Lee has three separate savings accounts. What is the total amount of

Question

Lee has three separate savings accounts. What is the total amount of money in the three accounts?

(1) The total amount of money in any two of the accounts is $8,000.
(2) At least one of the accounts contains $4,000.

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stne · Answer

(1) The total amount of money in any two of the accounts is $8,000.

This is only possible if all accounts have  $4000  each. So no matter which two we pick we will always land up with  $8000 .

Thus total amount is  $4000*3 =$12,000

SUFF.

(2) At least one of the accounts contains $4,000

We have no idea about the other two, so not sufficient.

INSUFF.

Ans A.

Hope it helped.

gmatophobia · Answer

Statement 1

(1) The total amount of money in any two of the accounts is $8,000.

As the total money in any of the two accounts is 8000, we can infer that each account consists of exactly $4000.

Hence, the total amount of money in the three accounts = 4000 * 3 = $12,000

This statement alone is sufficient. We can eliminate B, C, and E.

Statement 2

(2) At least one of the accounts contains $4,000.

While we know that at least one of the accounts contains $4,000, we don't know the amount of money in the other two accounts.

Assume that each account consists of $4000, the total amount of money in the three accounts = 4000 * 3 = $12,000.

However, if the other two accounts consist of a combined amount of $1000, the total amount of money in the three accounts = $5,000.

As we are getting multiple possibilities, Statement 2 alone is not sufficient to answer the question.

Option A

Shuvojoti · Answer

Hey stne, thanks for detailing. However, in opt A, how have you ASSUMED that the money is EQUALLY divided in each of the 3 accounts? Since it's total 8000, can't it be 5000 in one, and 3000 in another or anything like this?

Bunuel · Answer

If we use your example of a = $5,000 and b = $3,000, what would the third amount, c, be? If c = $3,000, then b = $3,000 and c = 3,000 would not total $8,000, and if it's c = $5,000, then a = $5,000 and c = $5,000 would not total $8,000. Hence, for the total amount of money in ANY two of the accounts to be $8,000, each of the three must be $4,000. You can also get this algebraically by solving: a + b = $8,000 a + c = $8,000 b + c = $8,000 Check similar question to practice: https://gmatclub.com/forum/are-all-of-t ... 44144.html Hope it helps.

MS61 · Answer

A : The total amount of money in any two of the accounts is $8,000.

A + B = 8000
B + C = 8000
C + A = 8000

Hence 2A+ 2B + 2C = 24000
A + B + C = 12000

Sufficient

shwetakoshija · Answer

Given:  Lee has three separate savings accounts.

To Find:  The total amount of money in the three accounts.

Statement 1:  The total amount of money in any two of the accounts is $8,000.
 
 Let the three accounts have balances A, B, and C. 
 From the statement, we have the following equations:
 
 A + B = 8000 
 B + C = 8000 
 C + A = 8000  
 
 Adding all three equations:
 
 (A + B) + (B + C) + (C + A) = 3 × 8000 
 2(A + B + C) = 24000 
 A + B + C = 12000 
 Thus, the total amount in all three accounts is $12,000, which answers the question.

Statement 1 alone is  sufficient .

Statement 2:  At least one of the accounts contains $4,000.
 
 This statement means that 1 or 2 or all 3 accounts contain $4000. 
 Since this doesn’t tell anything about the account(s) that do not contain $4000, we cannot determine the total sum.

Statement 2 alone is  insufficient .

Correct Answer: A

GMATinsight · Answer

Question: a+b+c = ?

Statement 1  : a+b = 8000 and b+c = 8000 and a+c = 8000
Adding all three equations we get
2*(a+b+c) = 24000
i.e. a+b+c = 12000
hence
  SUFFICIENT

Statement 2  : At least one of the accounts contains $4,000.
but the sum of three account can NOT be calculated hence 
  NOT SUFFICIENT

Answer: Option A

monarchme · Answer

Hey i also had the same doubt looking at the solution but the catch is the word " ANY .."  in statement A. So the question is demanding  no matter whatever values you take for the money in accounts keep in mind that you have to follow this rule: the sum of money of any two values must be $8000.

Lee has three separate savings accounts. What is the total amount of

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