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

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

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23 Jan 2004, 14:02
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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

Folks: Could you solve this mathmatically? (with steps shown)
Director
Joined: 28 Oct 2003
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23 Jan 2004, 14:19
Folks: Could you solve this mathmatically? (with steps shown)

Sort of:

100<3x+2<110

100<4y+1<110

3x+2=4y+1

Not really, then, though I tried. Anyway, the answer is clearly 101.
Senior Manager
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23 Jan 2004, 14:20
Of the five numbers given lets try to fit in the first condition...

multiple of 3 with 2 as the remainder..

only 101 = 3*33 +2 and 107 = 3*35 +2 satisfy this condition.

Now we apply the 2nd condition...multiple of 4 with 1 as the remainder..on these 2 numbers..

101 = 25*4 +1 and 107 = 25*26+3

Vivek.
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23 May 2007, 18:12
vivek_dj wrote:
Of the five numbers given lets try to fit in the first condition...

multiple of 3 with 2 as the remainder..

only 101 = 3*33 +2 and 107 = 3*35 +2 satisfy this condition.

Now we apply the 2nd condition...multiple of 4 with 1 as the remainder..on these 2 numbers..

101 = 25*4 +1 and 107 = 25*26+3

Vivek.

23 May 2007, 18:12
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