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Statistics Data Sufficiency

This topic has 3 expert replies and 0 member replies
Amrabdelnaby Master | Next Rank: 500 Posts Default Avatar
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Statistics Data Sufficiency

Post Mon Nov 16, 2015 4:40 am
Elapsed Time: 00:00
  • Lap #[LAPCOUNT] ([LAPTIME])
    Could you please help me with this one?

    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 of 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 2,600, 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 $2,625
    2- Last year the closing balance of Carl's account for June was less than $2,675

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    Post Mon Nov 16, 2015 6:15 am
    Quote:
    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 of 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 $2,600, 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 $2,625.
    (2) Last year the closing balance of Carl’s account for June was less than $2,675.
    May = 2600.

    Statement 1: Last year the closing balance of Carl’s account
    for April was less than $2,625.

    If 120 was deposited in May, then April = 2600-120 = 2480.
    If 50 was withdrawn in May, then April = 2600+50 = 2650.
    Since April < 2625, we know that a deposit of 120 was made in May, implying that 120 was deposited every month January through at least May.
    Thus, we can determine the balance of every month January - April:
    April = 2480, March = 2480-120 = 2360, etc.
    No information about June - December.
    Insufficient.

    Statement 2: Last year the closing balance of Carl’s account
    for June was less than $2,675.

    If 120 was deposited in June, then June = 2600+120 = 2720.
    If 50 was withdrawn in June, then June = 2600-50 = 2550.
    Since June < 2675, we know that a withdrawal of 50 was made in June, implying that 50 was withdrawn every month June - December.
    Thus, we can determine the balance of every month June - December:
    June = 2550, July = 2550-50 = 2500, etc.
    No information about January - April.
    Insufficient.

    Statements 1 and 2 combined:
    Statement 1 tells us the closing balances January - April.
    The question stem tells us the closing balance in May.
    Statement 2 tells us the closing balances June - December.
    Combining the information above, we can determine the closing balance of every month and determine the range for the whole year.
    Sufficient.

    The correct answer is C.

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    Post Mon Nov 16, 2015 7:36 am
    Quote:
    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 of 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 $2,600, 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 $2,625
    (2) Last year the closing balance of Carl’s account for June was less than $2,675
    Target question: What was the range of the monthly closing balances of Carl’s account last year?

    Given: The closing balance of Carl’s account for May of last year was $2,600

    IMPORTANT: To answer the target question we need only determine which month Carl STARTED withdrawing money.
    For example, if he started withdrawing money on March 15, we could use the fact that he had $2600 at the end of May to determine how much he had in the bank every month of the year, and thus determine the range of closing balances.
    Notice that, since this is a Data Sufficiency, we need not calculate the actual range. We need only determine which month the deposits stopped and the withdrawals started.

    So, we can rephrase our target question as . . .

    REPHRASED target question: In which month did Carl start withdrawing $50?

    Statement 1: Last year the closing balance of Carl’s account for April was less than $2,625
    Let's examine two cases:
    case a: In May, Carl DEPOSITED $120. So, balance at end of April = $2600 - $120 = $2480. This is possible, since we're told that the balance is less than $2625
    case b: In May, Carl WITHDREW $50. So, balance at end of April = $2600 + $50 = $2650. This is NOT possible, since we're told that the balance is less than $2625
    So, Carl definitely deposited $120 in May (and deposited $120 in April, March, Feb, and Jan).
    However, we don't know the first month that Carl started withdrawing $50
    Since we cannot answer the REPHRASED target question with certainty, statement 1 is NOT SUFFICIENT

    Statement 2: Last year the closing balance of Carl’s account for June was less than $2,675.
    Let's examine two cases:
    case a: In June, Carl DEPOSITED $120. So, balance at end of June = $2600 + $120 = $2720. This is NOT possible, since we're told that the balance is less than $2675
    case b: In June, Carl WITHDREW $50. So, balance at end of June = $2600 - $50 = $2550. This is possible, since we're told that the balance is less than $2675
    So, Carl definitely withdrew $50 in June, which means he also withdrew $50 in July, August, Sept, etc. However, we don't know the FIRST month that Carl started withdrawing $50
    Since we cannot answer the REPHRASED target question with certainty, statement 2 is NOT SUFFICIENT

    Statements 1 and 2 combined
    Statement 1 tells us that Carl deposited $120 in May.
    Statement 2 tells us that Carl withdrew $50 in June.
    So, June was the first month that Carl started withdrawing $50
    Since we can answer the REPHRASED target question with certainty, the combined statements are SUFFICIENT

    Answer = C

    Cheers,
    Brent

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    Post Mon Nov 16, 2015 10:45 am
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