On Monday, Karen had S dollars in her savings account

Question

On Monday, Karen had S dollars in her savings account and C dollars in her checking account. On Tuesday, Karen transferred half of the money in her savings account to her checking account. On Wednesday, Karen transferred 20% of the money in her checking account to her savings account, at which point she had the same amount of money in each bank account. If Karen made no other banking transactions during that time, which of the following describes the relationship between S and C?

A) S = C + 40
B) C = S/3
C) 2S = 3C
D) 3S = C
E) 3C = 10S

*kudos for all correct solutions

A) S = C + 40
B) C = S/3
C) 2S = 3C
D) 3S = C
E) 3C = 10S

*kudos for all correct solutions

Hero8888 · Answer

M => Tue => Wed 
 S => 0.5S => 0.5s+0.2(C+0.5S) 
 C => C+0.5S => 0.8(C+0.5S)

0.5s+0.2(C+0.5S)=0.8(C+0.5S)

S=3C, C=S/3 . Answer (B)

generis · Answer

Day 1  : S dollars are in savings, C dollars are in checking

S = S 
 C = C

Day 2  : Half of savings is transferred to checking

S: (S - \frac{1}{2}S) = \frac{1}{2}S 
 C: C + \frac{1}{2}S

Day 3  : 20 percent =  \frac{1}{5}  of checking is transferred back to savings

S: \frac{1}{2}S + (\frac{1}{5}(C+\frac{1}{2}S))

\frac{1}{2}S + \frac{1}{5}C + \frac{1}{10}S

• Just S term, then add to C term immediately above
  (\frac{1}{2}S + \frac{1}{10}S)=\frac{12}{20}S=\frac{3}{5}S

S FINAL :    \frac{3}{5}S+\frac{1}{5}C

C: (C + \frac{1}{2}S) - (\frac{1}{5}(C+\frac{1}{2}S))

C:\frac{4}{5}C + \frac{1}{2}S - \frac{1}{10}S

• Just S term, then add to C term immediately above 
  (\frac{1}{2}S-\frac{1}{10}S) = (\frac{10-2}{20}S) = \frac{8}{20}S =\frac{2}{5}S

C FINAL :    \frac{4}{5}C + \frac{2}{5}S

Day 3  :   S FINAL = C FINAL  , so
   \frac{3}{5}S + \frac{1}{5}C = \frac{4}{5}C + \frac{2}{5}S

\frac{1}{5}S=\frac{3}{5}C

S = \frac{3}{5}*\frac{5}{1}C

S = 3C

C = \frac{S}{3}

Answer B

BrentGMATPrepNow · Answer

Perfect solution! However, I think you meant to say the correct answer is B (not D)

Cheers,
Brent

generis · Answer

GMATPrepNow Brent, I did indeed mean Answer B. (In fact, I thought to myself about D, "Verrrrrry GMAT-esque sneaky! A trap.")

Thanks!

SSM700plus · Answer

Monday :  
Savings - S dollars
Checking - C dollars

Tuesday:   Half of savings is transferred to checking

Dollars in saving account becomes half -  \frac{S}{2} 
Dollars in Checking account -  C + \frac{S}{2}

Wednesday  : 20 percent of checking amount is transferred back to savings

Checking amount = 80% of current checking amount
 =  \frac{80}{100} * C + \frac{S}{2} 
 =  \frac{4C}{5} + \frac{2S}{5}

Savings amount = 20% of current checking amount + current savings amount
 =  \frac{20}{100}*(C + \frac{S}{2})+ \frac{S}{2}  
 =  \frac{C}{5} + \frac{S}{10} + \frac{S}{2} 
 =  \frac{C}{5} + \frac{3S}{5}

It is given that on this day the Checking amount = Savings amount
 \frac{4C}{5} + \frac{2S}{5}  =  \frac{C}{5} + \frac{3S}{5} 
 \frac{4C}{5} - \frac{C}{5} =  \frac{3S}{5} - \frac{2S}{5}

3C = S.

C = \frac{S}{3}

Answer B

BrentGMATPrepNow · Answer

Monday   
S dollars in savings account
C dollars in checking account

Tuesday : Karen transferred half of the money in her savings account to her checking account  
Amount in savings account =  0.5S 
Amount in checking account =  C + 0.5S

Wednesday : Karen transferred 20% of the money in her checking account to her savings account...  
20% of the money in her checking account = (0.2) C + 0.5S 
So, the new amount in savings account =  0.5S  + (0.2)( C + 0.5S )

NOTE:If Karen REMOVES 20% of the money in her checking account, then 80% of her money REMAINS
So, the new amount in checking account = (0.8)( C + 0.5S )

...at which point she had the same amount of money in each bank account  
So, we can write:  0.5S  + (0.2)( C + 0.5S ) = (0.8)( C + 0.5S )
Expand both sides to get: 0.5S + 0.2C + 0.1S = 0.8C + 0.4S
Simplify left side to get: 0.6S + 0.2C = 0.8C + 0.4S
Subtract 0.2C from both sides: 0.6S = 0.6C + 0.4S
Subtract 0.4S from both sides: 0.2S = 0.6C
To make things clearer/easier, let's multiply both sides by 10 to get: 2S = 6C
Divide both sides by 2 to get: S = 3C
Check answer choices....not there.

Take S = 3C and divide both sides by 3 to get: S/3 = C
Check answer choices.....

Answer: B

Cheers,
Brent

zishu912 · Answer

Saving Account Checking Account
 Mon S C
 Tue s /2 c + s/2
 Wed s/2 + 20/100*(c + s/2) c+s/2(1 - 20/100)

According to question

Balance in saving account on wed = Balance on checking account in wed

==>s/2 +c/5 + s/10 = 4c/5 + 2s/5
==>s/2 + s/10 - 2s/5 = 4c/5 - c/5
==>(5s + s - 4s)/ 10 = 3c/5
==>2s / 10 = 3c /5
therefore s = 3c or c = s/3

Kinshook · Answer

Given: On Monday, Karen had S dollars in her savings account and C dollars in her checking account. On Tuesday, Karen transferred half of the money in her savings account to her checking account. On Wednesday, Karen transferred 20% of the money in her checking account to her savings account, at which point she had the same amount of money in each bank account.

Asked: If Karen made no other banking transactions during that time, which of the following describes the relationship between S and C?

Monday:
Karen's savings account = S dollars
Karen's checking account = C dollars

Tuesday:
Karen's savings account = S - S/2 = S/2 dollars
Karen's checking account = C + S/2 dollars

Wednesday:
Karen's savings account = S/2 + .2(C+S/2) = .6S + .2C dollars
Karen's checking account = .8(C + S/2) = .8C + .4S dollars

Since Karen's savings account = Karen's checking account
.6S + .2C = .8C + .4S
.6C = .2S 
S = 3C
C = S/3

IMO B

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On Monday, Karen had S dollars in her savings account

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