1
00:00:19,819 --> 00:00:25,199
If I tell you that most law students study
past midnight, and,

2
00:00:25,279 --> 00:00:29,679
uh, and most people who study past
midnight drink espresso...

3
00:00:30,559 --> 00:00:35,520
what can you actually conclude with
absolute logical certainty?

4
00:00:36,232 --> 00:00:41,512
That, uh, that at least some law students
are drinking espresso late at night?

5
00:00:43,137 --> 00:00:44,418
Absolutely nothing.

6
00:00:45,297 --> 00:00:45,678
Zero.

7
00:00:46,597 --> 00:00:50,378
You can conclude precisely zero.

8
00:00:51,569 --> 00:00:52,569
Wait, really?

9
00:00:53,250 --> 00:00:53,429
But...

10
00:00:53,750 --> 00:00:55,449
but it feels so intuitive!

11
00:00:56,150 --> 00:01:02,789
Most do A to B, most do B to C, so at
least a couple of them must go all the way

12
00:01:02,869 --> 00:01:04,509
from A to C, right?

13
00:01:06,552 --> 00:01:11,672
That right there is probably the single
most common trap on the Logical Reasoning

14
00:01:11,773 --> 00:01:12,092
section.

15
00:01:13,032 --> 00:01:15,753
Test takers build a linear chain in their
heads.

16
00:01:16,432 --> 00:01:23,412
They see A most B, and then B most C, and
their brain just fills

17
00:01:23,452 --> 00:01:24,013
in the gap.

18
00:01:24,892 --> 00:01:25,833
But mathematically?

19
00:01:26,552 --> 00:01:32,052
The guaranteed overlap between A and C in
that chain is exactly zero.

20
00:01:32,776 --> 00:01:33,716
Okay, wait.

21
00:01:33,936 --> 00:01:35,417
Walk me through the numbers on that.

22
00:01:35,996 --> 00:01:39,756
How do you get zero overlap out of two
mosts?

23
00:01:40,405 --> 00:01:44,984
Alright, picture a group of 100 people who
study past midnight.

24
00:01:45,684 --> 00:01:47,944
That is group B, our middle term.

25
00:01:49,024 --> 00:01:52,304
Now, say most of those 100 people are law
students.

26
00:01:53,144 --> 00:01:55,864
That could be, uh, 51 law students.

27
00:01:57,004 --> 00:02:00,584
That leaves 49 people in that group who
are not law students.

28
00:02:01,264 --> 00:02:01,484
Right?

29
00:02:02,132 --> 00:02:06,111
Right, 51 law students, 49 non law
students.

30
00:02:06,777 --> 00:02:12,597
Now take the second statement: most people
who study past midnight drink espresso.

31
00:02:13,497 --> 00:02:19,678
Again, out of our 100 late night studiers,
that only requires 51 people to drink

32
00:02:19,697 --> 00:02:20,237
espresso.

33
00:02:21,197 --> 00:02:23,917
Where do those 51 espresso drinkers come
from?

34
00:02:24,387 --> 00:02:24,727
Oh!

35
00:02:25,407 --> 00:02:28,907
They could all be the 49 non law
students...

36
00:02:29,387 --> 00:02:31,167
plus just 2 law students!

37
00:02:32,047 --> 00:02:36,107
Wait, no, they could be the 49 non law
students, and...

38
00:02:37,527 --> 00:02:39,267
wait, why could it be zero?

39
00:02:39,982 --> 00:02:46,982
Because the 51 espresso drinkers could
easily be the 49 non law students plus 2 law

40
00:02:47,063 --> 00:02:51,682
students, sure, but if group B was larger,
or if...

41
00:02:52,622 --> 00:02:54,202
let us take a group of 50 people.

42
00:02:54,782 --> 00:02:56,782
Suppose group B is 50 people.

43
00:02:57,503 --> 00:03:02,003
If 26 of them are law students, and 26 of
them drink espresso...

44
00:03:02,843 --> 00:03:08,342
wait, if B is the middle term, where does
the overlap actually become guaranteed?

45
00:03:09,046 --> 00:03:12,147
Oh, when B is the shared starting point!

46
00:03:12,366 --> 00:03:13,466
The reference group!

47
00:03:14,215 --> 00:03:14,975
Precisely.

48
00:03:16,014 --> 00:03:21,855
Look at what happens when B radiates
outward to both A and C at the same time.

49
00:03:22,755 --> 00:03:29,674
If B is a group of 50 items, and most B
are A, that means at least 26 items

50
00:03:29,714 --> 00:03:30,954
in group B are A.

51
00:03:31,715 --> 00:03:37,474
If most B are also C, that means at least
26 items in group B are C.

52
00:03:38,091 --> 00:03:38,391
Ah!

53
00:03:38,792 --> 00:03:41,711
26 plus 26 is 52!

