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 --> z=9,312 --> the hundreds digit of z is 3. Sufficient. (2) z rounded to the nearest hundred is 9,300 --> 9,250<=z<9,350 --> the hundreds digit of z could be 2 or 3. Not sufficient. Answer: A. Please post PS questions in the PS subforum: gmat-problem-solving-ps-140/ Please post DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math 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

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What is the hundreds digit of the integer z?

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What is the hundreds digit of the integer z?

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