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There are between 100 and 110 cards in a collection of cards

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There are between 100 and 110 cards in a collection of cards [#permalink]

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There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?

(A) 101
(B) 103
(C) 106
(D) 107
(E) 109
[Reveal] Spoiler: OA

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Re: Number of Cards Between 100 - 110 [#permalink]

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New post 07 Apr 2012, 22:30
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It is not a combinatorics question. this question is about a remainder

let our number be x

then u are said in the question stem that -

x/3 =y+2 (remainder 2)

x/4=z+1 (remainder 1)

take 101

101/3=33*3+2

101/4=25*4+1

so, it means A is the answer
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Re: There are between 100 and 110 cards in a collection of cards [#permalink]

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boomtangboy wrote:
There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?

(A) 101
(B) 103
(C) 106
(D) 107
(E) 109


If the cards are counted out 3 at a time, there are 2 left over: x=3q+2. From the numbers from 100 to 110 following three give the remainder of 2 upon division by 3: 101, 104 and 107;

If the cards are counted out 4 at a time, there are 1 left over: x=4p+1. From the numbers from 100 to 110 following three give the remainder of 1 upon division by 4: 101, 105 and 109;

Since x, the number of cards, should satisfy both conditions then it equals to 101.

Answer: A.
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Re: There are between 100 and 110 cards in a collection of cards [#permalink]

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Hi Bunnel,

Is the below solution correct

n = 3q + 2 ==> put values we get 2, 5, 8

n = 4q + 1 ==> put values we get 1, 5, 9

LCM is 12

so number should be 12q + 5

101

Ans : A
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Re: There are between 100 and 110 cards in a collection of cards [#permalink]

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New post 09 Aug 2013, 01:10
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GMAT40 wrote:
Hi Bunnel,

Is the below solution correct

n = 3q + 2 ==> put values we get 2, 5, 8

n = 4q + 1 ==> put values we get 1, 5, 9

LCM is 12

so number should be 12q + 5

101

Ans : A


i think its working.

lets take a similar example just to verify:

a nymber when divided by 4 gives remainder 2 and when divided by 5 gives remainder 1
LCM of 4 and 5 = 20
now we will calculate first number which is satisfying this condition:
when divided by 4 gives remainder 2: 2 6 10
when divided by 5 gives remainder 1: 1 6 11

hence the number in generalized form = 20k+6
lets verify put k=1...number =26==>satisfies both
k=2....number = 46==>satisfying both...

so thats working.

takeaway:
step 1: find the LCM
step 2: find the first number satisfying both condition ...and then generalise. :-D
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Re: There are between 100 and 110 cards in a collection of cards [#permalink]

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New post 09 Aug 2013, 02:10
GMAT40 wrote:
Hi Bunnel,

Is the below solution correct

n = 3q + 2 ==> put values we get 2, 5, 8

n = 4q + 1 ==> put values we get 1, 5, 9

LCM is 12

so number should be 12q + 5

101

Ans : A



In Addition,this sum might help with the concept : positive-integer-n-leaves-a-remainder-of-4-after-division-by-93752.html
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Re: There are between 100 and 110 cards in a collection of cards [#permalink]

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New post 09 Aug 2013, 02:30
boomtangboy wrote:
There are between 100 and 110 cards in a collection of cards. If they are counted out 3 at a time, there are 2 left over, but if they are counted out 4 at a time, there is 1 left over. How many cards are in the collection?

(A) 101
(B) 103
(C) 106
(D) 107
(E) 109

.................

divide 101 by 3 and then divide 101 by 4 again, we have 2 and 1 as the remainder respectively.
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Re: There are between 100 and 110 cards in a collection of cards [#permalink]

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New post 27 Jan 2014, 10:18
blueseas wrote:
GMAT40 wrote:
Hi Bunnel,

Is the below solution correct

n = 3q + 2 ==> put values we get 2, 5, 8

n = 4q + 1 ==> put values we get 1, 5, 9

LCM is 12

so number should be 12q + 5

101

Ans : A


i think its working.

lets take a similar example just to verify:

a nymber when divided by 4 gives remainder 2 and when divided by 5 gives remainder 1
LCM of 4 and 5 = 20
now we will calculate first number which is satisfying this condition:
when divided by 4 gives remainder 2: 2 6 10
when divided by 5 gives remainder 1: 1 6 11

hence the number in generalized form = 20k+6
lets verify put k=1...number =26==>satisfies both
k=2....number = 46==>satisfying both...

so thats working.

takeaway:
step 1: find the LCM
step 2: find the first number satisfying both condition ...and then generalise. :-D


Yes actually the way of solving is getting that X = 12K +5

So then X is a multiple of 12 plus 5.
Only number in the given range is 101

Hope this clarifies
Cheers!
J :)
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Re: There are between 100 and 110 cards in a collection of cards [#permalink]

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New post 27 Jan 2018, 18:53
Dividing by 3 & 4 is the quickest way to get the answer. Refer remainders shortcut on math mega thread.
Re: There are between 100 and 110 cards in a collection of cards   [#permalink] 27 Jan 2018, 18:53
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There are between 100 and 110 cards in a collection of cards

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