LSAT Logic Games

Explanation

Though this appears to be an acceptability question, it only asks about an acceptable ordering of the items, and not the type of power for each item. Thus, this is a partial acceptability question in which only some of the rules will help to eliminate answer choices, and the rest of the answers will have to be eliminated by deductions.

• Rule 1: eliminates C (U cannot be second)
• Rule 2: does not eliminate any answer choices
• Rule 3: does not eliminate any answer choices
• Rule 4: does not eliminate any answer choices
• Rule 5: eliminates D (S must precede R) and A (R must precede W)

We are left with choices B and E, which we can cross-check with our final sketch. Since we were able to deduce that W must be in slot 6, it cannot be in slot 5, eliminating choice E.

Thus, B, the remaining answer choice, is correct.

Game Setup:

This is an advanced absolute ordering game; we must determine the order in which six items are arranged on a shelf, and whether each is powered by batteries or by an adapter. Our sketch will be an ordered list with one row for the items (R, S, T, U, V, and W), and one row for the type of power (a or b).

Rules:

1. U = 1 or 6
2. ~bb
3. (W,b)
4. Place b in slot 4 of the power row.
5. V...(R,b)...W and S...(R,b)...W

Deductions:

1. If the fourth item is powered by batteries, and no two adjacent items can be powered by batteries, both the third and fifth items must be powered by an adapter. Place a in slot slots 3 and 5 of the power row.
2. Since R is preceded by both S and V, it can be third at the earliest. But since the third item is powered by an adapter, and the razor is powered by batteries, R cannot be third. Thus, R can be fourth at the earliest.
3. Since R is followed by W, it can be fifth at the earliest. But since the fifth item is powered by an adapter, and the razor is powered by batteries, R cannot be fifth. Thus, R can be fourth at the latest.
4. If R can be fourth at the earliest and at the latest, it must be fourth. Place R in slot 4 of the item row.
5. Since W must follow R, it must be either fifth or sixth. But since the fifth item is powered by an adapter, and the watch is powered by batteries W cannot be fifth. Thus, W must be sixth.
6. If W is sixth, U cannot be. Thus, U must be first.
7. Since S and V must both precede R in slot 4, and slot 1 is occupied by U, one of S and V must be in slot 2 and the other in slot 3.
8. This leaves slot 5 for T.

Summary of Setup:

Explanation

Choices A, B, and C directly violate our sketch, which tells us that U is first, R is fourth, and the fifth item is powered by an adapter.

If, as in choice D, S is powered by batteries, it must be in slot 2, since the item in slot 3 is powered by an adapter. This, means V must be in slot 3, and U must be powered by an adapter, since two consecutive items cannot be powered by batteries. Our sketch is:

This is an acceptable sketch, so choice D is correct.

As for choice E, if both U and V are powered by batteries, V must be in slot 2, since the item in slot 3 is powered by an adapter. Since we cannot have items in consecutive slots powered by batteries, choice E can also be eliminated.

Game Setup:

This is an advanced absolute ordering game; we must determine the order in which six items are arranged on a shelf, and whether each is powered by batteries or by an adapter. Our sketch will be an ordered list with one row for the items (R, S, T, U, V, and W), and one row for the type of power (a or b).

Rules:

1. U = 1 or 6
2. ~bb
3. (W,b)
4. Place b in slot 4 of the power row.
5. V...(R,b)...W and S...(R,b)...W

Deductions:

1. If the fourth item is powered by batteries, and no two adjacent items can be powered by batteries, both the third and fifth items must be powered by an adapter. Place a in slot slots 3 and 5 of the power row.
2. Since R is preceded by both S and V, it can be third at the earliest. But since the third item is powered by an adapter, and the razor is powered by batteries, R cannot be third. Thus, R can be fourth at the earliest.
3. Since R is followed by W, it can be fifth at the earliest. But since the fifth item is powered by an adapter, and the razor is powered by batteries, R cannot be fifth. Thus, R can be fourth at the latest.
4. If R can be fourth at the earliest and at the latest, it must be fourth. Place R in slot 4 of the item row.
5. Since W must follow R, it must be either fifth or sixth. But since the fifth item is powered by an adapter, and the watch is powered by batteries W cannot be fifth. Thus, W must be sixth.
6. If W is sixth, U cannot be. Thus, U must be first.
7. Since S and V must both precede R in slot 4, and slot 1 is occupied by U, one of S and V must be in slot 2 and the other in slot 3.
8. This leaves slot 5 for T.

