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# A worker’s account activities consist of three types of

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A worker’s account activities consist of three types of [#permalink]  01 Nov 2012, 08:15
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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. (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.
[Reveal] Spoiler: OA

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Re: A worker’s account activities consist of three types of [#permalink]  01 Nov 2012, 08:47
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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(1)+(2) From (1) we know that the worker deposited at least once as well as withdrawn $300 and$400 at least once.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 If he deposited 4 times, so if he deposited 4*$500=$2,000, then he withdrawn$400, we cannot break $400 so that to have withdrawals of both$300 and $400. If he deposited 5 times, so if he deposited 5*$500=$2,500, then he withdrawn$900, we cannot break $900 so that to have withdrawals of both$300 and $400. If he deposited 6 times, so if he deposited 6*$500=$3,000, then he withdrawn$1,400 --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 If he deposited 7 or more times, so if he deposited 7*$500=$3,500 or more, then he withdrawn$1,900 or more, thus in any case he made more than 4 withdrawals, thus had more than 10 transactions.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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Re: A worker’s account activities consist of three types of [#permalink]  15 Jul 2014, 05:46
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Re: A worker’s account activities consist of three types of [#permalink]  06 Feb 2015, 03:55
using 1+2

Account has 0$initially then 500 *6 -300 *2 - 400*2 = 1600 so 6+2+2 = 10 what if worker had already 500$ in the account initially
Then

500 +500*5 -300*2 -400*2= 1600 here we have 5+2+2 = 9 transactions

So I am getting E.

Please point out my mistake. Should be assume that there was 0$in the account initially. Math Expert Joined: 02 Sep 2009 Posts: 29185 Followers: 4736 Kudos [?]: 50054 [0], given: 7525 Re: A worker’s account activities consist of three types of [#permalink] 06 Feb 2015, 04:01 Expert's post qlx wrote: using 1+2 Account has 0$ initially then 500 *6 -300 *2 - 400*2 = 1600 so 6+2+2 = 10
what if worker had already 500$in the account initially Then 500 +500*5 -300*2 -400*2= 1600 here we have 5+2+2 = 9 transactions So I am getting E. Please point out my mistake. Should be assume that there was 0$ in the account initially.

The initial amount does NOT matter.

We are told that at the end of last week, the amount in the worker’s account was $1,600 more than at the beginning of the week. Your example does not work: 500*5 - 300*2 - 400*2 = 1100, not 1600. _________________ Manager Joined: 17 Mar 2014 Posts: 65 Followers: 0 Kudos [?]: 29 [0], given: 36 A worker’s account activities consist of three types of [#permalink] 06 Feb 2015, 04:23 Bunuel wrote: qlx wrote: using 1+2 Account has 0$ initially then 500 *6 -300 *2 - 400*2 = 1600 so 6+2+2 = 10
what if worker had already 500$in the account initially Then 500 +500*5 -300*2 -400*2= 1600 here we have 5+2+2 = 9 transactions So I am getting E. Please point out my mistake. Should be assume that there was 0$ in the account initially.

The initial amount does NOT matter.

We are told that at the end of last week, the amount in the worker’s account was $1,600 more than at the beginning of the week. Your example does not work: 500*5 - 300*2 - 400*2 = 1100, not 1600. forgive me , still not able to comprehend At the beginning of the week he could have had 500 then make deposits of 500 *5 and withdrawals 300*2 and 400*2 So 500 + 500*5 -300*2 -400 *2 =1600 Sorry but where does it say that at the beginning of the week he had$0, or the Difference between the beginning and end of the week of $1600 was done only through transactions . He could still have 500$ on Monday and then make further deposits of 500 * 5 through the week , and withdraw 300 *2 and 400*2 through the week.

In this case also amount at the end of the week will be 1600$more than at the beginning of the week but he would have done only 9 transactions.( as he already had$500 on Monday , he did not deposit that through any transaction that week).

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Re: A worker’s account activities consist of three types of [#permalink]  06 Feb 2015, 04:29
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qlx wrote:
Bunuel wrote:
qlx wrote:
using 1+2

Account has 0$initially then 500 *6 -300 *2 - 400*2 = 1600 so 6+2+2 = 10 what if worker had already 500$ in the account initially
Then

500 +500*5 -300*2 -400*2= 1600 here we have 5+2+2 = 9 transactions

So I am getting E.

Please point out my mistake. Should be assume that there was 0$in the account initially. The initial amount does NOT matter. We are told that at the end of last week, the amount in the worker’s account was$1,600 more than at the beginning of the week.

Your example does not work: 500*5 - 300*2 - 400*2 = 1100, not 1600.

forgive me , still not able to comprehend

At the beginning of the week he could have had 500 then make deposits of 500 *5 and withdrawals 300*2 and 400*2

So 500 + 500*5 -300*2 -400 *2 =1600

Sorry but where does it say that at the beginning of the week he had $0, or the Difference between the beginning and end of the week of$1600 was done only through transactions . He could still have 500$on Monday and then make further deposits of 500 * 5 through the week , and withdraw 300 *2 and 400*2 through the week. In this case also amount at the end of the week will be 1600$ more than at the beginning of the week but he would have done only 9 transactions.( as he already had $500 on Monday , he did not deposit that through any transaction that week). Thank you for your understanding. If initially he had$500, then after 500*5 - 300*2 - 400 *2 he would have $1600, which is only$1100 more than the initial amount of $500, not$1600 more. Again initial amount does not matter it could have been $0,$500, $1000000000, ... _________________ Manager Joined: 17 Mar 2014 Posts: 65 Followers: 0 Kudos [?]: 29 [0], given: 36 Re: A worker’s account activities consist of three types of [#permalink] 06 Feb 2015, 04:44 Bunuel wrote: qlx wrote: forgive me , still not able to comprehend At the beginning of the week he could have had 500 then make deposits of 500 *5 and withdrawals 300*2 and 400*2 So 500 + 500*5 -300*2 -400 *2 =1600 Sorry but where does it say that at the beginning of the week he had$0, or the Difference between the beginning and end of the week of $1600 was done only through transactions . He could still have 500$ on Monday and then make further deposits of 500 * 5 through the week , and withdraw 300 *2 and 400*2 through the week.

In this case also amount at the end of the week will be 1600$more than at the beginning of the week but he would have done only 9 transactions.( as he already had$500 on Monday , he did not deposit that through any transaction that week).

If initially he had $500, then after 500*5 - 300*2 - 400 *2 he would have$1600, which is only $1100 more than the initial amount of$500, not $1600 more. Again initial amount does not matter it could have been$0, $500,$1000000000, ...

Thanks for not giving up on me, finally got it.
Re: A worker’s account activities consist of three types of   [#permalink] 06 Feb 2015, 04:44
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