54
00:03:42,111 --> 00:03:45,111
But there are only 50 items in group B
total!

55
00:03:45,882 --> 00:03:52,441
So by the pigeonhole principle, at least 2
items in group B must be both

56
00:03:52,561 --> 00:03:55,601
A and C at the exact same time.

57
00:03:56,542 --> 00:04:02,361
When two most claims share the same
reference group, their overlap guarantees a some

58
00:04:02,562 --> 00:04:03,101
conclusion.

59
00:04:03,897 --> 00:04:06,277
Let me rephrase that to make sure I have
it clean.

60
00:04:07,077 --> 00:04:12,958
If I say, most law students study past
midnight, and most law students drink

61
00:04:12,997 --> 00:04:14,338
espresso...

62
00:04:14,397 --> 00:04:16,777
now law students is the shared hub.

63
00:04:17,177 --> 00:04:19,917
It is the left side term for both claims.

64
00:04:20,549 --> 00:04:21,250
Exactly.

65
00:04:21,870 --> 00:04:26,549
Law students is the reference group of 100
percent in both statements.

66
00:04:27,294 --> 00:04:32,134
So if most of them study past midnight,
that is over 50 percent.

67
00:04:32,795 --> 00:04:37,894
If most of them drink espresso, that is
also over 50 percent of the exact same

68
00:04:38,014 --> 00:04:38,295
group.

69
00:04:38,854 --> 00:04:42,594
So those two majority groups have to crash
into each other.

70
00:04:43,295 --> 00:04:47,194
You are guaranteed that at least some law
students do both.

71
00:04:48,740 --> 00:04:49,299
Spot on.

72
00:04:49,960 --> 00:04:51,739
That is the Shared Hub Rule.

73
00:04:52,480 --> 00:04:58,260
You can only draw a valid some inference
from two most statements if they radiate

74
00:04:58,340 --> 00:05:00,960
outward from the exact same reference
group.

75
00:05:01,759 --> 00:05:06,479
If you try to chain them end to end like
dominoes, A to B, B to C,

76
00:05:06,959 --> 00:05:08,819
the chain snaps immediately.

77
00:05:09,424 --> 00:05:12,944
Okay, but what if we do want to chain
statements together?

78
00:05:13,384 --> 00:05:16,524
We are not always stuck with two most
claims, right?

79
00:05:17,184 --> 00:05:19,625
What happens when we mix in an all claim?

80
00:05:20,236 --> 00:05:22,536
Ah, the universal statement.

81
00:05:23,236 --> 00:05:27,076
I call All the ultimate amplifier on the
test.

82
00:05:27,877 --> 00:05:30,896
Suppose you have A, most B.

83
00:05:31,496 --> 00:05:34,636
And then you add, B, all, C.

84
00:05:35,476 --> 00:05:38,837
Every single B is inside set C.

85
00:05:39,564 --> 00:05:41,784
So if most A are B...

86
00:05:42,184 --> 00:05:44,244
and every single B is C...

87
00:05:44,824 --> 00:05:49,505
then all those B that were A are
automatically swept into C as well!

88
00:05:51,014 --> 00:05:51,714
Exactly.

89
00:05:52,414 --> 00:05:56,654
The universal statement acts like an
inescapable funnel.

90
00:05:57,494 --> 00:06:04,154
So A, most, B, all, C validly yields A,

91
00:06:04,494 --> 00:06:05,594
most, C.

92
00:06:06,414 --> 00:06:08,454
The quantifier passes right through.

93
00:06:09,072 --> 00:06:12,711
But wait, does the direction of the arrow
matter for All?

94
00:06:13,423 --> 00:06:15,042
It matters completely.

95
00:06:15,803 --> 00:06:17,042
If you flip that arrow...

96
00:06:17,563 --> 00:06:23,562
say you have A, most, B, but then C, all,
B...

97
00:06:24,463 --> 00:06:26,802
what do you know about A and C?

98
00:06:27,444 --> 00:06:31,744
Um, C is inside B, but...

99
00:06:31,904 --> 00:06:36,125
but the A items that are in B could be in
the other part of B!

100
00:06:36,564 --> 00:06:37,904
The part outside C!

101
00:06:38,629 --> 00:06:38,930
Right.

102
00:06:39,509 --> 00:06:44,049
C is just a small puddle inside the big
lake of B.

103
00:06:44,829 --> 00:06:49,769
The most A items might be swimming on the
completely opposite side of the lake.

104
00:06:50,569 --> 00:06:53,909
Reversing that arrow completely severs the
inference.

105
00:06:55,167 --> 00:07:00,007
It is so easy to fall for that when you
are rushing through a Must Be True question

106
00:07:00,067 --> 00:07:00,947
under time pressure.

107
00:07:01,847 --> 00:07:02,747
What about Some?

108
00:07:03,247 --> 00:07:05,947
How does Some play with All versus Most?