Summary of Setup:

Explanation

Since this question asks what must be true, we can cross-check the answer choices with our sketch to see if one of the answer choices matches one of our deductions. Since we have T and a in slot 5 in our sketch, choice A is correct.

Choices B and D could be true, but do not have to be.

Choices C and E must be false.

Game Setup:

This is an advanced absolute ordering game; we must determine the order in which six items are arranged on a shelf, and whether each is powered by batteries or by an adapter. Our sketch will be an ordered list with one row for the items (R, S, T, U, V, and W), and one row for the type of power (a or b).

Rules:

1. U = 1 or 6
2. ~bb
3. (W,b)
4. Place b in slot 4 of the power row.
5. V...(R,b)...W and S...(R,b)...W

Deductions:

1. If the fourth item is powered by batteries, and no two adjacent items can be powered by batteries, both the third and fifth items must be powered by an adapter. Place a in slot slots 3 and 5 of the power row.
2. Since R is preceded by both S and V, it can be third at the earliest. But since the third item is powered by an adapter, and the razor is powered by batteries, R cannot be third. Thus, R can be fourth at the earliest.
3. Since R is followed by W, it can be fifth at the earliest. But since the fifth item is powered by an adapter, and the razor is powered by batteries, R cannot be fifth. Thus, R can be fourth at the latest.
4. If R can be fourth at the earliest and at the latest, it must be fourth. Place R in slot 4 of the item row.
5. Since W must follow R, it must be either fifth or sixth. But since the fifth item is powered by an adapter, and the watch is powered by batteries W cannot be fifth. Thus, W must be sixth.
6. If W is sixth, U cannot be. Thus, U must be first.
7. Since S and V must both precede R in slot 4, and slot 1 is occupied by U, one of S and V must be in slot 2 and the other in slot 3.
8. This leaves slot 5 for T.

Summary of Setup:

Explanation

We know for sure that R and W in slots 4 and 6, respectively, are powered by batteries, thus the answer must be at least two. Eliminate choice A.

We also know that V/S and T in slots 3 and 5 are powered by adapters, thus the answer is at most four. Eliminate E.

It cannot be true that the items in both slots 1 and 2 are powered by batteries, since items in consecutive slots cannot both be powered by batteries. However, as we saw in our sketch for the previous question...

...it can be true that one of the first two items is powered by batteries. Therefore, at most three of the items are powered by batteries. Choice C is correct.

Game Setup:

This is an advanced absolute ordering game; we must determine the order in which six items are arranged on a shelf, and whether each is powered by batteries or by an adapter. Our sketch will be an ordered list with one row for the items (R, S, T, U, V, and W), and one row for the type of power (a or b).

Rules:

1. U = 1 or 6
2. ~bb
3. (W,b)
4. Place b in slot 4 of the power row.
5. V...(R,b)...W and S...(R,b)...W

Deductions:

1. If the fourth item is powered by batteries, and no two adjacent items can be powered by batteries, both the third and fifth items must be powered by an adapter. Place a in slot slots 3 and 5 of the power row.
2. Since R is preceded by both S and V, it can be third at the earliest. But since the third item is powered by an adapter, and the razor is powered by batteries, R cannot be third. Thus, R can be fourth at the earliest.
3. Since R is followed by W, it can be fifth at the earliest. But since the fifth item is powered by an adapter, and the razor is powered by batteries, R cannot be fifth. Thus, R can be fourth at the latest.
4. If R can be fourth at the earliest and at the latest, it must be fourth. Place R in slot 4 of the item row.
5. Since W must follow R, it must be either fifth or sixth. But since the fifth item is powered by an adapter, and the watch is powered by batteries W cannot be fifth. Thus, W must be sixth.
6. If W is sixth, U cannot be. Thus, U must be first.
7. Since S and V must both precede R in slot 4, and slot 1 is occupied by U, one of S and V must be in slot 2 and the other in slot 3.
8. This leaves slot 5 for T.

Summary of Setup:

Explanation

If the UV lamp is powered by batteries, then we know the item in slot 2 must be powered by an adapter, since it cannot be true that items in consecutive slots are both powered by batteries. Thus, our sketch is:

Each of the first four answer choices must be true, so they can all be eliminated.

