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Even positions, _2_4_6
Odd Positions, 1_3_5_

From 1 alone, B and C can be in 2-4, 4-2, 2-6, 6-2, 4-6, 6-4. No way to know if F is in 1 or not. Not sufficient alone. So, A and D not correct.
From 2 alone, D and E takes up 2 odd places. since A and B gotta be together, they take up one remaining odd position between them. so in this case F cant be in 1.

So, B is correct.


Bunuel
Six cars—A, B, C, D, E, and F—are parked in six adjacent spaces numbered 1 through 6, from left to right. Cars A and B are parked next to each other. Is Car F parked in space 1?

(1) Car B and Car C are both parked in even-numbered spaces.
(2) Car D and Car E are both parked in odd-numbered spaces.

 


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As per Q, AB is adjacent.
Statement 1: since B and C are at even numbered it can take 2,4,6 . Considering B takes 2 then A can only be placed at either 1 or 3 but F could also take either of this position based on where we place A. Hence Insuff.
Statement 2: Since D and E are at odd numbered positions - 1,3,5. Considering D takes 1 then F cannot be at 1.
And if D takes 3 then E takes 1, again F cannot be at 1. And if D takes 3 and E takes 5, again since AB are adjacent. F can only take 4 or 6. hence suff to say NO.
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St 2 gives away that in no circumstance will F be parked in space 1 if D and E are in odd numbered and A and B are together.
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If cars A & B have to be placed adjacent to each other, we have to make sure two spots right next to each other are given to them.

St 1 -
B & C are in even places like 2&4 or 4&6 or 2&6
Only 2nd position matters - in which case, if B is at 2, A can be at 1 or 3
Thus, F can be in 1st position or not
Not sufficient

St 2 -
D & E are in odd places like 1 & 3 or 3 & 5 or 1 & 5
In 1 & 3 case -> automatically F's position isn't at 1st parking lot since its been given to D or E
In 3 & 5 case -> since A & B have to be adjacent to each other, they can be given 1 & 2 positions only -> automatically F isn't at 1st lot space
In 1 & 5 case -> automatically F isn't allotted 1st place since its taken over by D or E

Thus in all cases F isn't in 1st parking lot
Hence B is the answer!
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My answer is B.

1) tells 2 of 3 even spots (2/4/6) will be taken by B and E and 1 odd spot (1/3/5) will be taken by A as it is together with B- Not sufficient cz F can be placed in 1st spot (if B is at 4 or 6) or it can be placed at 3 or 5 if B takes 2nd spot.
2) tells 2 of 3 odd spots (1/3/5) will be taken by D and E. Now D and E cannot take consecutive odd spots because A and B are together. Hence they can take only 1 and 5 hence proved that F is not at 1st spot.- Sufficient.
Bunuel
Six cars—A, B, C, D, E, and F—are parked in six adjacent spaces numbered 1 through 6, from left to right. Cars A and B are parked next to each other. Is Car F parked in space 1?

(1) Car B and Car C are both parked in even-numbered spaces.
(2) Car D and Car E are both parked in odd-numbered spaces.

 


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Bunuel
Six cars—A, B, C, D, E, and F—are parked in six adjacent spaces numbered 1 through 6, from left to right. Cars A and B are parked next to each other. Is Car F parked in space 1?

(1) Car B and Car C are both parked in even-numbered spaces.
(2) Car D and Car E are both parked in odd-numbered spaces.

 


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in first statement, B and C can be in 2 of the 3 spaces (2,4 and 6)
Consider that B is in slot 2, then A can occupy either 1 or 3. If A occupies 3, then F can occupy 1 and if A occupies 1 then F can occupy any of the remaining odd number spots except 1. Hence we have possibilities of F to occupy and not occupy 1. hence NOT SUFFICIENT

For statement 2- D and E can occupy slots 1, 3 and 5. we take 2 cases here
Case 1 - D or E take slot 1. either way F does not occupy 1
Case 2 - D or E take slot 3/5. As A and B have to be adjacent, they have to occupy slots 1 and 2. Hence F will not occupy slot 1 here as well
Hence Statement 2 alone is sufficient - (B)
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Second statement is sufficient alone.

(1) B and C are at even places, then at 1 place, F may or may not be there.
(2) D and E are at odd places, then, D and E can be at 1,3 or 3,5 or 1,5. In all cases, F doesn't has 1, thus, F is not at 1.
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For statement 1, car b and car c can occupy 2,4,6 and so A can be 1,3,5 and so F can occupy 1 if A does not and cannot occupy if A does. So 1 is insufficient.
For statement 2, car d and e can occupy 1,3,5 and since B & A has to occupy one odd place, F has to occupy an even place and so Car F cannot occupy 1. Therefore, 2 is sufficient.

B
Bunuel
Six cars—A, B, C, D, E, and F—are parked in six adjacent spaces numbered 1 through 6, from left to right. Cars A and B are parked next to each other. Is Car F parked in space 1?

(1) Car B and Car C are both parked in even-numbered spaces.
(2) Car D and Car E are both parked in odd-numbered spaces.

