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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.

Attachment:
2024-01-24_12-31-31.png


(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.

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?
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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.

Attachment:
2024-01-24_12-31-31.png


(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.

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?

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.
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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
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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
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guddo
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.

Attachment:
2024-01-24_12-31-31.png
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
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