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A team manager is distributing some gift boxes. The number of boxes

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A team manager is distributing some gift boxes. The number of boxes  [#permalink]

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New post 26 Sep 2019, 11:43
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A team manager is distributing some gift boxes. The number of boxes is a two digit number. If she distributes the boxes between herself and the two teammates who sit on either side of her, then two boxes remain. If she also includes two other teammates, then no boxes remain. How many values are possible for the number of gift boxes?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9
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Re: A team manager is distributing some gift boxes. The number of boxes  [#permalink]

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New post 26 Sep 2019, 17:53
Given
N= 2 mod 3
N=0 mod 5

Hence, N=5 mod 15
or N= 15k+5

k can take 6 values.

Hovkial wrote:
A team manager is distributing some gift boxes. The number of boxes is a two digit number. If she distributes the boxes between herself and the two teammates who sit on either side of her, then two boxes remain. If she also includes two other teammates, then no boxes remain. How many values are possible for the number of gift boxes?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9
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Re: A team manager is distributing some gift boxes. The number of boxes  [#permalink]

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New post 27 Sep 2019, 17:50
nick1816 wrote:
Given
N= 2 mod 3
N=0 mod 5

Hence, N=5 mod 15
or N= 15k+5

k can take 6 values.

Hovkial wrote:
A team manager is distributing some gift boxes. The number of boxes is a two digit number. If she distributes the boxes between herself and the two teammates who sit on either side of her, then two boxes remain. If she also includes two other teammates, then no boxes remain. How many values are possible for the number of gift boxes?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9


is there another way to solve this problem? or/ Can you share links to learn mod rules/ how to use mod
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Re: A team manager is distributing some gift boxes. The number of boxes  [#permalink]

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New post 27 Sep 2019, 18:11
N=3x+2
N=5y
N is a 2 digit positive integer
10≤5y<100
2≤y<20

3x+2=5y
3x=5y-2
x=(5y-2)/3
As x and y are integers, y can be 4, 7,10, 13, 16 or 19 (only these values of y lie in highlighted range).


wolvarun wrote:
nick1816 wrote:
Given
N= 2 mod 3
N=0 mod 5

Hence, N=5 mod 15
or N= 15k+5

k can take 6 values.

Hovkial wrote:
A team manager is distributing some gift boxes. The number of boxes is a two digit number. If she distributes the boxes between herself and the two teammates who sit on either side of her, then two boxes remain. If she also includes two other teammates, then no boxes remain. How many values are possible for the number of gift boxes?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9


is there another way to solve this problem? or/ Can you share links to learn mod rules/ how to use mod
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A team manager is distributing some gift boxes. The number of boxes  [#permalink]

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New post 28 Sep 2019, 00:48
To me the easiest way to solve this problem:

Given formulas :

A = 3X+2....i
A =5X+0 ... ii

here the L.C.M of 3 and 5 is 15. Therefore, 15 would be a common multiplier in every value.

Now, if I put 1 in the equation ii, I can get the same result in equation 1. Which means the lowest number of possible value could be 5. And to get the next value we need to add 15 with the lowest value (since 15 is the L.C.M.

Therefore, I can rewrite the equation

A=15X+5.

Now, the highest number X can have is 6. Otherwise A would be a three digit number. Where, the question says A is a 2 digit number.

B is the correct answer.

Thanks

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Re: A team manager is distributing some gift boxes. The number of boxes  [#permalink]

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New post 28 Sep 2019, 02:57
from given info
we know that 3x+2=5y
x=5y-2/3 ; so possible integer value of y & x will be when y = 4,7,10,13,16 ,19
total 6 possible cases
IMO B


Hovkial wrote:
A team manager is distributing some gift boxes. The number of boxes is a two digit number. If she distributes the boxes between herself and the two teammates who sit on either side of her, then two boxes remain. If she also includes two other teammates, then no boxes remain. How many values are possible for the number of gift boxes?

(A) 5

(B) 6

(C) 7

(D) 8

(E) 9
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Re: A team manager is distributing some gift boxes. The number of boxes  [#permalink]

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New post 21 Nov 2019, 00:04
Why are we taking N=5K ? Can someone explain ?
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A team manager is distributing some gift boxes. The number of boxes  [#permalink]

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New post 22 Nov 2019, 04:09
Rumsus wrote:
Why are we taking N=5K ? Can someone explain ?


Rumsus ,
Let me rephrase the question for you.
The number of gift boxes when divided among THREE people gives a remainder of 2.
The number of gift boxes when divided among FIVE people gives a remainder of 0.
The number of gift boxes is a two digit number.
Find how many such two digit numbers exist?

First point:
The number of gift boxes when divided among THREE people gives a remainder of 2.

2,5,8,11...17,20 23...35 ..50....65...80...95...101..104
All the above numbers when divided by 3 give a remainder of two, but we are only interested in such two digit numbers.(Bold ones)

Second point:
The number of gift boxes when divided among FIVE people gives a remainder of 0

5,10,15, 20,25,30,...35 ..50....65...80...95.......100....105
All the above numbers when divided by 5 give a remainder of zero, but we are only interested in such two digit numbers and which are common with the list above(Bold ones)


The number of gift boxes common in both lists above and satisfying the given criteria.
20 35 ..50....65...80...95

Hence there are six such numbers possible. Hope now it's is clear why we are taking the second point to be a multiple of 5 ( 5K).
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A team manager is distributing some gift boxes. The number of boxes   [#permalink] 22 Nov 2019, 04:09
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