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GMAT Club Olympics 2024 (Day 2): Nine individuals are sitting

1 2 3 4 5 6 7

BGbogoss

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09 Jul 2024, 16:43

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In the group we have 2 children, 1teenager, 2 young adults, 3middle-aged adults, and 1senior citizens.

Evidence : total number 9 ,senior citizen, who is the only individual in that age group. There are more middle-aged adults than individuals of any other age group. There are fewer teenagers than children, young adults, or middle-aged adults.

Then, the first three individuals from the left are a young adult, a teenager, and another young adult and the senior is in the other extremity.
We are left with 3 Middle aged and 2 children to place in position 4 to 8.
Since No two individuals from the same age group are sitting next to each other, Middle aged are in positions 4, 6, 8 and children in 5 and 7.

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09 Jul 2024, 18:54

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Children = C, teenagers = T, young adults = Y, middle-aged adults = M, and senior citizens = S from 1 -> 9 position
M > other
T < C/Y/M
1st = Y, 2nd = T, 3rd = Y ....., 9th = S

-> M = 5 -> C =1 Y = 1 T = 1 -> Conflict T < C/Y/M
-> M = 4 -> C or Y = 2, C or Y = 1, T = 1-> Conflict T < C/Y/M
-> M = 3 -> C = 2, Y = 2, T = 1 -> OK
1st = Y, 2nd = T, 3rd = Y, 4th = M, 5th = C, 6th = M, 7th = C, 8th = M, 9th = S

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09 Jul 2024, 19:05

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Since there are more middle - aged people, both position have to be filled by them, in order to follow that no two age groups can sit together

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09 Jul 2024, 19:39

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Bunuel

Nine individuals are sitting on the dais, from left to right, to receive an award at a local club. The awardees include at least one from each of five age groups: children, teenagers, young adults, middle-aged adults, and senior citizens. The first or the last seat is occupied by a senior citizen, who is the only individual in that age group. No two individuals from the same age group are sitting next to each other. For example, no young adult is sitting next to another young adult. There are more middle-aged adults than individuals of any other age group. There are fewer teenagers than children, young adults, or middle-aged adults. The first three individuals from the left are a young adult, a teenager, and another young adult.

In the table, select the age group of the Fifth individual from the left and the age group of the Seventh individual from the left. Make only two selections, one in each column.

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Based on the given info, If we plot the diagram of the position it looks like the below.

Where children, teenagers, young adults, middle-aged adults, and senior citizens. are represented by c,t,y,m & s respectively.

The positioning is like :

y t y m c m c m s

This fulfills all the conditions.
Hence 5th and 7th positions are both children.

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09 Jul 2024, 20:19

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Bunuel

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Constraints given:

Nine individuals.
Five age groups: children (C), teenagers (T), young adults (Y), middle-aged adults (M), senior citizens (S).
The first or last seat occupied by a senior citizen (S), who is the only one in that age group.
No two individuals from the same age group next to each other.
More middle-aged adults than any other age group.
Fewer teenagers than children, young adults, or middle-aged adults.
First three from the left: Y, T, Y.

Let us make the Arrangement:

Young adult (Y)
Teenager (T)
Young adult (Y)
Middle-aged adult (M)
Child (C)
Middle-aged adult (M)
Child (C)
Middle-aged adult (M)
Senior citizen (S)

This combination satisfies all of the given constraint, so 5th and 7th position age group in the list are children and children.

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09 Jul 2024, 20:35

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Nine individuals are sitting on the dais, from left to right, to receive an award at a local club. The awardees include at least one from each of five age groups: children, teenagers, young adults, middle-aged adults, and senior citizens. The first or the last seat is occupied by a senior citizen, who is the only individual in that age group. No two individuals from the same age group are sitting next to each other. For example, no young adult is sitting next to another young adult. There are more middle-aged adults than individuals of any other age group. There are fewer teenagers than children, young adults, or middle-aged adults. The first three individuals from the left are a young adult, a teenager, and another young adult.

children (C), teenagers (T), young adults (YA), middle-aged adults (MA), and senior citizens (SC)

we can conclude from the question that
C : 2
T : 1
YA : 2
MA : 3
SC : 1

Using this
The first or the last seat is occupied by a senior citizen. The first three individuals from the left are a young adult, a teenager, and another young adult.

