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[sana.noor]

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
OA is D
i know N!/n-2 = 90 and only 10.9 fits to the choice and 10 is the answer. is their any other way to do this question?

[vipulgoyal]

plug in to get desired no 90, suppose there are 10 ways to select P then ways to select VP 9, 10*9 = 90

[theCodeToGMAT]

The Answer would be

2!(nC2) = 90
2 ( (n)*(n-1)/2) = 90
n(n-1)=90
n = 10

Answer[spoiler]{D}[/spoiler]

[ganeshrkamath]

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
OA is D
i know N!/n-2 = 90 and only 10.9 fits to the choice and 10 is the answer. is their any other way to do this question?

NC2 * 2! = 90
N(N-1)/2 * 2 = 90
N(N-1) = 90
N = 10

Choose d

Cheers

[[email protected]]

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

[Brent@GMATPrepNow]

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

[vinay1983]

Thanks Rich and Brent!I really appreciate the way you have explained the question in a simple way!