Test Sherpa - LSAT Grouping Questions

In this article, we’ll take a look at the game we just sketched in its entirety so we can study typical LSAT grouping questions. This is the third in a series of articles on LSAT grouping questions. The series includes:

LSAT Grouping Questions

Here is the game in its entirety. Take a 5-8 minutes to consider the questions based on the sketch you’ve made from the previous article.

A clerk at a hardware store has to sort ten items into three boxed customer orders—Atkins, Brower, and Carter. The items are four yardsticks, two hammers, one screwdriver, and three wrenches. French occurs sometime after English

     Each customer ordered at least one yardstick
     No customer ordered more than one hammer
   The customer who ordered the screwdriver ordered at least on wrench
     Carter did not order the screwdriver

1. Which one of the following is an acceptable distribution of items in each box.
Atkins Brower Carter

(A) Atikins: two yardsticks, one hammer, one wrench
Brower: one yardstick, one hammer
Carter: one yardstick, one screwdriver, two wrenches

(B) Atikins: two yardsticks, one screwdriver, one wrench
Brower: one hammer, one wrench
Carter: two yardsticks, one hammer, one wrench

(C) Atikins: one yardstick, one screwdriver, two wrenches, one hammer
Brower: two yardsticks
Carter: one yardstick, one hammer, one wrench

(D) Atikins: one yardstick, one screwdriver, one hammer
Brower: two yardsticks, two wrenches
Carter: one yardstick, one hammer, one wrench

(E) Atikins: one yardstick, one screwdriver, two wrenches
Brower: two yardsticks, two hammers
Carter: one yardstick, one wrench

2. What is the maximum number of tools that can be put in the Brower box?

(A) five
(B) six
(C) seven
(D) eight
(E) nine

3. If the screwdriver is in Brower’s box and if Brower’s box contains no more than three tools, which of the following must be true?

(A) Brower’s box contains a hammer
(B) Brower’s box contains two wrenches
(C) Atkins’ box contains two yardsticks
(D) Atkins’ box contains one hammer
(E) Carter’s box contains two wrenches

4. If Atkins’ box contains no wrenches, which of the following must be true?

(A) Brower’s box contains one hammer
(B) Brower’s box contains one screwdriver
(C) Atkins’ Box contain one screwdriver
(D) Carter’s box contain one hammer
(E) Carter’s box contains two wrenches

5. If Carter’s box contains exactly five tools, which one of the following must be false?

(A) Atkins’ box contains two yardsticks
(B) Atkins box contains one screwdriver
(C) Carter’s box contains two yardsticks
(D) Brower’s box contain one hammer
(E) Brower’s box contains one wrench

6. If Atkins orders no tools at all, but all the other conditions still apply, what is the maximum number of items that Carter can order?

(A) four
(B) five
(C) six
(D) seven
(E) eight

LSAT Grouping Game Review

The first question is an acceptability question. These types of questions ask you to grab one of the rules and eliminate a wrong answer. Four answers will violate the rules, and one answer—the right answer—will not.

The rules:

Each customer ordered at least one yardstick. Cross out (B) since Brower doesn’t have a yardstick
No customer ordered more than one hammer. Cross out (E) since Brower has two hammers
The customer who ordered the screwdriver ordered at least on wrench. Cross out (D) since Atkins has a screwdriver and no wrench.
Carter did not order the screwdriver. Cross out (A) since Carter orders a screwdriver
The answer must be (C) by elimination.

The second question is a question of maximization, therefore a question of floaters. It’s basically telling you to distribute based on the limits and rules, then put all of the floaters into the Brower box. In other words, deal with all the must be trues, then put all the could be trues in Brower’s box.

We know Brower is starting with at least one Y. He could have the S–>W combo too. He could have one H, but not the other one based on the hammer rule. That brings us to four.
We can eliminate two Ys, because the other boxes have to have at least one yardstick. But there’s nothing preventing Brower from taking the remaining Y and Ws, bring us up to seven. We’re out of items so seven is the maximum, or answer (C).