This leaves correct answer choice E. It does not have to be true that S is in slot 3 in the sketch above, since S could be in slot 2.

Game Setup:

This is an advanced absolute ordering game; we must determine the order in which six items are arranged on a shelf, and whether each is powered by batteries or by an adapter. Our sketch will be an ordered list with one row for the items (R, S, T, U, V, and W), and one row for the type of power (a or b).

Rules:

1. U = 1 or 6
2. ~bb
3. (W,b)
4. Place b in slot 4 of the power row.
5. V...(R,b)...W and S...(R,b)...W

Deductions:

1. If the fourth item is powered by batteries, and no two adjacent items can be powered by batteries, both the third and fifth items must be powered by an adapter. Place a in slot slots 3 and 5 of the power row.
2. Since R is preceded by both S and V, it can be third at the earliest. But since the third item is powered by an adapter, and the razor is powered by batteries, R cannot be third. Thus, R can be fourth at the earliest.
3. Since R is followed by W, it can be fifth at the earliest. But since the fifth item is powered by an adapter, and the razor is powered by batteries, R cannot be fifth. Thus, R can be fourth at the latest.
4. If R can be fourth at the earliest and at the latest, it must be fourth. Place R in slot 4 of the item row.
5. Since W must follow R, it must be either fifth or sixth. But since the fifth item is powered by an adapter, and the watch is powered by batteries W cannot be fifth. Thus, W must be sixth.
6. If W is sixth, U cannot be. Thus, U must be first.
7. Since S and V must both precede R in slot 4, and slot 1 is occupied by U, one of S and V must be in slot 2 and the other in slot 3.
8. This leaves slot 5 for T.

Summary of Setup:

Explanation

If the fifth item is powered by batteries, and no two adjacent items can be powered by batteries, both the fourth and sixth items must be powered by an adapter. Place a, b, and a in slots 4, 5, and 6, respectively, of the power row.

From here we can try to place R in the sketch. Since it is preceded by S and V, R can be third at the earliest, and since it is followed by W, it can be fifth at the latest. However, if R were fifth, then W would have to be sixth, and we know the sixth item is powered by an adapter. Thus, R cannot be fifth. Likewise, it cannot be fourth, since the item in slot 4 is powered by an adapter. Therefore, R must be third, and W must be fifth. So far we have:

Since S and V must precede R, we can place S/V in slot 1 and V/S in slot 2. Since U can no longer be first, it must be sixth, pushing T to slot 4. Finally, we know the item in slot 2 cannot be powered by batteries, since the item in slot 3 is, so we can place a in slot 2 of the power row. Our sketch is:

Since it does not have to be true that V is powered by an adapter (it could be in slot 1, and powered by batteries), choice E is correct.

Game Setup:

This is an advanced absolute ordering game; we must determine the order in which six items are arranged on a shelf, and whether each is powered by batteries or by an adapter. Our sketch will be an ordered list with one row for the items (R, S, T, U, V, and W), and one row for the type of power (a or b).

Rules:

1. U = 1 or 6
2. ~bb
3. (W,b)
4. Place b in slot 4 of the power row.
5. V...(R,b)...W and S...(R,b)...W

Deductions:

1. If the fourth item is powered by batteries, and no two adjacent items can be powered by batteries, both the third and fifth items must be powered by an adapter. Place a in slot slots 3 and 5 of the power row.
2. Since R is preceded by both S and V, it can be third at the earliest. But since the third item is powered by an adapter, and the razor is powered by batteries, R cannot be third. Thus, R can be fourth at the earliest.
3. Since R is followed by W, it can be fifth at the earliest. But since the fifth item is powered by an adapter, and the razor is powered by batteries, R cannot be fifth. Thus, R can be fourth at the latest.
4. If R can be fourth at the earliest and at the latest, it must be fourth. Place R in slot 4 of the item row.
5. Since W must follow R, it must be either fifth or sixth. But since the fifth item is powered by an adapter, and the watch is powered by batteries W cannot be fifth. Thus, W must be sixth.
6. If W is sixth, U cannot be. Thus, U must be first.
7. Since S and V must both precede R in slot 4, and slot 1 is occupied by U, one of S and V must be in slot 2 and the other in slot 3.
8. This leaves slot 5 for T.

Summary of Setup: