Gregmat quant practice problem

GRE GRE Quant Problem Solving
1

A teacher is constructing a lottery game for his students. To win the game, a student must correctly guess two random, distinct letters (order not important) from a set of distinct letters. If the teacher designs the game so that the chance of winning is less than 1%1%, what is the minimum number of letters he should include in the set?

For this question, could we solve using this equation? This is what i thought of after reading the question.

1/(nC2) == 0.01

Solving the value of n would give us the number of minimum of letters. (but i do think the solution provided in the video is easier)

2

\frac{1}{\binom{n}{2}} < 0.01

What you have is also simple enough to work with. You just need to find the smallest pair of consecutive numbers whose product is greater than 200.

3

My method involves solving the equation using the quadratic formula and a few other calculations which would give me 14.65 as the answer. Rounding it off would give 15 which is the correct answer.

Hard to solve this with my method in 2 minutes in an actual exam :sweat_smile:

4

You obviously didn’t need to use the quadratic formula for this. It might be helpful to check what I wrote above; I continued from where you left off.

5

Got it.
i meant solving it through my way will involve solving a quadratic equation.