A certain office has 6 employees. If R employees

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


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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.

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.

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)

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.