Problem Solving

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

Answer: B
Difficulty level: 650-700
Source: www.gmatprepnow.com

Brent@GMATPrepNow wrote: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

Answer: B
Difficulty level: 650-700
Source: www.gmatprepnow.com

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