A worker’s account activities consist of three types of transactions—deposits of $500 and withdrawals of either $300 or $400. Last week, did the worker have at least ten account transactions?
(1) Last week the worker had at least one of each of the three types of transactions. Not sufficient.
(2) At the end of last week, the amount in the worker’s account was $1,600 more than at the beginning of the week. Not sufficient.
(1)+(2) From (1) we know that the worker deposited at least once as well as withdrawn $300 and $400 at least once. Also, since from (2) we know that in the worker’s account was $1,600 more, then he must have deposited at least 4 times.
If he deposited 4 times, so if he deposited 4*$500=$2,000, then he withdrawn $400, we cannot break $400 so that to have withdrawals of both $300 and $400.
If he deposited 5 times, so if he deposited 5*$500=$2,500, then he withdrawn $900, we cannot break $900 so that to have withdrawals of both $300 and $400.
If he deposited 6 times, so if he deposited 6*$500=$3,000, then he withdrawn $1,400 --> $1,400=2*$400+2*$300 (only possible solution). Thus he made 6+2+2=10 transactions.
If he deposited 7 or more times, so if he deposited 7*$500=$3,500 or more, then he withdrawn $1,900 or more, thus in any case he made more than 4 withdrawals, thus had more than 10 transactions.
So, we have that the worker had at least ten account transactions. Sufficient.
Hope it's clear.
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