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705-805 Level|   Non-Math Related|         
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 11:20
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Start by placing F on the steps as F is the only one with the exact position given.
Then, we see a bigger constraint with fewer possibilities in the placement of A and B.
Once this is done, we can place D and E with their constraint and lastly place C.
We will have total of 2 options of placements ( as that can be seen in the option choice also)

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

Ans: B = Second step from bottom and 3rd step from Top
C = Bottom step and 2nd step from Top
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 11:22
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Position of Ariel gives two different combinations:

if Ariel on top: A,C,B,F,D,E
if Ariel on 3rd step from top: D,E,A,F,B,C

Answer C & B
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 11:24
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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
Show more
First Attempt
1st: => B
2nd: =>E
3rd: => A
4th: F (Given)
5th: =>C/D
6th: =>C/D

Second Attempt
1st: =>C/D
2nd: =>C/D
3rd: =>B
4th: F (Given)
5th: =>A
6th: =>E

So the result of First Attempt:
1st: B
2nd: E
3rd: A
4th: F
5th: C/D
6th: C/D

Result of Second Attempt
1st: C/D
2nd: C/D
3rd: B
4th: F
5th: A
6th: E

So B may be 3rd step from top, top step
C may be 2nd step from from bottom, 2nd step from top
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 11:24
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Bailey: 2nd step from bottom, 3rd step from top
Corinne: Bottom step, 2nd step from top

It helps me to eliminate options and draw a diagram:

Fei: We know Fei is always third from bottom, or Step 4.
Alex & Bailey: We know Bailey is always two steps below Ariel. Their only options as a pair are Alex on Step 1 and Bailey on Step 3, or Alex on Step 3 and Bailey on Step 5.
Darryl & Edgar: We know they are next to each other, but can be in any order. Their only options as a pair are Steps 1 & 2, Steps 2 & 3, or Steps 5 & 6. However, if Alex is on Step 1 and Bailey is on Step 3, Darryl & Edgar must be on Steps 5 & 6. If Alex is on Step 3 and Bailey is on Step 5, Darryl & Edgar must be on Steps 1 & 2.
Corinne: As last remaining person, Corinne fills in where there is a remaining step, which could be Step 2 or Step 6.


1AlexDarryl/Edgar
2CorinneDarryl/Edgar
3BaileyAlex
4FeiFei
5Darryl/EdgarBailey
6Darryl/EdgarCorinne
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 11:32
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With the 2 scenarios
B=2nd step from bottom, 3rd step from top
C=Bottom step, 2nd step from top
Attachments

image_2024-12-19_000240243.png
image_2024-12-19_000240243.png [ 59.81 KiB | Viewed 643 times ]

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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 11:37
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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
Bailey Corinne
Bottom step, 3rd step from top
Bottom step, 2nd step from top
2nd step from bottom, 3rd step from top
2nd step from bottom, 2nd step from top
2nd step from bottom, top step
3rd step from top, top step

The possible positions are :
1 a e
2 c d
3 b a
4 f f
5 e b
6 d c

Hence B-2nd step from bottom, 3rd step from top
C- Bottom step, 2nd step from top
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 11:38
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B: Step 1
A: Step 3
F: Step 4
D & E: Steps 5 and 6
C: Step 2
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 13:18
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Bailey’s Position:

Bailey cannot be on the topmost or 2nd top step because she must be two steps below Ariel. She also can't be on the last step as Ariel can't be on the 4th step (due to the 2-step gap) because Fei is there. So, 5 out of 6 choices are eliminated.
Bailey's position is therefore 2nd step from bottom, 3rd step from top.

Corinne’s Position:

After placing Bailey, the only available spots are as follows:
  • When Bailey is on the 3rd step from top, the valid arrangements are: ACBFDE or ACBFED.
  • When Bailey is on the 2nd step from bottom, the valid arrangements are: DEAFBC or EDAFBC.

Corinne must be on either the 3rd step from top or top step.

Final Selections:
Bailey: 2nd step from bottom, 3rd step from top
Corinne: 3rd step from top, top step
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 13:27
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Now the best tip here to solve efficiently is to draw this in your scratch paper, so that it becomes obvious.

1.
2.
3.
4.
5.
6.

