GRE Prep Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Each participant in a certain study was assigned a sequence
[#permalink]
01 Apr 2020, 09:29
01 Apr 2020, 09:29
Expert Reply
00:00
Question Stats:
73% (00:53) correct
26% (01:31) wrong based on 30 sessions
Hide Show timer Statistics
Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)
A 20
B 92
C 300
D 372
E 476
Kudos for the right answer and explanation
A 20
B 92
C 300
D 372
E 476
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Each participant in a certain study was assigned a sequence
[#permalink]
01 Apr 2020, 09:45
01 Apr 2020, 09:45
Carcass wrote:
Each participant in a certain study was assigned a sequence of 3 different letters from the set {A, B, C, D, E, F, G, H}. If no sequence was assigned to more than one participant and if 36 of the possible sequences were not assigned, what was the number of participants in the study? (Note, for example, that the sequence A, B, C is different from the sequence C, B, A.)
A 20
B 92
C 300
D 372
E 476
Kudos for the right answer and explanation
A 20
B 92
C 300
D 372
E 476
Kudos for the right answer and explanation
Take the task of creating sequences and break it into stages.
Stage 1: Select the first letter of the sequence
There are 8 letters to choose from.
So, we can complete stage 1 in 8 ways
Stage 2: Select the second letter of the sequence
There are 7 REMAINING letters to choose from (since the three letters must be different).
So, we can complete stage 2 in 7 ways
Stage 3: Select the last letter of the sequence
There are 6 REMAINING letters to choose from.
So, we can complete stage 3 in 6 ways
By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a sequence) in (8)(7)(6) ways (= 336 ways)
This means we are able to create enough sequences to accommodate 336 participants in the study.
Since 36 of the possible sequences were not assigned, the number of participants = 336 - 36 = 300
Answer: C
Note: the FCP can be used to solve the MAJORITY of counting questions on the GRE. So, be sure to learn it.
RELATED VIDEOS
gmatclubot
Each participant in a certain study was assigned a sequence [#permalink]
01 Apr 2020, 09:45
Moderators:
