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Bill took 4 math tests, and each test received a score out of 100. What was Bill's average...

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Bill took 4 math tests, and each test received a score out of 100. What was Bill's average...

by BTGmoderatorLU » Fri Sep 04, 2020 10:11 am

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Source: Magoosh

Bill took 4 math tests, and each test received a score out of 100. What was Bill's average (arithmetic mean) score for all 4 tests?

1) Bill's first 3 tests received an average score of 50
2) Bill's last 2 tests received an average score of 50

The OA is E
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Re: Bill took 4 math tests, and each test received a score out of 100. What was Bill's average...

by deloitte247 » Sun Sep 06, 2020 2:09 pm

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Target question => what was Bill's average (arithmetic mean) score for all 4 tests?

Statement 1 => Bill's first 3 tests recovered an average score of 50
There is no information about the 4th test so overall average of the 4 test is unknown. Statement 1 is NOT SUFFICIENT

Statement 2 => Bill's last 2 tests received an average score of 50
There is no information about the1st and 2nd test so overall average of the test is unknown. Statement 2 is NOT SUFFICIENT

$$Combining\ both\ statements\ together\ =>\ $$
$$From\ statement\ 1\ =>\frac{test\ 1\ +\ test\ 2\ +\ test\ 3}{3}=50$$
$$From\ statement\ 2\ =>\frac{test\ 3\ +\ test\ 4}{2}=50$$
$$Scenarios\ that\ satisfy\ both\ statements\ include:$$
$$\frac{100+50+0+100}{4}=\frac{250}{4}\ Average\ =\ 62.5$$
$$or\ \frac{50+50+50+50}{4}=\frac{200}{4}\ Average\ =\ 50$$
$$or\ \frac{0+50+100+0}{4}=\frac{150}{4}\ Average\ =\ 37.5$$

Since the target question cannot be answered with certainty , both statements combined together ARE NOT SUFFICIENT

Answer = E
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Re: Bill took 4 math tests, and each test received a score out of 100. What was Bill's average...

by Brent@GMATPrepNow » Mon Sep 07, 2020 7:14 am

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BTGmoderatorLU wrote: ↑
Fri Sep 04, 2020 10:11 am
 Source: Magoosh

Bill took 4 math tests, and each test received a score out of 100. What was Bill's average (arithmetic mean) score for all 4 tests?

1) Bill's first 3 tests received an average score of 50
2) Bill's last 2 tests received an average score of 50

The OA is E
Target question: What was Bill's average (arithmetic mean) score for all 4 tests?

Statement 1: Bill's first 3 tests received an average score of 50.
Since we don't have any information about the 4th test, statement 1 is NOT SUFFICIENT

Statement 2: Bill's last 2 tests received an average score of 50.
Since we don't have any information about the first two tests, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
There are several scnenarios that satisfy BOTH statements. Here are two:
Case a: The 4 test scores, in order, are {50, 50, 50, 50}. In this case, the answer to the target question is The average score for all 4 tests is 50
Case b: The 4 test scores, in order, are {0, 50, 100, 0}. In this case, the answer to the target question is The average score for all 4 tests is 150/4
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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