Question

A group of college students decide to contribute equally to the purchase of a Rs. 36 gift for their friend. How many people are in the group? (1) The number of people in the group is equal to the size of each person's contribution, in rupees. (2) If three more people joined the group, each person's individual contribution would fall by Rs.2.

• A. if the question can be answered by using any of the statements alone but not by using the other statement alone.
• B. if the question can be answered by using either of the statements alone.
• C. if the question can be answered only by using both the statements together.
• D. if the question cannot be answered

Answer 1

The correct option is B

if the question can be answered by using either of the statements alone.

From statement 1 (Sufficient)

Let n be the number of people and x be the amount contributed by each person. Hence, from statement (1) n = x

Is is given that $n^2=36\Rightarrow$ n=6

From statement 2(Sufficient) the new number of people is n + 3, and the new contribution is x - 2. The product will still be 36.

Thus, we know that 36 = (n + 3)(x - 2). We also still know that 36 = nx, or $\frac{36}{n}$. Let's expand the new equation and swap out x.

36 = (n + 3)(x - 2) =nx + 3x - 2n - 6

Since nx equals 36, we can substitute in 36 for nx as follows:
36 = 36 + 3x - 2n - 6
6 = 3x - 2n

Now substitute in $\frac{36}{n}$ for x:
$6=3\left(\frac{36}{n}\right)-2n$
$6=\frac{108}{n}-2n$ $2n^2+6n-108=0$
Solving this, n=6.