109
00:07:06,712 --> 00:07:09,573
It is the same principle, but even
tighter.

110
00:07:10,352 --> 00:07:17,112
If you have A, some, B, and B, all, C...

111
00:07:17,932 --> 00:07:24,232
then yes, those specific A items that hit
B are guaranteed to be carried into C.

112
00:07:24,933 --> 00:07:28,492
So A, some, C is valid.

113
00:07:29,174 --> 00:07:32,214
Because All is 100 percent.

114
00:07:32,615 --> 00:07:34,375
It captures everything in B.

115
00:07:35,009 --> 00:07:35,649
Exactly.

116
00:07:36,269 --> 00:07:42,849
But if you try A, some, B, and then B,
most,

117
00:07:43,510 --> 00:07:43,809
C...

118
00:07:44,689 --> 00:07:47,210
think about where that some element lands.

119
00:07:49,022 --> 00:07:53,942
A, some, B just gives you, like, maybe one
or two items in B.

120
00:07:54,602 --> 00:07:59,662
And B, most, C means more than half of B
is C.

121
00:08:00,442 --> 00:08:05,843
But those one or two items from A could
easily be in the minority of B that is NOT

122
00:08:06,122 --> 00:08:06,343
C!

123
00:08:07,107 --> 00:08:11,967
You just dodged a trap that kills
thousands of test takers every year.

124
00:08:12,787 --> 00:08:18,487
That target element gets stranded in the
unrepresented minority every single time.

125
00:08:20,231 --> 00:08:22,411
I remember seeing those in my prep!

126
00:08:22,971 --> 00:08:27,271
In the heat of the section, your brain
sees Some and Most and thinks,

127
00:08:27,712 --> 00:08:30,951
well, Most is pretty big, so they probably
overlap.

128
00:08:31,531 --> 00:08:35,871
But probably is an absolute poison pill on
the LSAT.

129
00:08:36,549 --> 00:08:42,529
In my litigator days, when we audited
contracts, we looked for ambiguity designed to

130
00:08:42,629 --> 00:08:43,929
trap the unmindful.

131
00:08:44,789 --> 00:08:48,369
Test writers draft question choices the
exact same way.

132
00:08:49,250 --> 00:08:55,329
On Flaw and Must Be True questions, they
love subtly swapping a Some for a Most,

133
00:08:55,829 --> 00:09:01,769
or turning an All arrow backward, knowing
rushing students read for broad context

134
00:09:01,849 --> 00:09:03,389
rather than structural rigor.

135
00:09:04,149 --> 00:09:08,549
So how do you stop yourself from making
those silly errors when the clock is

136
00:09:08,630 --> 00:09:09,029
ticking?

137
00:09:09,731 --> 00:09:13,511
You run what I call the 3 second Arrow
Head Audit.

138
00:09:14,252 --> 00:09:19,351
Before you even look at the answer
choices, you draw your terms on scratch paper and

139
00:09:19,411 --> 00:09:21,571
audit the arrows at the shared junction.

140
00:09:22,252 --> 00:09:23,752
Give me the checklist for that audit.

141
00:09:24,546 --> 00:09:27,306
Step one: find the shared term.

142
00:09:28,066 --> 00:09:31,886
Step two: check the arrow directions
meeting at that term.

143
00:09:32,606 --> 00:09:37,786
If you have two Most claims, are both
arrows pointing AWAY from the shared term?

144
00:09:38,326 --> 00:09:42,746
If yes, Shared Hub Rule applies, valid
Some conclusion.

145
00:09:43,526 --> 00:09:48,566
If one points in and one points out, stop
right there, zero conclusion.

146
00:09:49,132 --> 00:09:51,672
And if it is an All statement in the
chain?

147
00:09:52,441 --> 00:09:59,002
Step three: verify the All arrow points
AWAY from the middle term toward the final

148
00:09:59,081 --> 00:09:59,421
target.

149
00:10:00,121 --> 00:10:02,401
It has to act as an outgoing funnel.

150
00:10:03,241 --> 00:10:07,042
If the arrow points toward the middle
term, the chain is broken.

151
00:10:08,875 --> 00:10:14,014
It takes literally three seconds on
scratch paper, but it prevents you from falling

152
00:10:14,034 --> 00:10:17,474
for three different trap choices in a
single stimulus.

153
00:10:18,211 --> 00:10:22,672
Logical Reasoning does not reward speed or
vibe reading.

154
00:10:23,311 --> 00:10:26,212
It rewards a calm, repeatable audit.

155
00:10:27,191 --> 00:10:33,091
Learn where the overlaps are guaranteed,
and the traps just look like obvious noise.

156
00:10:33,736 --> 00:10:38,297
Alright, shared hubs point out, funnels
point away.

157
00:10:38,756 --> 00:10:39,616
Good rule to live by.

158
00:10:40,116 --> 00:10:41,156
Talk to you next time, Adrian.