Logical Reasoning · Inference (Must Be True)

PrepTest 145 · Section 4 · Question 13

Phase 1 (your first ~400 questions): read the guidance, then answer. No clock.

Step 1 · Pre-Question Guidance · read this first

Question type

Inference (Must Be True)

The one idea it tests

Two 'most' statements pointing in opposite directions tell you which group is bigger.

The basic logic

If most of group X are also in group Y, but most of group Y are not in X, the overlap is more than half of X and less than half of Y. So Y must be the bigger group. Draw two circles and check.

Tiny words that decide it

“most”
“also”
“not”

Playground logic

Most kids who can juggle can also yo-yo, but most yo-yo kids cannot juggle. The overlap is a big slice of the jugglers but a small slice of the yo-yo crowd, so there must be more yo-yo kids than jugglers.

Step 2 · The kid story

The Talent Show Count

Lulu was counting acts for the talent show. "Interesting," she said, tapping her clipboard. "Most kids who can juggle can also do yo-yo tricks. But most kids who can do yo-yo tricks cannot juggle." Marcus shrugged. "So juggling is harder. Obviously." Priya shook her head. "We do not know that. But we do know something." She drew two circles. "The both-kids are more than half of the jugglers. The same both-kids are less than half of the yo-yo kids. The same number is a big piece of one group and a small piece of the other." Owen grinned. "So the yo-yo group has to be bigger!" Lulu underlined it twice. "More yo-yo kids than jugglers. Guaranteed." Marcus muttered, "I still think juggling is harder."

Step 3 · Try the model question

Most students who can juggle can also do yo-yo tricks. But most students who can do yo-yo tricks cannot juggle.

If these statements are true, which choice must be true as well?

Step 4 · The courtroom tale

The Club Roster Dispute

Two clubs argued over a bigger meeting room. The chess club's lawyer read the facts: "Most members of the chess club also belong to the hiking club. But most hiking club members do not play chess." The hiking club's lawyer smiled. "Your Honor, think of the members who are in both clubs. They make up more than half of the chess club, yet less than half of the hiking club." Judge Pell did the math on a napkin. "So the same group of people is a large share of one and a small share of the other. The hiking club must be the larger club." The chess lawyer frowned. "Checkmate, I suppose." The judge awarded the big room to the hikers.

Step 5 · Work the real question

Open PrepTest 145, Section 4, Question 13 in your official copy from LSAC (for example in LawHub) and read it there.

Your answer

How to apply it

Draw two circles that overlap. Use the first 'most' statement to say the overlap is more than half of one circle, and the second to say it is less than half of the other. Ask which circle must be larger. Then pick the choice that states only that size comparison. Reject choices about difficulty, learning, or how the groups split up, because two 'most' statements cannot prove any of that.