The third question is a hypothetical. Hypothetical must be true questions usually ask us to follow the chain of deductions that starts with the “If” clause. So plug in the “if” and whatever is the last thing you can figure out is probably the answer.

If the screwdriver is in Brower’s box then we know a wrench is in there too. Add the mandatory yardstick and we’re up to three tools already: Y, and S–>W. Brower is done. Scan for the Brower answers—already we can cross out (A) and (B).

The only thing else we know is that the hammers can’t be in Browers box, so they have to be split between Atkins and Carter. All the other items are floaters, so they’re “could-be-trues,” not “must-be-trues.” Scan for hammer and you get the right answer, (D).

The fourth question is a gimme’ point based on taking the contra-positive of the S–>W rule:

If S, then W

Contra-positive: If not W, then not S

We know then that if Atkins’ box has no wrenches, it has no screwdrivers either. Carter can’t have a screwdriver, so Brower must have the S–>W pair. Scan for screwdriver and Brower and you’ll find (B) as the right answer.

The fifth question is a little vague. First, deal with the Carter box because that’s the new hypothetical limit. Don’t be intimidated because the question doesn’t give you a concrete hypothetical, like put a wrench in Carter’s box. This hypothetical is just as good.

Remember the LSAT likes to hide relatively simple things behind intimidating questions. Don’t be intimidated. Just see what happens when Carter is limited to exactly five tools.

Right off the bat we know what can’t go in Carter’s box: Y, Y, one H, and the S–>W pair. That’s five tools right there. So if Carter’s box has to have five tools in it, it has to have the five remaining: Y, Y, H, W, W.

That leaves the H and S–>W pair out there as floaters.

Now, if you reinterpret the question, “which of the following must be false,” you know that the wrong answers are “could-be-trues,” and the right answer can never be true. (A) should jump out as the right answer since Atkins cannot contain more than one Y.

The last question is another unusual hypothetical, but don’t be intimidated. Just cross out your Atkins box. If anything, this question should be even easier since you only have two boxes to deal with. Again the LSAT has asked us to do something simple, but asked it in an intimidating way. It looks like the LSAT is pulling the rug out from under us by changing the rules around, but really, they are just simplifying things by removing a box. No big deal.

This is also another maximizing question. You’re probably getting the picture that distribution games often deal with numbers. This is because you use all of the items and typically have limits on which items can go where and how many items can be used total. Get used to dealing with numbers when you’re grouping.

To maximize Carter’s box, isolate all of the things that must go in Brower’s box, and then toss the floaters in Carter’s box. We know Brower has to at least have one Y, one of the Hs, and the S–>W pair (Carter can’t have an S). That leaves six items for Carter, so (C) is the right answer.

Grouping Game Questions Summary Tips

Grouping is the second most common skill used in Analytical Reasoning—practice it frequently.
Learn to quickly differentiate between sequencing, grouping and matching games so you can pick which games are easier for you to start with.
There are two types of grouping games. Selection asks you to choose from a larger list to form a smaller list. Sorting asks you to use all of the entities and put them into different groups. Sometimes the LSAT asks you to do both.
Typical rules deal with what item can go where, what items can’t go together, what items must go together, and what numbers are involved.
Typical inferences use the contra-positive for if-then style rules and focus on numbers and maximization.
The contra-positive gives you extra rules, so learn to recognize your if-then style rules. The following rules all mean the same thing as “If A, then B.”
- All apples come with bananas
- No apple is without a banana
- Whoever eats the apple also eats the banana
- If there is no banana used in the pie, no apple will be used either.
As always, be on the lookout for hypotheticals. Don’t be intimidated if a question seems to change everything around or uses thick language. Whenever the LSAT gives you more information—no matter how poorly written—It is to your advantage.