(YA) (T) (YA) () () () () () (SC)
No two individuals from the same age group are sitting next to each other.
(YA) (T) (YA) (MA) (C) (MA) (C) (MA) (SC)

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09 Jul 2024, 20:44

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C: Children
T: Teenagers
Y: Young adults
M: Middle aged
S: Senior

C + T + Y + M + S = 9

S = 1 => C + T + Y + M = 8
M > C, T, Y,
T < C, Y

=> The only possibility is T = 1, C = Y = 2, M = 3

The first three individuals from the left are a young adult, a teenager, and another young adult
The first or the last seat is occupied by a senior citizen, who is the only individual in that age group

1 => Y
2 => T
3 => Y
4 => M
5 => C
6 => M
7 = > C
8 => M
9 => S

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09 Jul 2024, 20:54

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Facts -
0. Start or end by S
1. No 2 of same age group together
2. Middle aged > Children / Young Adults / Middle Aged / Senior Citizens
3. Teenagers < Children / Young Adults / Middle Aged
4. The first three individuals from the left are a young adult, a teenager, and another young adult.

Using 4 and 0,
Y T Y _ _ _ _ _ S

We also know, T < C/ Y / M
T can be 1+ that implies, C / Y / M can be 2+ but we also know that only 5 blanks are vacant so we need to accomodate C and M. If we give C - 2 seats and M - 3 seats (as M>others), this would work.

Now, how can we give M, 3 seats.

Y T Y M _ M _ M S

Give remaining seats to C

Y T Y M C M C M S

Hence, answer to both questions is Children

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09 Jul 2024, 20:59

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Given that,
No two individuals from the same age group are sitting next to each other
Middle aged adults (M) > children (C), teenagers (T), young adults (Y), senior citizens (S)
S = 1
T < C, Y, S.
Seating order: Y T Y _ _ _ _ _ S.

As the number of M is the largest. M > 2 ........... (since we already know that there are 2 Ys and there is atleast one of each age group)
Hence, M = 3. Placing M in the order below:
Y T Y M _ M _ M S

We are only left with either T or C taking the vacant places ......... (as S is done with 1, Y can't be greater than 2)
Now, T < C. Thus there can't be 2 Ts and only 1 C.
Therefore, the only option we have is to fill both the void places with C.

The final placement shall be: Y T Y M C M C M S

For the question, we have C at 5th place from the left and C at 7th place from the left.

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09 Jul 2024, 21:44

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Let C- children, T - teenager, YA - young adult, MA - middle aged adult, S - senior citizen.
Question provides 1st 3 seats from left as - YA, T, YA
Question also states S will be in first or last seat. Given above, S will be in last seat.

So far arrangement for 9 seats is : YA, T, YA, _, _, _, _, _, S

Its also provided that MA >C, T, YA, S and T < C, YA, MA
Since no two individuals with same age group can sit next to each other 4th is not YA and 8th is not S.
Since MA > YA we need atleast 3 MA which also cannot sit next to each other.

So arrangement for 8 seats is : YA, T, YA, MA, _, MA, _, MA, S

Since T < C, and we already have 1 T, we need atleast 2 C's which are remaining seats.

Fifth individual: Children
Seventh individual: Children

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09 Jul 2024, 22:00

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Given: 9 seats, 5 Groups
Senior C: 1 ; Middle A : Highest ; Teenage<Child/Young A<Middle A

Senior C occupies 1st or last seat; also given that arrangement starts with YA, T, YA

Soln : To maximize MA : 3 seats max can be given ; rest Young A and Child will be 2 so that condition that only MA has max seats is satisfied.

Senior C will come at seat 9.

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09 Jul 2024, 22:28

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Let c, t, y, m and s be used as IDs for children, teenagers, young adults, middle-aged adults, and senior citizens respectively

Initial assignmnet:
Nc Nt Ny Nm Ns
1 1 1 1 1

The first or the last seat is occupied by a senior citizen, who is the only individual in that age group
Ns = 1
Nc Nt Ny Nm Ns
1 1 1 1 1

Nm > Nc, Nt, Ny, Nm, Ns
Since, each group will have at least 1, we can say,
Nm > 1, lets assume 2
Nc Nt Ny Nm Ns
1 1 1 2 1

There are fewer teenagers than children, young adults, or middle-aged adults.
Nt < Nc, Ny, Nm
This means Ny > 1 & Nc > 1 since Nb is at least 1, lets assume both to be 2
Also we have to update Nm > 2 since Ny and Nc are at least 2. Lets assume 3.
Nc Nt Ny Nm Ns
2 1 2 3 1

Since we have only 9 individuals, we already have our numbers.

