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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne

1 2 3 4

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18 Dec 2024, 22:33

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There will be two possible sequences-

A
C
B
F
D/E
E/D

and

D/E
E/D
A
F
B
C

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We can consider the steps to range from numbers 1 (Starting from the top stair) to 6 (the bottom stair).

It is stated that:
Darryl and Edgar will be on consecutive steps, but not necessarily in that order.
Bailey will be two steps below Ariel
Fei will be on the step third from the bottom.

Hence Fei will be at step number 4 (third from bottom). There are two situations where Darryl & Edgar can be consecutive in this case which is 1,2 & 5.6. 2,3 will not be applicable as the condition around Bailey being two steps below Ariel will not be satisfied.

If Darryl & Edgar are 1,2 then Ariel will be at number 3 & Bailey will be number 5 ( second step from bottom) while Corinne would be at number 6 (bottom step)

If Darryl & Edgar are 5,6 then Ariel will be at number 1 & Bailey will be number 3 ( third step from top) while Corinne would be at number 2 (second step from top)

Hence based on these parameters possible steps for Corinne are (Bottom step, 2nd step from top) & for Bailey they are (2nd step from bottom, 3rd step from top)

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Given
__ __ F __ __ __
D/E or E/D are consecutive
B is 2 steps below A
Possible sequences
__BFAED or __BFADE OR CBFAED or CBFADE
DEFB__A or EDFB__A OR DEFBCA or EDFBCA

Answer: Bailey (2nd step from bottom, 3rd step from top)
Corinne (Bottom step, 2nd step from top)

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Bunuel

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Ariel, Bailey, Corinne, Darryl, Edgar, and Fei are positioning themselves on a flight of six steps for a picture. Darryl and Edgar will be on consecutive steps, but not necessarily in that order. Bailey will be two steps below Ariel, and Fei will be on the step third from the bottom.

If all of the people will be on different steps, select for Bailey the possible steps that Bailey could be standing on for the picture, and select for Corinne the possible steps that Corinne could be standing on for the picture. Make only two selections, one for each column

Lets A be Arieal, B be Bailey, C for Corinne, .... D E and F for rest.
D and E together Like DE or ED.
B _ A
And F is at 3rd from bottom.

(Bottom) _ _ _ _ _ _ (Top)

(Bottom) _ _ F _ _ _ (Top)
now B cant take 1st place because A will come at 3rd step that already taken by F
So possible places for B are 2nd and from bottom and 3rd from top
now sequence will look like this

(Bottom) _ B F A _ _ (Top) OR (Bottom) _ _ F B _ A (Top)
Considering These 2 lets place C, D and E.
D and E are consecutive but there is no order So
(Bottom) _ B F A D/E E/D (Top) OR (Bottom) D/E E/D F B _ A (Top)
Now Remaining blank will be taken by C. So total 4 Combinations are possible.

1 - (Bottom) C B F A D E (Top)
2 - (Bottom) C B F A E D (Top)
3 - (Bottom) D E F B C A (Top)
4 - (Bottom) E D F B C A (Top)

Answer for,
Bailey the possible steps = 2nd step from bottom, 3rd step from top
Corinne the possible steps = Bottom step, 2nd step from top

nishantswaft

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19 Dec 2024, 01:02

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In TPA questions it’s always better to form a strategy first before solving. Let's take all the details/constrains on our notepad.

The question stem tells us that;

Ariel, Bailey, Corinne, Darryl, Edgar, and Fei are positioning themselves on a flight of six steps for a picture
Darryl and Edgar will be on consecutive steps, but not necessarily in that order
Bailey will be two steps below Ariel
Fei will be on the step third from the bottom.

And we have to find;

the possible steps that Bailey could be standing on for the picture
the possible steps that Corinne could be standing on for the picture.

In such questions, it's always better to start from a position that is relatively fixed.

So let's place fei first,

_ _ F _ _ _;

Now let's place Bailey and Ariel,
This could be done in two ways;

_ B F A _ _
_ _ F B _ A

Now let's place Darryl and Edgar,
Since they'll hold consecutive stairs;

_ B F A D E
D E F B _ A

Since, at last, we are not concerned about Darryl and Edgar, their relative positions won't matter.

Let's fill the final spot with Corinne,
So we have two possibilities now;

C B F A D E
D E F B C A

So,
The possible steps that Bailey could be standing on for the picture = [color=#000000]2nd step from bottom, 3rd step from top [/color]
[color=#000000]The possible steps that Corinne could be standing on for the picture = Bottom step, 2nd step from top.[/color]

Hence we can choose these respective options.

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19 Dec 2024, 01:03

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let's first write what we know for sure.

1- F is third from bottom.
2- D and E are together.
3- B is 2 steps below A.

Let's number the steps starting from below as 1 and the topmost step numbered as 6.