 


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Bunuel
Six cars—A, B, C, D, E, and F—are parked in six adjacent spaces numbered 1 through 6, from left to right. Cars A and B are parked next to each other. Is Car F parked in space 1?

(1) Car B and Car C are both parked in even-numbered spaces.
(2) Car D and Car E are both parked in odd-numbered spaces.

 


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Statement 1

We can have multiple possibilities and in one of the them we can have F in the space 1, and in other not. Hence, this statement alone is not sufficient to answer the question. Let's look at the following cases

Case 1

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

Case 2

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

Statement 2

Let's assume that F is at spot 1

1 - F
2 -
3 - D
4 -
5 - E
6 -

D & E can swap places, however in either cases, A and B can't be adjacent. However it is given that A and B are adjacent. Hence, this arrangement is not possible and F cannot be at spot 1. This statement alone is sufficient. Option B is correct.

Option B
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A always occupies odd number adjacent to B.
D/E are always assigned remaining odd number positions.
Hence both 1 & 2 statements are required together.
Bunuel
Six cars—A, B, C, D, E, and F—are parked in six adjacent spaces numbered 1 through 6, from left to right. Cars A and B are parked next to each other. Is Car F parked in space 1?

(1) Car B and Car C are both parked in even-numbered spaces.
(2) Car D and Car E are both parked in odd-numbered spaces.

 


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Answer is C Both Statements together are sufficient.

Because with statement 1, we cannot say for sure whether F can take Space 1. There are multiple possibilities and one of them allow F to be in space 1.

Even statement 2 , does not help for sure. Because it only helps with placements for D& E and tells nothing about where the F can be fixed.

WHen we combine the two statements, the possibilities that show up makes it evident that F cannot take space 1 and can only take either 2, 4 or 6.
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Statement One: Allow B or C to be in 2 4 6; A and B have to next to one another which mean A can occupy an odd space to left or right of B. Which then allows F to be in spot 1 with F B A C D E and does not with A B F C D E

Not Sufficient

Statement Two: Allows for D or E to be in 1 3 5, A and B have to be next to one another which means F can not occupy spot 1 because when D or E are in position 3 and 5 the only adjacent spots left are 1 and 2 for AB or BA leaving F to only fill 4 or 6. A B D F E C or B A D C E F

Sufficient.
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1.
BC being even means they can be placed at 2,4,6. Doesnt tell much about F
2.
DE being even tells they can be placed at 1,3,5 Doesnt tell much about F, again
3.
If we merge this information block!
B is in even block, hence A adjacent will be odd block.
And DE are odd.

All odd places are filled!

hence, F is not in any odd places.
Hence, F is not in 1st space

IMO C
Bunuel
Six cars—A, B, C, D, E, and F—are parked in six adjacent spaces numbered 1 through 6, from left to right. Cars A and B are parked next to each other. Is Car F parked in space 1?

(1) Car B and Car C are both parked in even-numbered spaces.
(2) Car D and Car E are both parked in odd-numbered spaces.

 


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Cars A and B are parked next to each other, i.e. one will be odd and the other will be even.

(1) B, C are even. Hence, A is odd. F can be odd or even as we don't know about D or E. Not sufficient.
(2) D, E are odd. One of A or B will also be odd. Hence, F is even. Sufficient.

Option B.
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1) B and C even, and A is any odd beside B. Not sufficient alone. F can be anywhere.
2) D and E odd places, we have 1,3,5. again F can be anywhere.
But after combining both, A,D,E has to occupy odd places which is 1,3,5 so F cannot take 1st. Sufficient, So C.
Bunuel
Six cars—A, B, C, D, E, and F—are parked in six adjacent spaces numbered 1 through 6, from left to right. Cars A and B are parked next to each other. Is Car F parked in space 1?

(1) Car B and Car C are both parked in even-numbered spaces.
(2) Car D and Car E are both parked in odd-numbered spaces.

 


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answer : b.

all odd numbered spaces are occupied. in the coase of b
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Constraints in the question - A & B are adjacent implying if A = n, B = (n-1) or (n+1) with 1 <= A, B <= 6
Now let's test both conditions.

1) B and C can take 2, 4, 6 positions.
Assuming B = 2: A = 1 or 3, C = 4 or 6. No conclusion on the position of F.
Insufficient.

2) D and E can take 1, 3, 5 positions.
Assuming D or E = 1, F will take other positions and will not be equal to 1.
Assuming D = 3 or 5, E cannot be 1 because the only positions where A and B can be together is 1 and 2 now => F not equal to 1. Similarly, if E = 3 or 5, D cannot be 1 and F not equal to 1.
Sufficient.
Bunuel
Six cars—A, B, C, D, E, and F—are parked in six adjacent spaces numbered 1 through 6, from left to right. Cars A and B are parked next to each other. Is Car F parked in space 1?

(1) Car B and Car C are both parked in even-numbered spaces.
(2) Car D and Car E are both parked in odd-numbered spaces.

 


This question was provided by Manhattan Prep
for the GMAT World Cup Competition

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