These are the spots available and which have to be filled with A,B,C,D,E & F.
Now, since F must be in the 3rd row, from the bottom = 4 we can place the rest from this first step.
1.
2.
3.
4. F
5.
6

ED or DE, but both must be consecutive and A must go 2 places on top of B, no restrictions on C. Let's start filling spots and alternatives.
1. E/D
2. D/E
3. A
4. F
5. B
6. C

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

Now B can go either to the 3rd or the 5th place and C can be 2nd or 6th.
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 14:10
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Quote:
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
Show more
On these, I like to rule out options from the most restrictive to the least restrictive. We have A, B, C, D, E, and F. F will be third from the bottom. D and E are together, and their order doesn’t matter because we don’t care where they stand, so that brings us down to A, B, C, DE, and F. B will be two steps below A, so B can only be on steps 3 or 5 from the top, and A can only be on steps 1 or 3 from the top. Sometimes drawing a graph and filling it in is easiest.

Top Step23456
ArielCorinneBaileyFeiD/ED/E
D/ED/EArielFeiBaileyCorinne


Alternatively, you could say D&E can be in spots (1,2), (2,3), (3,4), (4,5), or (5,6).
A and B could be in spots (1,3), (2,4), (3,5), or (4,6)
F has to be in 4, so cross out the options with 4 in them and you get:
D&E can occupy (1,2), (2,3), or (5,6)
A and B can respectively stand in (1,3) or (3,5).
Cross check for double booked spots, and you’ll see that if A and B are in (1,3), then D&E are left with (5,6) and C in 2. If A and B are in (3,5), that leaves D&E in (1,2) and C in spot 6.
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 14:12
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What we need to do is to illustrate all possible arrangements step-by-step (I also attach the drawing):
  1. F is set on third from bottom
  2. There must be one space between B and A => so the only ways to do it are steps 2-4 and 4-6
  3. For each of the above variants there's a sub-scenario:
    1. With steps 2-3-4 taken, D&E can only take 5-6 => this leaves C on 1
    2. With steps 3-4-6 taken, D&E can only take 1-2 => this leaves C on 5

Therefore, the answer is:
  • 2nd from bottom and 3rd from top for Bailey
  • Bottom step and 2nd from top for Corinne

Attachments

File comment: Both possible scenarios, numeration from bottom to top
Possible arrangements.jpg
Possible arrangements.jpg [ 118.65 KiB | Viewed 612 times ]

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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 14:47
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Quote:
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
Show more


Possible arrangements-

-E/D
-E/D
-A
-F
-B
-C

or

-A
-C
-B
-F
-E/D
-E/D


hence C can either take 2nd from top or the bottom step
and B can take either 3rd from top or 2nd from bottom step
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 14:54
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There will be two possible scenarios:

Scenario 1

Darryl and Edgar will be on consecutive steps - _ _ _ _ D E

Bailey will be two steps below Ariel - A _ B _ D E

Fei will be on the step third from the bottom - A _ B F D E

Leaving only one place for Corinne - A C B F D E

Scenario 2

Darryl and Edgar will be on consecutive steps - D E _ _ _ _

Bailey will be two steps below Ariel - D E A _ B _

Fei will be on the step third from the bottom - D E A F B _

Leaving only one place for Corinne - D E A F B C

Therefore, Bailey can be on the 2nd step from bottom, 3rd step from top
Corinne can be Bottom step, 2nd step from top
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 15:58
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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
Show more
Baily: 2nd from bottom, 3rd from top
Corinne: bottom, 2nd from top

1st option from top to bottom: A > C > B > F > D > E
2nd option from top to bottom E > D > A > F > B > C
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 17:44
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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
Show more
Assuming _ _ _ _ _ _ : Bottom -> Top => Left -> Right

Given: _ _ F _ _ _

Possible scenarios for BA:
1. _ B F A _ _ => since DE are together only one place is available => C B F A (D, E)
2. _ _ F B _ A => since DE are together only one place is available => (D, E) F B C A

Hence B can 2nd from bottom or 3rd from top and C can bottom and 2nd from top.
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 18:24
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A,B,C,D.E.F

D and E must be together.

A and B:
A
x
B

1 is botton and 6 is top:
6
5
4
3 F
2
1

A can be only in 6 or in 4 -> B can be in 4 (3rd step from top) or in 2 (2nd step from botton)

If B is in 4 (3rd step from top) -> D and E must be in 1 and 2 -> C must be in 5 (2nd step from top)
If B is in 2 (2nd step from botton) -> D and E must be in 5 and 6 -> C must be in 1 (Botton step)

B can be in 2 (2nd step from botton) or in 4 (3rd step from top)
C can be in 1 (Botton step) or in 5 (2nd step from top)
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 18:53
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As Fei is in 3rd step from botton, Ariel can be in the 3rd step from top or in the top step and Bailey can be in the 2nd step from bottom or in the 3rd step from top, respectively.

