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B
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Difficulty:
55%
(hard)
Question Stats:
58% (01:19) correct
42%
(01:26)
wrong
based on 209
sessions
History
Date
Time
Result
Not Attempted Yet
Two boys, Neil and Sam, were having a squabble about a pastry their father had given them to slice and share; each wanted to have more of the pastry. Their father came up with a suggestion: One of them should slice the pastry in two and the other should choose which piece he wanted. The children agreed to use the suggestion—and also agreed that Neil should slice the pastry. Was each child able to get half the pastry?
(1) The piece Sam chose was at least as large as the other piece.
(2) Neil sliced the pastry such that it would be impossible for him to get less than half of it.
(1) The piece Sam chose was at least as large as the other piece.
(2) Neil sliced the pastry such that it would be impossible for him to get less than half of it.
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16 Jan 2026, 02:13
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Two important things to take care of here:
1. Sam chooses the bigger slice always after Neil cuts it
2. Both want to maximize their pastry share
(1) states that the piece Sam chose was at least as large as the other piece
Initially I was a little confused thinking that if Neil acts optimally then there'd be no way where he would divide the pastry into two unequal halves since that'd lead to Sam choosing the bigger share. However, the argument doesn't enforce this. Each child wanting more doesn't logically force Neil to cut perfectly. It can very well be the case that Neil cuts the pastry either equally, 0.5 and 0.5, so that each child gets half the pastry or unequally, say 0.6 and 0.4, in which case Sam gets the bigger share. Notice, that in both cases Sam chose a piece at least as large the other piece.
Hence, insufficient.
(2) states that Neil sliced the pastry such that it would be impossible for him to get less than half of it
The only way Neil can do this is to slice the pastry into two equal halves, 0.5 and 0.5. In this case, each child would be able to get half the pastry and there are no other possibilities.
Hence, sufficient.
Answer is (B).
1. Sam chooses the bigger slice always after Neil cuts it
2. Both want to maximize their pastry share
(1) states that the piece Sam chose was at least as large as the other piece
Initially I was a little confused thinking that if Neil acts optimally then there'd be no way where he would divide the pastry into two unequal halves since that'd lead to Sam choosing the bigger share. However, the argument doesn't enforce this. Each child wanting more doesn't logically force Neil to cut perfectly. It can very well be the case that Neil cuts the pastry either equally, 0.5 and 0.5, so that each child gets half the pastry or unequally, say 0.6 and 0.4, in which case Sam gets the bigger share. Notice, that in both cases Sam chose a piece at least as large the other piece.
Hence, insufficient.
(2) states that Neil sliced the pastry such that it would be impossible for him to get less than half of it
The only way Neil can do this is to slice the pastry into two equal halves, 0.5 and 0.5. In this case, each child would be able to get half the pastry and there are no other possibilities.
Hence, sufficient.
Answer is (B).
