Hey folks - long time lurker, first time poster. Looking for some alternative methods or explanations for 2 questions from the OG. I just can't seem to wrap my head around them and the official explanations aren't helping.
In a way, I'm hoping I missed something obvious here. Thanks for the help!
Hi, welcome to the club.If Carmen had 12 more tapes, she would have twice as many as Rafael. Does Carmen have fewer tapes than Rafael?
(1) Rafael has more than 5 tapes
(2) Carmen has fewer than 12 tapes
Given \(c+12=2r\), question is \(c<r\)?
(1) \(r>5\). If \(r=6>5\), \(c=0\) --> \(c<r\) BUT if \(r=14>5\), \(c=16\) --> \(c>r\). Two different answers. Not sufficient.
(2) \(c<12\). Max number of tapes Carol can have is 10 (for \(c=11\), \(r=11.5\) is not an integer, thus this value for \(c\) is not good, as \(c\) and \(r\) are the # of tapes, thus they must be integers). \(c_max=10\), \(r=11\) --> \(c<r\). Sufficient (if for \(c_max\) we got that \(c<r\), then for all other possible values of \(c\), \(c<r\) will also hold true).
Answer: B.Beginning in January of last year Carl made deposits of $120 into his account on the 15th of each month for several consecutive months and then made withdrawals of $50 from the account on the 15th of each of the remaining months last year. There were no other transactions in the account last year. If the closing balance of Carl's account for May of last year was $2600, what was the range of the monthly closing balances of Carl's account last year?
(1) Last year the closing balance of Carl's account for April was less than $2625
(2) Last year the closing balance of Carl's account for June was less than $2675
To find the range we should know:
A. Balance before he started depositing, initial balance = x (we know that there was initial balance because for May balance was 2600 and maximum amount he could deposited for this period is: 5 months*120=600).
B. Till what month he deposited $120.
C. From which month he started withdrawing $50.
(1) April balance< 2625 --> he deposited in May
(Because if he didn't then April balance=2600+50=2650 and we know that in April balance was<2625).
So for may balance=2600=x(initial balance)+5months*120 --> x+600=2600 --> x=2000.
We know initial balance, but we still don't know: till what month he deposited $120 and from which month he started withdrawing $50
(2) June balance < 2675 --> he didn't deposited in June --> he withdrawn in June (if he deposited, in June deposit would be May balance 2600+120=2720>2675)
(1)+(2) we know:
Initial balance: x=2000
Till what month he deposited $120: till May
From which month he started withdrawing $50: from June
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