Question

Every member of a certain club volunteers to contribute equally to the purchase of a $60giftcertificate.Howmanymembersdoestheclubhave?\left(1\right)Eachmembe{r}^{\prime }scontributionistobe$4.
(2) If 5 club members fail to contribute, the share of each contributing member will increase by $2.

• A. Statement (1) alone is sufficient, but statement (2) alone is not sufficient.
• B. Statement (2) alone is sufficient, but statement (1) alone is not sufficient.
• C. Both statements together are sufficient, but neither statement alone is sufficient.
• D. Each statement alone is sufficient.
• E. Statements (1) and (2) together are not sufficient.

Answer 1

The correct option is D Each statement alone is sufficient.

1. If each member’s contribution is to be $4andthetotalamounttobecollectedis$60, then members in the club; SUFFICIENT.
2. Let c represent each person’s contribution, and let x represent the number of members in the club. From the given information, it is known that . From this, it is also known that . These two equations can be solved simultaneously for x: ;
   

;

;

;

$2(x-15)(x+10)=0$;

Therefore, x could be $15$ or $–10$. Since there cannot be $–10$ members, x must be $15$; so there are $15$ members in the club; SUFFICIENT.

• The correct answer is D; each statement alone is sufficient.