A worker’s account activities consist of three types of

Question

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.

Bunuel · Answer

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(1)+(2) From (1) we know that the worker deposited at least once as well as withdrawn $300 and $400 at least once.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If he deposited 4 times, so if he deposited 4*$500=$2,000, then he withdrawn $400, we cannot break $400 so that to have withdrawals of both $300 and $400.

If he deposited 5 times, so if he deposited 5*$500=$2,500, then he withdrawn $900, we cannot break $900 so that to have withdrawals of both $300 and $400.

If he deposited 6 times, so if he deposited 6*$500=$3,000, then he withdrawn $1,400 --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If he deposited 7 or more times, so if he deposited 7*$500=$3,500 or more, then he withdrawn $1,900 or more, thus in any case he made more than 4 withdrawals, thus had more than 10 transactions.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.

Answer: C.

Hope it's clear.

qlx · Answer

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.

Bunuel · Answer

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.

qlx · Answer

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.

Bunuel · Answer

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, ...

qlx · Answer

Thanks for not giving up on me, finally got it.

mohsint25 · Answer

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.

Hi, 
i have been thinking about this but couldnt understand it.

the question says "the amount is $16000 more than" not "exactly $16000". Therefore, in the above mentioned example if he withdrew $300*1 and $400*1 ($700) he would be left left $1800$. which makes it sufficient and hence the answer E.

Any help will he highly appreciated.

thanks

Konstantin1983 · Answer

Hi mohsint25!
Your explanation is not correct. First, the amount is 1600, not 16000 as you wrote. Second, please read statement 2 again. It says "1600 more than.." and that means that we have exact figure - 1600. This is not the same as "more than 1600". If this had been the case your explanation would have been correct. Hope it is clear.

mohsint25 · Answer

Thanks for the explanation . I confused 1600 more than with more than 1600

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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.
 
This is a frequently tested question in nowadays Chinese math. Looking at the original condition, there are 3 variables (x,y,z) if we let x be the no. of deposits of $500, y for that of $300, and z for $400. We will therefore need 3 equations to match the numbers, but there are only 2 equations given from the 2 conditions, so (E) is likely to be our answer.
Looking at them in detail, x=6, y=2, z=2 and the answer to the question becomes ‘yes’, and this condition is sufficient. In other words, 500*6-300*2-400*2=1,600 and 6+2+2=10.
But for condition 2, the answer is ‘yes’ for x=6, y=z=2, but ‘no’ for x=4, y=0, z=1. So this condition is insufficient, and the answer becomes (C).

For cases where we need 3 more equation, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

A worker’s account activities consist of three types of

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A worker’s account activities consist of three types of

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