A certain office has 6 employees. If R employees

Question

A certain office has 6 employees. If R employees are chosen to be on the party planning committee, what is the value of R?

(1) R² + 2R - 8 = 0

(2) There are 15 different ways to choose R employees to be on the party planning committee

NOTE: Kudos for all correct solutions

Our video solution to this question can be found here: https://www.gmatprepnow.com/module/gmat ... /video/799

mgcon · Answer

S1 - Sufficient (R can not be negative & you get R = 4 on solving the equation)
S2 - Insufficient. Cannot get any value of R on solving the equation - 6Cr = 15

Hence  A

atshy21saraf · Answer

S1: By solving, (R-2)*(R-4)=0;
R can't be negative so, R=4 >>> SUFFICIENT
S2: There are two possible values i.e. R=2 or R=4 >>> INSUFFICIENT

Hence, A

acegmat123 · Answer

St 1:

R^2 + 2R -8=0

(R+4)(R-2)=0

R=-4 or 2

R can't be negative

So R = 2

Sufficient

Statement 2:

6C4 = 6C2 = 15

So R can be 2 or 4

Insufficient

A

Sent from my iPhone using  GMAT Club Forum mobile app

anox · Answer

mankodim  please note that your reasoning for Stmt 2 is not correct. The statement is  Insufficient  because you can get 15 for two values of R i.e. 2 and 4 and not because you can not solve for R

Others have provided more detailed solution that you can refer above.

CrackverbalGMAT · Answer

Hi,

My two cents to this question

nCr means selecting “r” things out of “n”.

Remember this, if in a question total number of ways is given (the value of nCr) and how many are selected is also given (the value of r), then “n” will always a unique value.

For an example, nC2 = 10, then “n” has to be 5.

But if in a question total number of ways is given (the value of nCr) and total number of things is given (the value of n), then “r” may have more than one value.

For an example, 5Cr = 10 means “r” could be 2 or 3.

Just to add to that, remember nCr = nC(n-r).

So “r” could have more than one value.

So here in this question, n is given,

So we are finding “R”.

Statement I is sufficient:

No need to factorize this,

Just remember in a quadratic equation of the form Ax^2+Bx+ C = 0,

If B is positive and C is negative, then one root positive and one root will be negative.

So here also one value of R will be positive and one value of R will be negative.

Here negative value doesn’t make sense because we are selecting things.

So it is sufficient.

So answer has to be either A or D.

Statement II is insufficient:

It’s the first case which mentioned above,

So it could be 6C2 or 6C4

So not sufficient.

So the answer is A.

Abhishek009 · Answer

FROM STATEMENT - I   (POSSIBLE)

r^2 + 2r - 8 = 0

r^2 + 4r - 2r - 8 = 0

r ( r + 4 ) - 2 ( r + 4 ) = 0

r = 2 , - 4

Since, r can not be -ve value of r must be 2

FROM STATEMENT - I   (NOT POSSIBLE)

6c_r  = 15

So, r can be 2 or 4
 
We can not have a unique solution for r from this statement ... 
  
Hence, Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient to answer the question asked, answer will be (A)

SVaidyaraman · Answer

What is tested in statement 2 is whether one can use the fact nCr = nC(n-r) and therefore see that two values of R are possible and in statement 1 of course, that R cannot be negative.

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.

A certain office has 6 employees. If R employees

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

A certain office has 6 employees. If R employees

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