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There are N students in a class. When the students are distributed int

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There are N students in a class. When the students are distributed int  [#permalink]

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New post 24 Mar 2019, 09:53
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There are N students in a class. When the students are distributed into groups that contain \(4A\) number of students each, \(3\) students are left without a group. When the students are distributed into groups that contain \(\frac{A}{3}\) number of students each, no students are left without a group. Which of the following statements is correct?

I) If the students are distributed into groups that contain \(A+1\) students each, the number of students that are left without a group can be \(2\).
II) If the students are distributed into groups that contain \(3\) students each, no students are left without a group
III) If the students are distributed into groups that contain \(12\) students each, 9 students are left without a group


A) I only
B) II only
C) III only
D) I and II only
E) II and III only

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There are N students in a class. When the students are distributed int  [#permalink]

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New post 25 Mar 2019, 21:34
There are N students in a class.
When the students are distributed into groups that contain \(\frac{A}{3}\) number of students each, no students are left without a group. This means A is a multiple of 3
When the students are distributed into groups that contain \(4A\) number of students each, \(3\) students are left without a group. This means N=4Ax+3, and since A is multiple of 3, N is also a multiple of 3

Which of the following statements is correct?

I) If the students are distributed into groups that contain \(A+1\) students each, the number of students that are left without a group can be \(2\).
N=4Ax+3... now let A=3, so A+1=3+1=4 and N=4*3x+3=12x+3, then N divided by A+1 means 12x+3 divided by 4 will leave a remainder 3 . Hence need not be true.

II) If the students are distributed into groups that contain \(3\) students each, no students are left without a group
Correct we know N=4Ax+3 and Ax=3, so N=12+3=15.. 15 divided by 3 does not leave any remainder TRUE

III) If the students are distributed into groups that contain \(12\) students each, 9 students are left without a group
Now, 4A=12, so N=12x+3, so whenever we divide the N students in groups of 12, 3 will be left. Hence false

Only option II is correct

A) I only
B) II only
C) III only
D) I and II only
E) II and III only
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Re: There are N students in a class. When the students are distributed int  [#permalink]

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New post 26 Mar 2019, 01:37
Using the info given ,
N=4A+3 and A/3 gives equal groups , let so let A= 6 and N= 27
so
case 1:
If the students are distributed into groups that contain \(A+1\) students each, the number of students that are left without a group can be \(2\).
6+1 ; 7 ; when 7/4 = 3 is remainder and when 7/3 ; remainder is 1 so not true
case 2:
If the students are distributed into groups that contain \(3\) students each, no students are left without a group
N=27 ; yes no student is left w/o group
case 3:
If the students are distributed into groups that contain \(12\) students each, 9 students are left without a group
N= 27 divided by 12 ; 3 remainder ; not true
IMO B


PriyankaPalit7 wrote:
There are N students in a class. When the students are distributed into groups that contain \(4A\) number of students each, \(3\) students are left without a group. When the students are distributed into groups that contain \(\frac{A}{3}\) number of students each, no students are left without a group. Which of the following statements is correct?

I) If the students are distributed into groups that contain \(A+1\) students each, the number of students that are left without a group can be \(2\).
II) If the students are distributed into groups that contain \(3\) students each, no students are left without a group
III) If the students are distributed into groups that contain \(12\) students each, 9 students are left without a group


A) I only
B) II only
C) III only
D) I and II only
E) II and III only

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Re: There are N students in a class. When the students are distributed int  [#permalink]

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New post 13 Apr 2019, 07:02
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chetan2u wrote:
There are N students in a class.
When the students are distributed into groups that contain \(\frac{A}{3}\) number of students each, no students are left without a group. This means A is a multiple of 3
When the students are distributed into groups that contain \(4A\) number of students each, \(3\) students are left without a group. This means N=4A+3, and since A is multiple of 3, N is also a multiple of 3

Which of the following statements is correct?

I) If the students are distributed into groups that contain \(A+1\) students each, the number of students that are left without a group can be \(2\).
N=4A+3... now let A=3, so A+1=3+1=4 and N=15, then N divided by A+1 means 15 divided by 4 will leave a remainder 3 . Hence need not be true.

II) If the students are distributed into groups that contain \(3\) students each, no students are left without a group
Correct we knoe N=4A+3 and A=3x, so N=12x+3=3(4x+1).. TRUE

III) If the students are distributed into groups that contain \(12\) students each, 9 students are left without a group
Now, N=12x+3, so whenever we divide the N students in groups of 12, 3 will be left. Hence false

Only option II is correct

A) I only
B) II only
C) III only
D) I and II only
E) II and III only


Hi,

I fail to understand how N=4A+3, students are divided into groups of 4A, so it should be N=4A * y(number of groups) + 3. This additional factor of "y" will change the equation and the way we are deducing things. Please correct me if i am wrong.

TIA.
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Re: There are N students in a class. When the students are distributed int  [#permalink]

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New post 13 Apr 2019, 07:12
1
neha283 wrote:
chetan2u wrote:
There are N students in a class.
When the students are distributed into groups that contain \(\frac{A}{3}\) number of students each, no students are left without a group. This means A is a multiple of 3
When the students are distributed into groups that contain \(4A\) number of students each, \(3\) students are left without a group. This means N=4A+3, and since A is multiple of 3, N is also a multiple of 3

Which of the following statements is correct?

I) If the students are distributed into groups that contain \(A+1\) students each, the number of students that are left without a group can be \(2\).
N=4A+3... now let A=3, so A+1=3+1=4 and N=15, then N divided by A+1 means 15 divided by 4 will leave a remainder 3 . Hence need not be true.

II) If the students are distributed into groups that contain \(3\) students each, no students are left without a group
Correct we knoe N=4A+3 and A=3x, so N=12x+3=3(4x+1).. TRUE

III) If the students are distributed into groups that contain \(12\) students each, 9 students are left without a group
Now, N=12x+3, so whenever we divide the N students in groups of 12, 3 will be left. Hence false

Only option II is correct

A) I only
B) II only
C) III only
D) I and II only
E) II and III only


Hi,

I fail to understand how N=4A+3, students are divided into groups of 4A, so it should be N=4A * y(number of groups) + 3. This additional factor of "y" will change the equation and the way we are deducing things. Please correct me if i am wrong.

TIA.



Hi,

You are correct on the observation. However the answer will not change.
I will change the related portion accordingly.
Thanks
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Re: There are N students in a class. When the students are distributed int   [#permalink] 13 Apr 2019, 07:12
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