In a certain conference room each row of chairs has the same number of

Question

In a certain conference room each row of chairs has the same number of chairs, and the number of rows is 1 less than the number of chairs in a row. How many chairs are in a row?

(1) There is a total of 72 chairs.
(2) After 1 chair is removed from the last row, there is a total of 17 chairs in the last 2 rows.

Bunuel · Accepted Answer

In a certain conference room each row of chairs has the same number of chairs, and the number of rows is 1 less than the number of chairs in a row. How many chairs are in a row?

Say # of rows is R and # of chairs per row is C. 
Given: R=C-1. Question: C=?

(1) There is a total of 72 chairs --> CR=72 --> C(C-1)=72 --> C=9. Sufficient.

(2) After 1 chair is removed from the last row, there is a total of 17 chairs in the last 2 rows --> C+(C-1)=17 --> C=9. Sufficient.

Answer: D.

TeamGMATIFY · Answer

Given  : Number of rows is 1 less than the number of chairs in a row and each row has same number of chairs.
Assuming the number of Chairs = C.
Number of rows = C-1

Required  : C = ?

Statement 1  : Total chairs = 72
Total chairs = (chairs in a row)*(number of rows) = C*(C-1)
C*(C-1) = 72, Hence C =9
 SUFFICIENT

Statement 2  : C + (C-1) =17
Hence C = 9
 SUFFICIENT

Option D

redfield · Answer

How do we calculate C(C-1)=72? Doesn't that become C^2-C =72? What is the next step there

Bunuel · Answer

There is an easier way. Since C must be a positive integer, then C(C-1) is the product of 2 consecutive integers. The product of 2 consecutive integers equal to 72 is 9*8.

Hope it helps.

anairamitch1804 · Answer

Let number of rows is a, number of the chairs in a row is b.
So, b-a=1
From 1, ab72, a8, b9, sufficient alone.
From 2, 2b-1=17, b=9, sufficient alone.
Answer is D.

cman2010 · Answer

Where does "C(C-1)" come from? Why aren't you just plugging 72 into the equation C-1=R?

Bunuel · Answer

We are told that the number of rows is 1 less than the number of chairs in a row. So, if the number of chairs per row is C, then the number of rows is C - 1 and thus the total number of chairs is (the number of chairs per row)*(the number of rows) = C(C-1).

nkmungila · Answer

From A There is a total of 72 chairs. So it should be 9*8 Sufficient
From B After 1 chair is removed from the last row, there is a total of 17 chairs in the last 2 rows. last 2 total is enough to calculate So sufficient.

bumpbot · Answer

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.

In a certain conference room each row of chairs has the same number of

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

GMAT Data Sufficiency (DS) Questions

In a certain conference room each row of chairs has the same number of

Prep Toolkit

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