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# Susan, Jordan, and Mitchell each purchased a used car. The average (ar

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Math Expert
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Susan, Jordan, and Mitchell each purchased a used car. The average (ar  [#permalink]

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13 Feb 2015, 07:51
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Difficulty:

45% (medium)

Question Stats:

62% (01:24) correct 38% (01:19) wrong based on 140 sessions

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Susan, Jordan, and Mitchell each purchased a used car. The average (arithmetic mean) price of the three used cars was \$8,000.00. What was the median price of the three cars?

(1) The price of Susan's car was \$7,000.00.
(2) The price of Jordan's car was \$8,000.00.

Kudos for a correct solution.

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Re: Susan, Jordan, and Mitchell each purchased a used car. The average (ar  [#permalink]

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13 Feb 2015, 13:47
1
If the average of three purchases is \$8,000, then the sum of the purchases is \$8,000 * 3 = \$24,000.
We need two values in order to determine the third. Once we have these three values, we can determine the median.

Each statement alone gives one value, so they are insufficient.
Combining both statements, we can find the third purchase is \$24,000 - \$8,000 - \$7,000 = \$9,000.
The median value is \$8,000 and the correct answer is C.
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Re: Susan, Jordan, and Mitchell each purchased a used car. The average (ar  [#permalink]

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13 Feb 2015, 18:29
Hi sterling19,

I'm going to give you a couple of hints so that you can re-attempt this question:

You ARE correct that since the average of the 3 cars is \$8,000.....the sum will be \$24,000.

Now, take that logic a step further. In Fact 1, what COULD the answer be? Remember that we're looking for the MEDIAN of the three values. Can you come up with more than one possibility? How about in Fact 2. Write your examples down and you'll see that your original assumption is incorrect (you don't need 2 of the values to answer this question).

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Re: Susan, Jordan, and Mitchell each purchased a used car. The average (ar  [#permalink]

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13 Feb 2015, 18:42
Yes, thank you.
After testing some numbers, I can see now that B is the answer.

Statement 1 leaves \$17,000 for the other two values. Testing numbers shows this is insufficient. This could be split between \$8,000 and 9,000 payments (\$8,000 is the median) or \$6,000 and \$11,000 payments (\$7,000 is the median).

Statement 2 leaves \$16,000 for the remaining two values. \$8,000 will be the median no matter how you split it up. Any payment over \$8,000 must be accompanied by a payment less than \$8,000 in order for the three payments to total \$24,000. This is sufficient.
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Re: Susan, Jordan, and Mitchell each purchased a used car. The average (ar  [#permalink]

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13 Feb 2015, 18:54
1
Hi sterling19,

YES, you are correct.

As you continue to work on DS questions, remember that trying to "talk your way past" the prompt can be dangerous. If you're "off", even a little bit, then you'll get the question wrong and not even know it. If you have an idea that you think is correct, then you should be able to prove it. Since the math is almost always really easy, spending the extra time to PROVE that something is sufficient or insufficient is the difference between getting the points and not.

GMAT assassins aren't born, they're made,
Rich
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# Rich Cohen

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Re: Susan, Jordan, and Mitchell each purchased a used car. The average (ar  [#permalink]

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14 Feb 2015, 14:33
I made the same mistake too, however EMPOWERgmatRichC's guidance helped me to find the right answer. I want to know the level of this question. Thank you
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Posts: 52108
Re: Susan, Jordan, and Mitchell each purchased a used car. The average (ar  [#permalink]

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16 Feb 2015, 05:38
Bunuel wrote:
Susan, Jordan, and Mitchell each purchased a used car. The average (arithmetic mean) price of the three used cars was \$8,000.00. What was the median price of the three cars?

(1) The price of Susan's car was \$7,000.00.
(2) The price of Jordan's car was \$8,000.00.

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION

Explanation: From the question stem, we know that S + J + M = (3) (\$8,000) = \$24,000, since Average * Quantity = Sum. Statement (1) tells us that S, the price of Susan's car, is \$7000. This statement alone is not sufficient because it leaves more than one possible median price. For example, the median could be \$8000 if M = \$8000 and J = \$9000. The median could also be \$7000 if M = \$7000 and J = \$10,000. Statement (2) tells us that J, the price of Jordan's car, is \$8000. This statement alone is sufficient, because if one of the three prices is the mean, then either the prices of the other two cars must also equal the mean, or the price of one of the cars must be higher than the mean price and the cost of the other car must be lower than the mean price (such as, M = \$7000 and S = \$9000). In any case, \$8000 will be the median. Statement (2) provides sufficient information while statement (1) does not, and accordingly B is the correct answer.
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Re: Susan, Jordan, and Mitchell each purchased a used car. The average (ar  [#permalink]

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17 Feb 2015, 04:07
average of 3 cars is 8000 and statement 2 states that jordan's price is 8000 so its proved median is 8000
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Susan, Jordan, and Mitchell each purchased a used car. The average (ar  [#permalink]

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09 May 2017, 11:18
This one is tricky if you are not careful.
1 is insufficient because we do not know the price of Jordan and Mitchell Car
Some people would say 2 is insufficient. However, it is sufficient.
If the average is 8000 and the price of Jordan Car is 8000 then let's say Mitchell car must be below 8000 and
let's say Susan car must be higher than 8000.

OR
All 3 persons car price is 8000.
Therefore, the median is always going to be 8,000.

The answer is B
Susan, Jordan, and Mitchell each purchased a used car. The average (ar &nbs [#permalink] 09 May 2017, 11:18
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# Susan, Jordan, and Mitchell each purchased a used car. The average (ar

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