A list contains the six numbers $5,7,7,20,a,b$. Th... | Free GMAT Practice Question | GMAT Panda

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A list contains the six numbers 5, 7, 7, 20, a, b . The arithmetic mean of the list is 9. If a and b are integers and a is not equal to b, what is the median of the list?

Explanation	Calculations	Help
$We know "arithmetic mean of the list" is 9, so the sum of the six numbers equals 9 times 6.$	$5 + 7 + 7 + 20 + a + b = 9 \times 6$
$We group the constant terms to simplify the sum.$	$5 + 7 + 7 + 20 + a + b = 9 \times 6 = 54 = (5 + 20) + (7 + 7) + a + b = 25 + 14 + a + b = 39 + a + b$	Theory & Tactics Method Card CALC1-A Click to view full details
$We isolate the sum of a and b.$	$a + b = 54 - 39 = 15$
$Because "a and b are integers and a is not equal to b", one of the values is less than 7.5 and the other is greater than 7.5.$	$one of the values a or b is less than 7.5 the other is greater than 7.5$
$We arrange the numbers in increasing order and find the 3rd and 4th values.$	$3^{rd} value = 7 4^{th} value = 7$
$The median is the average of the two middle values.$	$\frac{7 + 7}{2} = 7$

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B

A list contains the six numbers 5, 7, 7, 20, a, b . The arithmetic mean of the list is 9. If a and b are integers and a is not equal to b, what is the median of the list?

Explanation	Calculations	Help
$We know "arithmetic mean of the list" is 9, so the sum of the six numbers equals 9 times 6.$	$5 + 7 + 7 + 20 + a + b = 9 \times 6$
$We group the constant terms to simplify the sum.$	$5 + 7 + 7 + 20 + a + b = 9 \times 6 = 54 = (5 + 20) + (7 + 7) + a + b = 25 + 14 + a + b = 39 + a + b$	Theory & Tactics Method Card CALC1-A Click to view full details
$We isolate the sum of a and b.$	$a + b = 54 - 39 = 15$
$Because "a and b are integers and a is not equal to b", one of the values is less than 7.5 and the other is greater than 7.5.$	$one of the values a or b is less than 7.5 the other is greater than 7.5$
$We arrange the numbers in increasing order and find the 3rd and 4th values.$	$3^{rd} value = 7 4^{th} value = 7$
$The median is the average of the two middle values.$	$\frac{7 + 7}{2} = 7$

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B