The first three individuals from the left are a young adult, a teenager, and another young adult.
y t y _ ? _ ? _ _

Since senior sitizen can only be forst or last, we know they are last
y t y _ ? _ ? _ s

Since no two indivisuals of same age group can sit together, we have to populate the 3 middle aged adults as follows
y t y m ? m ? m s

So remaining spots are for 2 children

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09 Jul 2024, 22:29

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Answer: First, we need to properly digest what the question is asking for. The question is asking that we examine each of the following statements and see which one, if it is true, supports bringing in a "ringer" and which one, if it is true, supports casting among existing members of the troupe.

Before looking at the statements, note the "Story": Troupe managers are contemplating bringing in a professional performer for an upcoming festival that is important to them. The troupe they manage is "amateur," but the troupe has had "some of their most successful shows" using only troupe members.

(The statements are quoted below with analysis in bold)

"Any actor would be eager to play a lead role at a festival this prestigious." This is irrelevant because the eagerness of actors do factor into the managers' decision—it is unrelated to the "Story." Also, "Any actor" is encompasses both professional ringers and troupe members who are amateur.

"An organization should not alter regular practices unless they have failed to produce results." This statement would support casting troupe members for the upcoming festival because the troupe has had some of their most successful performances using their own troupe members. Pick this for "Cast from the troupe."

"A theatre troupe should cast actors with the most experience in stage acting in lead roles." This is irrelevant because "most experience in state acting as lead roles" does not distinguish between ringers and troupe members. For example, ringers might have less stage experience "acting in lead roles" but they have a longer training period under the best of masters.

"In casting any role, a theatre troupe must take care not to alienate its members." This is also irrelevant because bringing in a ringer need not "alienate" anyone.

"Theatre troupes often deliver exceptional performances when they cast professional actors." This supports bringing in a trouper because ringers are professional actors, and if the statement is true, ringers will "deliver exceptional performances" for the upcoming festival. Pick this for "Ringer."

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09 Jul 2024, 22:32

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Quote:

The first three individuals from the left are a young adult, a teenager, and another young adult.

The first or the last seat is occupied by a senior citizen, who is the only individual in that age group

Quote:

There are more middle-aged adults than individuals of any other age group

Which means M>2, as M>Y and Y=2

Quote:

No two individuals from the same age group are sitting next to each other.

There are 5 spots to fill, M can be 3 but cannot be 4 or 5 because if it is, then at least 2 M's will sit next to each other

Quote:

There are fewer teenagers than children, young adults, or middle-aged adults.

T must be less than C, Y, M
Since we have 2 spots left, both have to be C

Answer:
FIFTH INDIVIDUAL = CHILDREN
SEVENTH INDIVIDUAL = CHILDREN

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09 Jul 2024, 22:36

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Bunuel

This question was provided by Experts' Global
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Given,
9 individuals (childern(c) + teenager(t) + young(y) + middle aged(m) + senior(s))
No idividuals of same group are sitting next to each other.
At least one individual is there from each age group.
Means rest 4 are repeating.

Senior cetizen is either on the right most or left most position of dais, and only 1 is there from that age group.
=> sa x x x x x x x x sa (any of 1st or last), sa = 1

There are fewer teenagers than children, young adults, or middle-aged adults.
=> t = 1 as out of rest 4 if we consider one more teenager than it would not satisfy above condition.

There are more middle-aged adults than individuals of any other age group.
=> m = 3, c = 2, y = 2. If m > all other age group then out of rest 4 individuals we have to consider 2 middle aged adults and 1 child and 1 young aged else it will not satisfy above condition.

Now we have c = 2, t = 1, y = 2, m = 3, s = 1.

The first three individuals from the left are a young adult, a teenager, and another young adult.
=> y t y x x x x x s

Now, we have m = 3 and c = 2, as we know no 2 of same age group are sitting next to each other we can deduce the sitting positions as below.
=> y t y m c m c m s

So, we have child at both 5th and 7th position from left.

Answer: Children for both the columns.

