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04 Feb 2021, 03:00
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C
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Difficulty:
45%
(medium)
Question Stats:
70% (02:16) correct
30%
(02:18)
wrong
based on 272
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If Sam has 5 more marbles than Jack, Jack has 4 more marbles than Frank, and Frank has 5 more marbles than Ted, what is the least number of marbles that must change hands if the four boys are to have an equal number of marbles?
A. 7
B. 8
C. 9
D. 14
E. 28
A. 7
B. 8
C. 9
D. 14
E. 28
05 Feb 2021, 00:08
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Ted has X
Frank Has X+5
Jack has X+9
Sam has X+14
Now for them to have same marbles
I take out all extras and take out that is 14 +9+5=28 marbles need to be divided among 4 that i.e 28/4=7
So we know every person needs to have X+7 marbles to be equal.
Now for minimum exchange of hands
i take 2 marbles form Jack who has 9 and give to frank so both become X+7
and 7 marbles form Sam who has X+14 and give it to Ted so both have X+7.
Thus total marbles exchanged would be 9
Answer option C
Frank Has X+5
Jack has X+9
Sam has X+14
Now for them to have same marbles
I take out all extras and take out that is 14 +9+5=28 marbles need to be divided among 4 that i.e 28/4=7
So we know every person needs to have X+7 marbles to be equal.
Now for minimum exchange of hands
i take 2 marbles form Jack who has 9 and give to frank so both become X+7
and 7 marbles form Sam who has X+14 and give it to Ted so both have X+7.
Thus total marbles exchanged would be 9
Answer option C
General Discussion
04 Feb 2021, 22:26
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"If Sam has 5 more marbles than Jack, Jack has 4 more marbles than Frank, and Frank has 5 more marbles than Ted, what is the least number of marbles that must change hands if the four boys are to have an equal number of marbles?"
Sam = 5 + Jack; Jack = 4 + Frank; Frank = 5 + Ted .
So, Sam - 5 - 4 -5 = Jack - 4 - 5= Frank - 5 = Ted
So, if Sam were to give up 14 marbles, Jack were to give up 9 marbles, Frank were to give up 5 marbles, we would have a total of 28 marble to be distributed between the 4 boys at 7 marbles per head to achieve equal number of marbles.
Hence,
The change in number of marbles for Sam would be = -14+7 = -7
The change in number of marbles for Jack would be = -9+7 = -2
The change in number of marbles for Frank would be = -5+7 = +2
The change in number of marbles for Ted would be = -0+7 = +7
Hence, 9 marbles would need to be given from Sam+Jack to Frank+Ted. Answer (IHO) C.
Sam = 5 + Jack; Jack = 4 + Frank; Frank = 5 + Ted .
So, Sam - 5 - 4 -5 = Jack - 4 - 5= Frank - 5 = Ted
So, if Sam were to give up 14 marbles, Jack were to give up 9 marbles, Frank were to give up 5 marbles, we would have a total of 28 marble to be distributed between the 4 boys at 7 marbles per head to achieve equal number of marbles.
Hence,
The change in number of marbles for Sam would be = -14+7 = -7
The change in number of marbles for Jack would be = -9+7 = -2
The change in number of marbles for Frank would be = -5+7 = +2
The change in number of marbles for Ted would be = -0+7 = +7
Hence, 9 marbles would need to be given from Sam+Jack to Frank+Ted. Answer (IHO) C.
