What is the hundreds digit of the integer z?

Question

(1) 10z = 93,120
(2) z rounded to the nearest hundred is 9,300.

Bunuel · Answer

What is the hundreds digit of the integer z?

(1) 10z = 93,120
(2) z rounded to the nearest hundred is 9,300.

Show Answer

Official Answer

A

Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.

For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum

gmat1220 · Answer

2) is insuff since hundreds digit has range. Hence not suff to determine the exact value.

A is best.

subhashghosh · Answer

Hi Bunuel

Could you please explain how this is correct ?

9,250<z<9,350

Regards,
Subhash

Bunuel · Answer

Any number from this range rounded to the nearest hundreds will be 9,300.

subhashghosh · Answer

Please elaborate a bit more on this :

"Any number from this range rounded to the nearest hundreds will be 9,300."

One of my doubts is, how are we converting the ten's and unit's place to 0 while rounding off ?

Regards,
Subhash

fluke · Answer

The statement says nearest 100.

Take few examples;

575: 575 is between 500 and 600 but which one is the nearest 100 to 564; 600 or 500; 600 because it is just 25 away from 600 and 75 away from 500. So; 564 rounded to nearest hundred is 600.

Likewise;
9,230 is between 9200 and 9300; but the nearest 100 for 9230 is 9200.

For the range; 9250<z<9350; take any number; 9251, 9260, 9270, 9299, 9300, 9315, 9340, 9349; there is only one number that is their nearest 100; that number is 9300.

So; if z=9260, then the nearest hundred is 9300
If z=9340; the nearest integer is 9300.

Thus, Statement 2 is not sufficient to uniquely deduce the hundreds digit of z. It could be either "2" as in 9260 or "3" as in 9340.

Spidy001 · Answer

My answer is A.

A is sufficient to answer this. 
 10z =93120 => z =9312 , hundreds digit is 3.

B is not enough as z can be anything from 9296.....9300...9305( so in some case hundreds digit is 2 and in some its 3).

pra1785 · Answer

Hi  Bunuel ,

For option A, z can be 9312 which gives the answer 3. 
Why can't z also be 93.12 ?

Bunuel · Answer

First of all we are told that z is an integer. But even more importantly, 10z = 93,120, gives z = 93,120/10 = 9,312.

pra1785 · Answer

Silly me. Totally ignored the fact that z is an integer. I thought the answer cannot be so straightforward and there has to something else to it that I am missing. Thank you!

Tonkotsu · Answer

What is the hundreds digit of the integer z?

(1) 10z = 93,120
We can solve for z, sufficient.

(2) z rounded to the nearest hundred is 9,300.
z not rounded to the nearest hundred can be any number from 1-9.

v12345 · Answer

Statement 1 : Sufficient
z = 9312
Hundreds digit of the integer z = 3

Statement 2 : Insufficient
z rounded to nearest hundred is 9300
Hundreds digit of the integer z = 2 or 3

Hence, OA is (A)

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

What is the hundreds digit of the integer z?

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