help

Hi sana.noor,

You could TEST THE ANSWERS on this question.

Since there are only two position, after you "pick" the president, there will be one fewer person who could be vice president. If you TEST each answer, here's what you'd get:

A: 7x6 = 42 options
B: 8x7 = 56 options
C: 9x8 = 72 options
D: 10x9 = 90 options
E: 11x10 = 110 options

Since we're told that there are 90 ways to make the selections, the answer must be D

GMAT assassins aren't born, they're made,
Rich

sana.noor wrote:A student committee on academic integrity has 90 ways to select a president and vice president from a group of candidates. The same person cannot be both president and vice president. How many candidates are there?
a)7
b)8
c)9
d)10
e)11

Here's a slightly different approach, same result.

Let x = the number of students.

Take the task and break it into stages.

Stage 1: Select a president
There are x students to choose from, so we can complete stage 1 in x ways

Stage 2: Select a vice-president
There are x-1 students remaining, so we can complete stage 2 in x-1 ways

By the Fundamental Counting Principle (FCP) we can complete both stages (x)(x-1) ways

Since we are told that there are 90 ways to select a president and vice-president, we can conclude that: (x)(x-1) = 90

At this point, there would be answer choices, so we could just start plugging in values for x, to get x = 10

Answer: D

Cheers,
Brent

Aside: For more information about the FCP, watch our free video: https://www.gmatprepnow.com/module/gmat-counting?id=775