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Arick
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If 1 s P s 40, how many values of P exist such that (P-1)! Updated on: 08 Jun 2023, 12:14
Originally posted by Arick on 01 Jun 2023, 11:14.
Last edited by Arick on 08 Jun 2023, 12:14, edited 1 time in total.
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Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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85% (hard)

Question Stats:

51% (02:33) correct 49% (02:00) wrong based on 251 sessions

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If 1 <= P <= 40, how many values of P exist such that (P-1)! is not divisible by P?

(A) 11

(B) 10

(C) 12

(D) 13

(E) 9


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D
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gmatophobia
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If 1 s P s 40, how many values of P exist such that (P-1)! 01 Jun 2023, 12:41
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Arick
If 1 <= P <= 40, how many values of P exist such that (P-1)! is not divisible by P?

(A) 11

(B) 10

(C) 12

(D) 13

(E) 9

Kupos please 😀

Posted from my mobile device
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As (P-1) ! should not be divisible by P, P should be a prime number.

Example: 2 ! is not divisible by 3, 6! is not divisible by 7, and so on

Hence, we want to find the number of prime numbers between 1 and 40.

There are 12 prime numbers between 1 and 40.

Option C
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If 1 s P s 40, how many values of P exist such that (P-1)! Updated on: 02 Jun 2023, 02:16
Originally posted by Kinshook on 01 Jun 2023, 22:14.
Last edited by Kinshook on 02 Jun 2023, 02:16, edited 1 time in total.
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Asked: If 1 <= P <= 40, how many values of P exist such that (P-1)! is not divisible by P?

P = {2,3,5,7,11,13,17,19,23,29,31,37} : 12 values of P

IMO C
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If 1 s P s 40, how many values of P exist such that (P-1)! 01 Jun 2023, 22:39
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Kinshook
Asked: If 1 <= P <= 40, how many values of P exist such that (P-1)! is not divisible by P?

P = {1, 2,3,5,7,11,13,17,19,23,29,31,37} : 13 values of P

IMO D
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Hi Kinshook

Can you please explain why 1 is a part of the set?

If P = 1

(1-1)! = 0! = 1

Isn't 0! divisible by 1 or am I missing something?
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If 1 s P s 40, how many values of P exist such that (P-1)! 01 Jun 2023, 23:03
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Hi Kinshook,

How can 1 be the value of P?
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If 1 s P s 40, how many values of P exist such that (P-1)! 02 Jun 2023, 02:17
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Corrected. Thanks
Bunuel Please check OA and correct it.

gmatophobia
Kinshook
Asked: If 1 <= P <= 40, how many values of P exist such that (P-1)! is not divisible by P?

P = {1, 2,3,5,7,11,13,17,19,23,29,31,37} : 13 values of P

IMO D

Hi Kinshook

Can you please explain why 1 is a part of the set?

If P = 1

(1-1)! = 0! = 1

Isn't 0! divisible by 1 or am I missing something?
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If 1 s P s 40, how many values of P exist such that (P-1)! 05 Jun 2023, 05:57
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Arick
If 1 <= P <= 40, how many values of P exist such that (P-1)! is not divisible by P?

(A) 11

(B) 10

(C) 12

(D) 13

(E) 9

Kupos please 😀

Posted from my mobile device

As (P-1) ! should not be divisible by P, P should be a prime number.

Example: 2 ! is not divisible by 3, 6! is not divisible by 7, and so on

Hence, we want to find the number of prime numbers between 1 and 40.

There are 12 prime numbers between 1 and 40.

Option C
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Can someone explain to me why 4 is not that number as (4-1)
! is not divisible by 4. Shouldn't the correct answer be 13 instead of 12?
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If 1 s P s 40, how many values of P exist such that (P-1)! 05 Jun 2023, 13:17
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I believe 4 should be included too in the list because 3*2/4 is not divisible basically, so in total it's 13 integers including 1 and the prime numbers.
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If 1 s P s 40, how many values of P exist such that (P-1)! 06 Jun 2023, 08:56
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This misses 4. 3! is not divisible by 4. something is wrong here
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If 1 s P s 40, how many values of P exist such that (P-1)! 06 Jun 2023, 11:00
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[quote="Arick"]If 1 <= P <= 40, how many values of P exist such that (P-1)! is not divisible by P?

(A) 11

(B) 10

(C) 12

(D) 13

(E) 9

Why are we looking for prime numbers in this question? If we take non prime numbers then also we can get the same result
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If 1 s P s 40, how many values of P exist such that (P-1)! 08 Jun 2023, 12:16
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Kinshook
Asked: If 1 <= P <= 40, how many values of P exist such that (P-1)! is not divisible by P?

P = {2,3,5,7,11,13,17,19,23,29,31,37} : 12 values of P

IMO C
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If p is any prime number, (p - 1)! is not divisible by p. 1 <= P <= 40 Each prime value of P satisfies the given condition

There are 12 such values.

When P is 1, (P - 1)! = 1 (which is divisible by P).

The only composite number satisfying the condition is 4.

There are 13 values of P satisfying the condition

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If 1 s P s 40, how many values of P exist such that (P-1)! 23 Nov 2024, 03:17
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I think u missed 4 (3*2/4) not divisible
Kinshook
Asked: If 1 <= P <= 40, how many values of P exist such that (P-1)! is not divisible by P?

P = {2,3,5,7,11,13,17,19,23,29,31,37} : 12 values of P

IMO C
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If 1 s P s 40, how many values of P exist such that (P-1)! 11 Feb 2026, 11:56
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since P ranges from 1 to 40 inclusive.
just checking certain observations ,
!39 is div by 40
!37 is div by 38
!36 is not div by 37
!4 is not div by 5
!6 is not div by 7
!9 is div by 10
we can conclude that every prime no.P satisfies the given condition.
only exception !3=6 which is not divisible by 4.
so it can be just rephrased to count the no. of primes less than equal to 40 +1
=12+1=13 D.
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