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06 Jul 2026, 08:00
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Difficulty:
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61%
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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.
(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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06 Jul 2026, 09:00
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Manhattan Prep Official Explanation
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.
Glance at the question stem: six cars (A through F) parked in six spaces numbered 1-6, with A and B next to each other. The question asks a specific yes/no question: Is Car F parked in space 1? The information given in the prompt is not mathematical, but instead focuses on the spatial relationships between the cars, indicating that this is a Logic question based on a Linear Ordering. A useful approach here will be to Draw A Diagram to visually map out the slots and the rules:
Glance at the statements. They provide information about which cars are in even or odd spaces. Consider whether the constraints in the problem can be related to odd and even spaces. Cars A and B occupy consecutively numbered spaces, so one of A and B must be in an even space and the other in an odd space. Since there are three odd and three even spaces, once A and B are accounted for only two odd and two even spaces remain for the other four cars.
Spatial logic-based data sufficiency questions are often solvable by testing cases, especially when there are a limited number of elements to arrange or group. For each statement, try to prove insufficiency—look for a valid order in which F is in space 1 and another valid order in which F is in a different space.
(1) INSUFFICIENT. This statement tells us that B and C are both in even-numbered spaces.
Case 1: Start with F in space 1, and then place B and C in even-numbered slots: A B C D E F B and C even
Place the remaining cars to test whether a valid arrangement can be found. Car A must be placed next to Car B, and Cars D and E are unconstrained:
B and C even
For this arrangement, the answer to the question stem is YES, Car F is in space 1.
Case 2: Try to find a valid test case in which Car F is not in space 1. Among several other possibilities, F can be swapped with A, keeping A next to B, and leaving B and C in even-numbered spaces:
B and C even
For this arrangement, the answer to the question stem is NO, Car F is not in space 1. Since one case yields an answer of YES and the other an answer of NO, this statement is not sufficient.
Alternatively, note that once B and C are in even-numbered spaces, and A is placed in an odd-numbered space next to B, there remains one even-numbered space, and two odd-numbered spaces for the remaining cars (D, E, F). There are no remaining constraints governing these three cars; each of the three could go in any of the remaining three spaces. F can be, but does not have to be, in space 1. Not sufficient.
(2) SUFFICIENT. This statement tells us that D and E are both parked in odd-numbered spaces, occupying two of the three odd-numbered spaces available. From the question stem, the adjacent pair (A, B) must use exactly one odd-numbered space and one even-numbered space. That means that either Car A or Car B will occupy the third and final odd-numbered space. For example:
D and E odd
Since there are exactly three odd-numbered spaces in total (spaces 1, 3, and 5), all three odd-numbered spaces are now completely occupied by D, E, and one of the cars from the (A, B) pair. Therefore, the remaining cars—C and F—must be parked in the even-numbered spaces. The question asks if Car F is parked in space 1. Since space 1 is odd, and Car F is forced to park in an even-numbered space, Car F cannot be in space 1. In all cases, the answer is a definitive NO. This statement is sufficient.
The correct answer is (B): Statement (2) ALONE is sufficient.
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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.
Glance at the question stem: six cars (A through F) parked in six spaces numbered 1-6, with A and B next to each other. The question asks a specific yes/no question: Is Car F parked in space 1? The information given in the prompt is not mathematical, but instead focuses on the spatial relationships between the cars, indicating that this is a Logic question based on a Linear Ordering. A useful approach here will be to Draw A Diagram to visually map out the slots and the rules:
Glance at the statements. They provide information about which cars are in even or odd spaces. Consider whether the constraints in the problem can be related to odd and even spaces. Cars A and B occupy consecutively numbered spaces, so one of A and B must be in an even space and the other in an odd space. Since there are three odd and three even spaces, once A and B are accounted for only two odd and two even spaces remain for the other four cars.
Spatial logic-based data sufficiency questions are often solvable by testing cases, especially when there are a limited number of elements to arrange or group. For each statement, try to prove insufficiency—look for a valid order in which F is in space 1 and another valid order in which F is in a different space.
(1) INSUFFICIENT. This statement tells us that B and C are both in even-numbered spaces.
Case 1: Start with F in space 1, and then place B and C in even-numbered slots: A B C D E F B and C even
Place the remaining cars to test whether a valid arrangement can be found. Car A must be placed next to Car B, and Cars D and E are unconstrained:
B and C even
For this arrangement, the answer to the question stem is YES, Car F is in space 1.
Case 2: Try to find a valid test case in which Car F is not in space 1. Among several other possibilities, F can be swapped with A, keeping A next to B, and leaving B and C in even-numbered spaces:
B and C even
For this arrangement, the answer to the question stem is NO, Car F is not in space 1. Since one case yields an answer of YES and the other an answer of NO, this statement is not sufficient.
Alternatively, note that once B and C are in even-numbered spaces, and A is placed in an odd-numbered space next to B, there remains one even-numbered space, and two odd-numbered spaces for the remaining cars (D, E, F). There are no remaining constraints governing these three cars; each of the three could go in any of the remaining three spaces. F can be, but does not have to be, in space 1. Not sufficient.
(2) SUFFICIENT. This statement tells us that D and E are both parked in odd-numbered spaces, occupying two of the three odd-numbered spaces available. From the question stem, the adjacent pair (A, B) must use exactly one odd-numbered space and one even-numbered space. That means that either Car A or Car B will occupy the third and final odd-numbered space. For example:
D and E odd
Since there are exactly three odd-numbered spaces in total (spaces 1, 3, and 5), all three odd-numbered spaces are now completely occupied by D, E, and one of the cars from the (A, B) pair. Therefore, the remaining cars—C and F—must be parked in the even-numbered spaces. The question asks if Car F is parked in space 1. Since space 1 is odd, and Car F is forced to park in an even-numbered space, Car F cannot be in space 1. In all cases, the answer is a definitive NO. This statement is sufficient.
The correct answer is (B): Statement (2) ALONE is sufficient.
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General Discussion
06 Jul 2026, 08:14
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Statement 1 - Car B and C, can be parked at spot 2 ,4 and 6. Which means Car A will be parked at spot 1 if car B parked at spot 2 or Car A will be parked in spot 3 if Car B parked at spot 4 or Car A will be parked at Spot 5 if Car B parked at Spot 6. So, F may or may not me at spot 1. Insufficient.
Statement 2 - Car D and E parked at odd spots, which means we do not know were would the Cars A,B,C be parked at, we only know that Car A and B will be parked next to each other. Insufficient.
Statement 1 + 2 - We know that if Car B is parked at spot 2 then Car A will be parked at spot 1 or if Car B parked at spot 4 or 6, Car A will be parked at Spot 3 or 5 respectively and Cars D and E will be parked at spots 1 and 5 or 1 and 3. Hence Car F does not occupy Spot 1. Sufficient.
Statement 2 - Car D and E parked at odd spots, which means we do not know were would the Cars A,B,C be parked at, we only know that Car A and B will be parked next to each other. Insufficient.
Statement 1 + 2 - We know that if Car B is parked at spot 2 then Car A will be parked at spot 1 or if Car B parked at spot 4 or 6, Car A will be parked at Spot 3 or 5 respectively and Cars D and E will be parked at spots 1 and 5 or 1 and 3. Hence Car F does not occupy Spot 1. Sufficient.
