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
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given range : 100 to 110
counted out to 3 : multiples of three ….99,102,105,108,111,….
leaves remainder 2 cards: 99+2,102+2,105+2,108+2
new range : 101,104,107,110
now whwn counted to 4 leaves one card : divide above range by 4 and see which one has a remainder of 1 (given leaves out 1 card)
hence answer : 101.
hope tis correct.
101
A
definitely A because it is the only no. of the form 3x+2 and 4y+1 as required
hmm. ‘A’ s rite
a
A
a
ya the answer is A
Plug and check
101 has a remainder of 2 when divided by 3, and a remainder of 1 when divided by 4
103, 106, 109 all have a remainder of 1 when divided by 3
107 has a remainder of 2 when divided by 3, but a remainder of 3 when divided by 4
The answer is 101, after I redid my math…
101. first choice..
A
A
a