here. Here's the thing about rounding:

Whenever you round to a given digit, you only pay attention to the digit directly to the right of that digit. Never round twice.

x is a digit in the decimal 12.15x9, which, if rounded to the nearest hundredth, would equal 12.16.

If you want to round this to the nearest hundredth, you only look at the thousandth digit. If we want a digit that will round UP to 6, x needs to be 5 or greater.

Your logic would require rounding twice:

12.1549

If we round to the nearest thousandth: 12.155

THEN, round to the nearest hundredth: 12.16

We'd get the number we want. But you can't round twice like this. If you're rounding to the nearest hundredth, you only look to the thousandth digit and round once.

Hope that helps!

-t

[tommywallach]

Yep!

So if you were asked to round 549 to the nearest hundred, you would go:

549 --> 500

Not:

549 --> 550 --> 600

That being said, I'm not sure I've ever seen a GRE question that asked for rounding with non decimals! But hey, it could happen!

-t