As Darryl and Edgar must be together, if Ariel is the 3rd step from top and Bailey in the 2nd step from bottom, Darryl and Edgar must be in the top step and in the 2nd step from top and Corinne must be in the botton step.

As Darryl and Edgar must be together, if Ariel is the top step and Bailey in the 3rd step from top, Darryl and Edgar must be in the botton step and in the 2nd step from botton and Corinne must be in the 2nd step from top.

Answers: Bailey (2nd step from bottom, 3rd step from top), Corinne (Bottom step, 2nd step from top)
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 22:11
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Given the 6 steps: _ _ _ _ _ _

We have F fixed at the step third from the bottom: _ _ F _ _ _

And " Bailey will be two steps below Ariel" = B _ A

Possible outcomes: _BFADE or _ _ FBCA

So B: [color=#000000]2nd step from bottom, 3rd step from top[/color]
And C: [color=#ffffff][color=#000000]Bottom step, 2nd step from top[/color] [/color]

The key is starting by B and then it will be faster to answer for Corinne. Notice that D and E must be together, but the order does not matter, just count it as 1 option and see the rest.

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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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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 22:12
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There are total 6 steps and three conditions are given -
  • 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.

Let's place Fie on the step third from the bottom.
6
5
4
3Fei
2
1

Bailey and Ariel will have two cases. Darryl and Edgar in both cases just need to be in consecutive positions. Their positions are interchangeable as their order is not given. We can ignore the order because question asks only about the possible positions of Bailey and Corinne. After placing Darryl and Edgar, one empty position is left for Corinne.

Case I -
6Ariel
5Corrine
4Bailey
3Fei
2Darryl
1Edgar

Case II -
6Darryl
5Edgar
4Ariel
3Fei
2Bailey
1Corinne

Bailey - 2nd step from bottom - Case II, 3rd step from top - Case I
Corinne - Bottom step - Case II, 2nd step from top - Case I
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12 Days of Christmas GMAT Competition - Day 3: Ariel, Bailey, Corinne 18 Dec 2024, 22:25
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Given Information:
  • 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 (Step 3).
We have six steps, and everyone will be on a different step:
  • Step 1: Bottom step
  • Step 2: 2nd step from bottom
  • Step 3: Fei (3rd step from bottom)
  • Step 4: 3rd step from top
  • Step 5: 2nd step from top
  • Step 6: Top step
Determine Possible Steps for Bailey:
Since Bailey is two steps below Ariel:
  • If Ariel is on Step 6 (top step), Bailey will be on Step 4 (3rd step from top).
  • If Ariel is on Step 5 (2nd step from top), Bailey will be on Step 3 (3rd step from bottom), but this conflicts with Fei's position.
  • If Ariel is on Step 4 (3rd step from top), Bailey will be on Step 2 (2nd step from bottom).
So, the possible steps for Bailey are:
  • Step 2 (2nd step from bottom)
  • Step 4 (3rd step from top)
Determine Possible Steps for Corinne:
Considering Darryl and Edgar must be on consecutive steps and Ariel and Bailey have specific positions:
  • Darryl and Edgar could occupy Steps 1 and 2, Steps 2 and 3 (but Fei is on Step 3), Steps 4 and 5, or Steps 5 and 6.
Now, let's see the steps Corinne could be on:
  • If Bailey is on Step 2, Darryl and Edgar could be on Steps 1 and 3 or Steps 4 and 5. Corinne can then be on Step 6 (top step).
  • If Bailey is on Step 4, Darryl and Edgar could be on Steps 1 and 2, or Steps 5 and 6. Corinne can then be on Step 5 (2nd step from top), or Step 1 (bottom step).
Selections:
  • Bailey: Step 2 (2nd step from bottom), Step 4 (3rd step from top)
  • Corinne: Bottom step (Step 1), 2nd step from top (Step 5), top step (Step 6)
So the possible choices are:
  • Bailey: 2nd step from bottom, 3rd step from top
  • Corinne: Bottom step, 2nd step from top, top step
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