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09 Jul 2024, 23:14

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On both the positions, fifth and seventh there will be a children

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09 Jul 2024, 23:46

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Solution: From the given information we can summarize that:

There is at least one individual from each of the five age groups: children (C), teenagers (T), young adults (Y), middle-aged adults (M), and senior citizens (S).
The first or last seat is occupied by the only senior citizen (S).
No two individuals from the same age group sit next to each other.
There are more middle-aged adults than individuals of any other age group.
There are fewer teenagers than children (C), young adults, or middle-aged adults (M).
The first three individuals from the left are a young adult (Y), a teenager (T), and another young adult (Y).

Let's symbolize the seats by numbers such that
Seats: 1 2 3 4 5 6 7 8 9
Initial positions: Y T Y _ _ _ _ _ _

Since the middle-aged adults count is more than any other group

The number of middle-aged adults (M) is the highest.
The number of teenagers (T) is the lowest but at least 1

Let's assume possible values:

Middle-aged adults (M): 3
Young adults (Y): 2 (given two young adults are already placed)
Children (C): 2
Teenagers (T): 1
Senior citizen (S): 1

Total: 3 (M) + 2 (Y) + 2 (C) + 1 (T) + 1 (S) = 9

Now, fill the positions ensuring no two same age groups are adjacent and the S is either in the first or last position. Since the first three are Y T Y, let's place S at the last position for convenience and fulfill the rest as:

1 2 3 4 5 6 7 8 9
Y T Y _ _ _ _ _ S

Given the restrictions, the M must appear three times and cannot be next to each other:

1 2 3 4 5 6 7 8 9
Y T Y M _ M _ M S

Finally, place children (C) and ensure no adjacencies:

1 2 3 4 5 6 7 8 9
Y T Y M C M C M S

Thus, the age group of the fifth and seventh individual from the left is a child (C)

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09 Jul 2024, 23:50

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Nine individuals are sitting on the dais, from left to right, to receive an award at a local club. The awardees include at least one from each of five age groups: children(CH), teenagers(T), young adults(YA), middle-aged adults(MA), and senior citizens(SC). The first or the last seat is occupied by a senior citizen, who is the only individual in that age group. No two individuals from the same age group are sitting next to each other. For example, no young adult is sitting next to another young adult. There are more middle-aged adults than individuals of any other age group(MA= 2 or more than 2). There are fewer teenagers than children, young adults, or middle-aged adults (T=1, CH=2,YA=2, MA=3). The first three individuals from the left are a young adult, a teenager, and another young adult----This also means that SC gonna be in the extreme right (YA--T--YA).

It has to be like

YA--T--YA--MA--CH--MA--CH--MA--SC

So 5th and 7th person has to be a child.

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10 Jul 2024, 00:07

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Bunuel

This question was provided by Experts' Global
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Accordign to the q:
we have 9 places to sit and 9 individuals

Children, teenagers, young adults, middle-aged adults, and senior citizens.
The first or the last seat is occupied by a senior citizen, who is the only individual in that age group.
No two individuals from the same age group are sitting next to each other.
There are more middle-aged adults than individuals of any other age group.
There are fewer teenagers than children, young adults, or middle-aged adults
The first three individuals from the left are a young adult, a teenager, and another young adult.
so the senior citizen would be on the other end (right extreme)

YA, T, YA 4th, 5th, 6th, 7th, 8th, SC

5th and 7th
they both can be the MA since MA are the most than any other group

so answer:
MA MA

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10 Jul 2024, 00:21

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Let children= C, teenagers= T young adults = Y, middle-aged adults= M and senior citizens = S

C+T+Y+M+S=9
The first or the last seat is occupied by a senior citizen, who is the only individual in that age group. S=1

C+T+Y+M = 8
There are more middle-aged adults than individuals of any other age group.
M is highest, M can be 3/4/5.

There are fewer teenagers than children, young adults, or middle-aged adults. T<C T<Y and T<M

So, T=1 , C=2 Y=2 M=3.

For arrangement
1- The first three individuals from the left are a young adult, a teenager, and another young adult.

2- The first or the last seat is occupied by a senior citizen,
1 2 3 4 5 6 7 8 9
Y T Y S

Now for M to sit alternatively they have to occupy 4 6 and 8. Remaining two seats will be occupied by
2 C

1 2 3 4 5 6 7 8 9
Y T Y M C M C M S

IMO 5- Childern 7- Childern