F is on step 3

If A is on 6th, B will have to be on 4th (which is 3rd from the top).
A cannot be on 5th, as then B will have to be on 3rd and 3rd is already taken by F.
If A is on 4th, B will have to be on 2nd (which is 2nd from the bottom).

Therefore, Positions of B can be 3rd from the top, 2nd from the bottom.

If A is on 6th, and B on 4th (which is 3rd from the top), D and E have to be together and only 1 and 2 are steps that can accomodate them. This leaves 5th step (Second from the top) for C.

If A is on 4th, B on 2nd (which is 2nd from the bottom), D and E have to be together and only 5 and 6 are steps that can accomodate them. This leaves 1st step (bottom) for C.

Bunuel

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Ariel, Bailey, Corinne, Darryl, Edgar, and Fei are positioning themselves on a flight of six steps for a picture. Darryl and Edgar will be on consecutive steps, but not necessarily in that order. Bailey will be two steps below Ariel, and Fei will be on the step third from the bottom.

If all of the people will be on different steps, select for Bailey the possible steps that Bailey could be standing on for the picture, and select for Corinne the possible steps that Corinne could be standing on for the picture. Make only two selections, one for each column

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19 Dec 2024, 01:44

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Hi All,

Let assume this is the steps from the left most being the at the buttom and the right most being at the top

_ _ _ _ _ _

Given:

Step 1) D and E are concecutive --> D E or E D
Step 2) B two steps below A --> B _ A
Step 3) F will be on the 3rd step from button --> _ _ _ F _ _

Formations for step 2 can be in either two ways

B _ A F_ _ -equation 1

or

_ _ B F A _ -equation 2

Putting Step 1 in equation 1 and equation 2

B _ A F D E or B _ A F E D , there fore C will be at the 1st step from the buttom in this case

and

D E B F A _ or E D B F A _ , therefore C will be at top step in this case

We can see in the above final 4 possibilites, B is either at the buttom or 3rd step from the top

And for Arragement for C, its either 1st from the buttom/4th from the top or top step. This option is obviously not present , i updated the closed one i could find.
Will check the reasoning once the answers are released.

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Bunuel

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Step	1st Instance	2nd Instance
6	A	E
5	C	D
4	B	A
3	F	F
2	E	B
1	D	C

Criteria:
1. D and E will be on consecutive steps but the order can be DE or ED.
2. B will be 2 steps below A, which means there is a gap of 1 step between them.
3. F will be on the 3rd step from the bottom.

As per the table, Bailey is 3rd from the top and 2nd from the bottom whereas Corinne is 2nd from the top and at the bottom. These are the possibilities.

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19 Dec 2024, 02:13

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Following are the possibilities :

Sno	Possibility 1	Possibility 2
1	A	D/E
2	C	D/E
3	B	A
4	F	F
5	D/E	B
6	D/E	C

Bunuel

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19 Dec 2024, 03:17

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Let 1-6 represents the steps from top to bottom.

As F takes 4, A is 2 steps higher than B, B must take either 5 (A takes 3) or 3 (A takes 1). So we only have 2 scenarios:

	Scenario 1	Scenario 2
1	D (or E)	A
2	E (or D)
3	A	B
4	F	F
5	B	D (or E)
6		E (or D)

So C must take either 2 or 6.

Answer: B = Bottom step, 3rd step from top . C = Bottom step, 2nd step from top

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19 Dec 2024, 03:37

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For me, this question looks incorrect. Waiting for Explanation.

The order I created from the top:
1st (Top) : D / E
2nd : E / D
3rd: A
4th: F
5th: C
6th: B

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19 Dec 2024, 04:40

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From the given information & the restrictions, there are 2 ways that positioning of people can be done on the stairs -

1st :
Bottom c > b > f > a > d/e > e/d Top

2nd:
Bottom e/d > d/e > f > b > c > a Top

So, the possible steps for Bailey are - 2nd step from bottom, 3rd step from top
& the possible steps for Corinne are - Bottom step, 2nd step from top

Bunuel

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19 Dec 2024, 06:14

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Because F is fixed at the 3rd step from bottom and B has to be 2 steps below A => this leaves 2 options for A - the 4th step from bottom and the top step.
(A cannot be at 1st, 2nd, 3rd,5th because there will either be no place for B within the scale or B will be on the same step as F, which is not possible)
As that, B is left with 2 options: 2nd step from bottom (when A is at the 4th from bottom) or 4th step from bottom (when A is at the top step)
Now, we know that D and E have to be consecutive.
Opt.1: B is at 2nd from the bottom, A is at 4th from the bottom => D and E have to be in the 5th from the bottom and the top step (whatever the order, D-E or E-D)
=> C will be at the bottom step

Opt.2: B is at the 4th from the bottom, A is at the top step. => D and E have to be in the bottom step and the 2nd from the bottom (whatever the order, D-E or E-D)
=> C will be in between A and B, which is 2nd step from the top.

