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Contests & Programs AMC and other contests, summer programs, etc.
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9 When To Start Grinding Math Again
Existing_Human1   142
N 3 minutes ago by xTimmyG
For context, I got a 103.5 on AMC 10B, so I am not sure if I made AIME. I have AMC 8 and Mathcoutns coming up as competitions
142 replies
Existing_Human1
Nov 23, 2024
xTimmyG
3 minutes ago
Counterexample
avn   35
N 4 minutes ago by xTimmyG
Source: 2019 AMC 10B #2 / 12B #2
Consider the statement, "If $n$ is not prime, then $n-2$ is prime." Which of the following values of $n$ is a counterexample to this statement?

$\textbf{(A) } 11 \qquad \textbf{(B) } 15 \qquad \textbf{(C) } 19 \qquad \textbf{(D) } 21 \qquad \textbf{(E) } 27$
35 replies
avn
Feb 14, 2019
xTimmyG
4 minutes ago
No more topics!
Problem 2
evt917   50
N Nov 17, 2024 by sadas123
Source: 2024 AMC 12B #2 / AMC 10B #2
What is $10! - 7! \cdot 6!$?

$
\textbf{(A) }-120 \qquad
\textbf{(B) }0 \qquad
\textbf{(C) }120 \qquad
\textbf{(D) }600 \qquad
\textbf{(E) }720 \qquad
$
50 replies
evt917
Nov 13, 2024
sadas123
Nov 17, 2024
Problem 2
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Source: 2024 AMC 12B #2 / AMC 10B #2
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froliop
58 posts
#37
Y by
Jack_w wrote:
Divisible by $6!$ so $\textbf{(E) }720$

LMAOO
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AbhayAttarde01
1154 posts
#38
Y by
Jack_w wrote:
Divisible by $6!$ so $\textbf{(E) }720$

no bro why :sob:
its $3628800-5040*720$
which is $3628800-3628800$
which is $\boxed{\textbf{(B) }0}$
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blueberryfaygo_55
338 posts
#39
Y by
Reducing modulo $7$ kills
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pingpongmerrily
2552 posts
#40
Y by
AbhayAttarde01 wrote:
Jack_w wrote:
Divisible by $6!$ so $\textbf{(E) }720$

no bro why :sob:
its $3628800-5040*720$
which is $3628800-3628800$
which is $\boxed{\textbf{(B) }0}$

bro why are you bashing :skull:
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GAMER100
2107 posts
#41
Y by
GAMER100 wrote:
andrewcheng wrote:
Jack_w wrote:
Divisible by $6!$ so $\textbf{(E) }720$

you poor poor fool

Stop bullying him, guys. We all make mistakes. In fact, this is a good way to narrow down the answers, he only missed that $0$ was also divisible by $6!$.

In fact, $0$ is the only one divisible by $7!$, so he was pretty close to a really quick clever answer!
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AbhayAttarde01
1154 posts
#42
Y by
pingpongmerrily wrote:
AbhayAttarde01 wrote:
Jack_w wrote:
Divisible by $6!$ so $\textbf{(E) }720$

no bro why :sob:
its $3628800-5040*720$
which is $3628800-3628800$
which is $\boxed{\textbf{(B) }0}$

bro why are you bashing :skull:

I didn't do the AMC 10 unfortunately (I'm in 9th but I didn't complete precalc bc I'm on algebra 2) so I decided to bash becase
no time limit!
its very freeing
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ethanzhang1001
980 posts
#43
Y by
AbhayAttarde01 wrote:
I didn't do the AMC 10 unfortunately (I'm in 9th but I didn't complete precalc bc I'm on algebra 2)
its very freeing

ok what why you can still take it it's only algebra and geometry
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Alex_Yang
373 posts
#44
Y by
Jack_w wrote:
Divisible by $6!$ so $\textbf{(E) }720$

Erm acc it should be divis by $7!$ so $0$
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Yiyj1
1005 posts
#45
Y by
just memorize that $10!=6!\cdot7!$ stop trying to do all those mod tricks or whatnot just memorize it at least that's what i did

saved me a few seconds so i could solve number 25 just in time :cool:
This post has been edited 1 time. Last edited by Yiyj1, Nov 16, 2024, 6:26 AM
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youngjin
190 posts
#46
Y by
unironically one of the nicest problems on the test
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AbhayAttarde01
1154 posts
#47
Y by
ethanzhang1001 wrote:
AbhayAttarde01 wrote:
I didn't do the AMC 10 unfortunately (I'm in 9th but I didn't complete precalc bc I'm on algebra 2)
its very freeing

ok what why you can still take it it's only algebra and geometry

I haven't completed algebra 2 yet that's why
I finish algebra 2 in like the end of January (yes in half a school year I have to complete it
This post has been edited 1 time. Last edited by AbhayAttarde01, Nov 16, 2024, 2:55 PM
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MC_ADe
135 posts
#48 • 3 Y
Y by AbhayAttarde01, evt917, giratina3
I can confirm E due to engineers induction
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jb2015007
675 posts
#49
Y by
i just bashed it out in fear of sillying it
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Catcumber
104 posts
#50 • 2 Y
Y by forestcaller2010, AbhayAttarde01
Jack_w wrote:
Divisible by $6!$ so $\textbf{(E) }720$

Divisible by 1 so $\textbf{(A) }-120$
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sadas123
139 posts
#51
Y by
evt917 wrote:
What is $10! - 7! \cdot 6!$?

$
\textbf{(A) }-120 \qquad
\textbf{(B) }0 \qquad
\textbf{(C) }120 \qquad
\textbf{(D) }600 \qquad
\textbf{(E) }720 \qquad
$
I got 0 because if you do 10!-7!x6! you just get that 8x9x10-6! which simplifies to 720-720 which gets you the answer of "0" This was like number 1 on AMC 10 b
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