MGMAT DS question -Ans makes sense??

khurram

Any easier way to explain this. I get what they are trying to say till the point the combine both the questions.
Thanks
khurram

What is the value of the tenths digit of number x?

(1) The hundredths digit of x is 5
(2) Number x, rounded to the nearest tenth, is 54.5
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
Both statements TOGETHER are sufficient, but NEITHER one ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT sufficient.

To answer the question, let's recall that the tenths digit is the first digit to the right of the decimal point. Let’s evaluate each statement individually:

(1) INSUFFICIENT: This statement provides no information about the tenths digit.

(2) INSUFFICIENT: Since the value of the rounded number is 54.5, we know that the original tenths digit prior to rounding was either 4 (if it was rounded up) or 5 (if it stayed the same); however, we cannot answer the question with certainty.

(1) AND (2) SUFFICIENT: Since the hundredths digit of number x is 5, we know that when the number is rounded to the nearest tenth, the original tenths digit increases by 1. Therefore, the tenths digit of number x is one less than that of the rounded number: 5 – 1 = 4.

The correct answer is C.

codesnooker · Posted: Tue Apr 08, 2008 9:14 pm Post subject:

If you understand that why they have combined the statement the solution, then hope you got the solution also.

Anyway, let check it again...

Let the x = AB.CD (I am taking AB because, they have taken 54 in 2nd statement.)

Target: Determine the value of C.

So, according to 1st statement:- D = 5

As it explained in your post, getting only the value of D, its impossible to determine the value of C.

Now, according to 2nd statement.
AB.CD is rounded of and reduced to AB.Y

and A = 5, B = 4 and Y = 5.

now, by this the possible values of C could be

i) C = Y or
ii) C = Y - 1 (as rounding off results into increment of value of C by 1, i.e. if D >= 5)

As it reveals two values of C, that's why its again insufficient.

Now lets take both the statement together...

Now we now that D = 5, so it means Y should be increased by in the rounding operation, so C should be equal to 4 (i.e. the 2nd possible condition mentioned above C = Y - 1)

So it means both statement together are sufficient.

Since this is a DS question, so no need to solve fully, you may solve this quickly just in your mind (I guess only after few practice).

Unfortunately there is no shortcut to this problem as far as I know, lets wait for Struat's comment.

Hope I have answered to your question a bit.

khurram · Posted: Wed Apr 09, 2008 6:14 am Post subject:

thanks

I got the solution but wanted to confirm that we can assume that 5 for the tenth is a result of rounding up.

Khurram

khurram · Posted: Wed Apr 09, 2008 9:00 pm Post subject:

I am reading it again and D is not the hundreth. It is the unit.

So still do not get the solution.

Khurram

khurram · Posted: Wed Apr 09, 2008 9:03 pm Post subject:

I am reading it again and D is not the hundreth. It is the unit.

So still do not get the solution.

Khurram

camitava · Posted: Wed Apr 09, 2008 9:54 pm Post subject:

khurram · Posted: Fri Apr 11, 2008 11:19 am Post subject:

thanks for the explanation

Now I need to ask one question

1234

is not 4 unit, 3 ten, 2 hundred, and 1 thousand digit.

that is why I am thinking ab.cd, d is the unit digit.

thanks
Khurram

Stuart Kovinsky · Posted: Fri Apr 11, 2008 11:40 am Post subject:

khurram · Posted: Sun Apr 13, 2008 9:40 am Post subject: Thanks

I get it

Just did not notice that hundreth is 1/100 being a non native speaker.

Khurram

rainbowpo · Posted: Thu Apr 24, 2008 6:45 pm Post subject:

I will go with C

hillzheng · Posted: Sun May 11, 2008 4:29 pm Post subject:

Yes, C is the correct answer.

chidcguy · Posted: Mon May 12, 2008 10:19 am Post subject:

This a good Q and I bit the dust the first time I saw similar Q. Here is how I am solving going forward.

(1) The hundredths digit of x is 5

Doesn't tell any thing about tenth's digit

(2) Number x, rounded to the nearest tenth, is 54.5

It tells us that there is a number X and was rounded to get 54.5. So We need to know what all numbers can be rounded to 54.5 and if all of them have the same tenth's digit

54.4[5-9] and 54.5[0-4] when rounded up/down will all give 54.5 So that means the tenths can be either 4 or5. Not sufficient

Both statements together fix the hundreth's digit of the above possibilities. if hundredth's is 5 and the rounded number is 54.5 the tenths must be 4.