Rounding - Need back-up !

[gander123]

Hey guys,

The following caused some confusion to my understanding of rounding principles....

GMAT Prep Software, Problem QDS14011:

" 3.2XY6

If X and Y each represent single digits in the decimal above, what digit does X represent?

(1) When the decimal is rounded to the nearest tenth, 3.2 is the result.

(2) When the decimal is rounded to the nearest hundredth, 3.24 is the result.

OA: E

OA Explanation:

(1) Since the tenths digit is 2 in both 3.2XY6 and 3.2, the decimal must have been rounded down. Therefore, X can represent 0,1,2,3 or 4; NOT SUFFICIENT.

--> Totally Fine with that !

(2) If the value of Y is 5,6,7,8 or 9, X can represent 3, and the decimal must have been rounded up. If the value of Y is 0,1,2,3, or 4, X can represent 4, and the decimal must have been rounded down; NOT SUFFICIENT.

A variety of numbers, for example 3.2376 and 3.2416, could still satisfy both (1) and (2). Both statements together are still not sufficient.

My question:

Concerning the bold-faced portion of statement two:

From my understanding, if I took Y = 4 then the last digit (tenthousandths digit, which is 6) would round Y = 4 up to 5. Then, it would no longer be possible that X = 4... I'm a bit lost, which is taken as the decisive digit for rounding?!?!

Can you help me please ?!

brgds,

Tobi

[Jim@StratusPrep]

Not sure I completely follow your question, but I think the issue is that you are continuing to round.

Look at the following examples where I round to the nearest 10th.

.146 = .1 (not .15 = .2)
.156 = .2
.153 = .2

Hope this helps. Let me know if I did not answer the question.

[gander123]

Hey Jim,

thanks for answering so quickly..

.146 = .1 (not .15 = .2)

I would have rounded that expression to 0.2 by taking the thousandths digit first, then the hundredths digit and so on.

I would have done the same on statement (2) in the problem.

So when the statement gives

"rounded to the nearest hundredth"

you only take the next digit (i.e. the thousandth digit) in order to decide whether to round up or down ??

Sorry, but I'm really confused about the concept..

Appreciate your answer!

Cheers,
Tobi[/b]

[GMATGuruNY]

What is .3ABC rounded to the nearest tenth?

If A<5, we round DOWN to .3.
If A≥5, we round UP to .4.
The values of B and C are IRRELEVANT.

Thus:
.3499 is rounded DOWN to .3.
The reason is that .3499 is LESS THAN HALFWAY between .3 and .4.

.35 is rounded UP to .4.
The reason is that .35 is AT LEAST HALFWAY between .3 and .4.

[Jim@StratusPrep]

Yes, you will only round by the very next digit (not the string).

[gander123]

Hey there,

The values of B and C are IRRELEVANT.

Yes, you will only round by the very next digit (not the string).

THANK YOU very much. That's exactly what I was looking for.

Brgds,

Tobi