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A student committee on academic integrity has 90 ways to select a pres
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08 Jul 2022, 06:27
08 Jul 2022, 06:27
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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
A. 7
B. 8
C. 9
D. 10
E. 11
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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GRE Math Essentials (2022)
GRE Geometry Formulas for a Q170
GRE - Math Book
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Re: A student committee on academic integrity has 90 ways to select a pres
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08 Jul 2022, 06:35
08 Jul 2022, 06:35
Carcass 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
A. 7
B. 8
C. 9
D. 10
E. 11
Let t = TOTAL number of candidates
So....
# of ways to select a president = x
# of ways to select a vice-president = x - 1
Total number of ways to select both = (x)(x - 1)
We're told that 90 ways are possible
So, (x)(x - 1) = 90
Expand: x² - x = 90
Rearrange: x² - x - 90 = 0
Factor: (x - 10)(x + 9) = 0
So, x = 10 OR x = -9
Since x cannot be negative, it must be the case that x = 10
Answer: D
gmatclubot
Re: A student committee on academic integrity has 90 ways to select a pres [#permalink]
08 Jul 2022, 06:35
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