IMO, part 1: C, part 2:B

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Top	Option I	Option II
6	Ariel
5	Corrine
4	Bailey	Ariel
3	Fei	Fei
2		Bailey
1		Corrine
Bottom

Given, Fei will be on the step third from the bottom - so her position is fixed at 3.

Bailey will be two steps below Ariel - So,
Option I
When Ariel stands at the top step (6th step), Bailey will be at 4

Option II
When Ariel stands at 4th step, Bailey will be at 2

Now, Darryl and Edgar will be together (not necessarily in the same order)
In option I, only 1 combination is possible - Steps 1 and 2
in option II, only 1 combination is possible - Steps 5 and 6

So, for Corinne,
In Option I, only step 5 is left
In option II, only step 1 is left

Final answer:
Bailey: 2nd step from bottom, 3rd step from top
Corrine: Bottom step, 2nd step from top

Bunuel

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19 Dec 2024, 06:16

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Hi Everyone

6 Steps & 6 People
The 2 options as the constraints limit us are:
option 1:
A
C
B
F
E
D

Option 2:
D
E
A
F
B
C

Thus, the answer is 3 and 5 for Bailey
and 2 and 6 for Corinne.

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19 Dec 2024, 06:52

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Ans: Bailey-> Bottom step, 3rd step from top
Corinne-> 2nd step from bottom, 2nd step from top

In the question it is mentioned that Darryl and Edgar are on consecutive steps but not necessarily in that order and Bailey is two steps below Ariel i.e., there is a gap of 1 staircase between them. Additionally, it is mentioned that Fei is on the step third from the bottom

Keeping these 3 data in mind, we can make a table

1	A	D/E
2	C	D/E
3	B	A
4	F	F
5	D/E	C
6	D/E	B

From this we can see that we can arrange them in these 2 possible scenarios (4 if we have to fix the positions for Darryl and Edgar as well)
From the table we can see that Bailey will either be on the bottom step or the 3rd step from top and Corinne will either be on the 2nd step from bottom or the 2nd step from top

Bunuel

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19 Dec 2024, 07:57

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Let us visualize the steps horizontally ;
Left Extreme = TOP most , Gradually decreasing as it goes towards right, & Right extreme = Bottom most

Six Steps: _ , _ , _ , _ , _ , _

According to question:
Ariel, Bailey, Corinne, Darryl, Edgar, and Fei = Let it be A, B, C, D, E, F respectively.

Fei will be on the step third from the bottom
=> _ , _ , _ , F , _ , _

Darryl and Edgar will be on consecutive steps, but not necessarily in that order
=> _ , _ , _ , F , D, E or _ , D , E , F , _ , _ or D , E, _ , F , _ , _

Bailey will be two steps below Ariel
=> A , _ , B , F , D, E or (_ , D , E , F , _ , _ )=not possible or D , E, A , F , B , _

Now, Corinne will have only one place left within two possibilities:
=> A , C , B , F , D, E or D , E, A , F , B , C

ANSWER:
=> Bailey = 2nd step from bottom, 3rd step from top
=> Corinne = Bottom step, 2nd step from top

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Bunuel

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Fei will be on the step third from the bottom

Bottom					Top
		F

Bailey will be two steps below Ariel

Hence, B cannot occupy the last step, as F has already occupied the third last step.

Possible arrangements

Bottom					Top
C	B	F	A	D	E
C	B	F	A	E	D
D	E	F	B	C	A
E	D	F	B	C	A

Therefore

Bailey = 2nd step from the bottom or the 3rd step from the top
Corinne = bottom step or the 2nd step from the top

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19 Dec 2024, 08:20

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Assume these are the steps (in increasing order)

1(_) 2(_) 3(_) 4(_) 5(_) 6(_)

Known that
1. F = 3
2. D,E consecutive
3. (B) (_) (A)

1(_) 2(_) 3(F) 4(_) 5(_) 6(_)

Possibilities for B in this are only in 2 and 4 to ensure A is also accommodated

Possibility 1 - 1(_) 2(B) 3(F) 4(A) 5(_) 6(_)

D and E have to be consecutive so they can take 5, 6. So C gets 1

1(C) 2(B) 3(F) 4(A) 5(D/E) 6(D/E)

Possibility 2 - 1(_) 2(_) 3(F) 4(B) 5(_) 6(A)

D and E have to be consecutive so they can take 1, 2. So C gets 5

1(D/E) 2(D/E) 3(F) 4(B) 5(C) 6(A)

B -> 2, 4 -> 2nd from bottom and 3rd from top
C -> 1, 5 -> Bottom and 2nd from top

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19 Dec 2024, 08:59

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Given that the 3rd step is already occupied by F, DE can only occupy 1&2 or 5&6 leaving B to ether occupy 1 or 4 and C to occupy either 2 or 5. That there will always be two steps between A and B hence the answer is AD

Bunuel

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