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Few marbles are put into 8 pouches such that each pouch contains at le
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20 Nov 2023, 02:13
20 Nov 2023, 02:13
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28% (01:49) wrong based on 7 sessions
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Few marbles are put into 8 pouches such that each pouch contains at least one marble. At the most 4 pouches can contain the same number of marbles, and no two of the remaining pouches can contain an equal number of marbles. What is the least possible number of marbles in the 8 pouches?
(A) 8
(B) 17
(C) 18
(D) 24
(E) 30
(A) 8
(B) 17
(C) 18
(D) 24
(E) 30
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Re: Few marbles are put into 8 pouches such that each pouch contains at le
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21 Nov 2023, 18:54
21 Nov 2023, 18:54
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We need to calculate the least possible number of marbles in the 8 pouches, so the least possible number would be 8 , considering we have 1 marble in each pouch , now with this in mind let us look at the restrictions/conditions:
Let us number the pouches from P1 to P8
we are given that at the most 4 pouches can contain the same number of marbles -- thus P1,P2,P3 and P4 can have a minimum of 1 marble each i.e. total 4 marbles
Now the second condition states that no two of the remaining pouches can contain an equal number of marbles , so we can have P5=1, P6=2, P7=3, and P8=4 , but if we have P5=1 , it will violate the first condition that at the most 4 pouches can contain the same number of marbles , thus the minimum value of P5=2, then P6=3, P7=4 and P8=5 , thus P5+P6+P7+P8 = 2+3+4+5 = 14 marbles
Thus total = 4 + 14 = 18 marbles answer C
Let us number the pouches from P1 to P8
we are given that at the most 4 pouches can contain the same number of marbles -- thus P1,P2,P3 and P4 can have a minimum of 1 marble each i.e. total 4 marbles
Now the second condition states that no two of the remaining pouches can contain an equal number of marbles , so we can have P5=1, P6=2, P7=3, and P8=4 , but if we have P5=1 , it will violate the first condition that at the most 4 pouches can contain the same number of marbles , thus the minimum value of P5=2, then P6=3, P7=4 and P8=5 , thus P5+P6+P7+P8 = 2+3+4+5 = 14 marbles
Thus total = 4 + 14 = 18 marbles answer C
Re: Few marbles are put into 8 pouches such that each pouch contains at le
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24 Dec 2023, 04:35
24 Dec 2023, 04:35
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I assigned: P1=P2=P3=P4=3 marbles each
P5=P6=2 marbles each
P7=P8=1 marble each.
Total =18
Is this approach correct? Since it says no two of the remaining pouches can contain an equal number of marbles
P5=P6=2 marbles each
P7=P8=1 marble each.
Total =18
Is this approach correct? Since it says no two of the remaining pouches can contain an equal number of marbles
