Linda purchased 3 books at a book fair. What was the median price of

Question

Linda purchased 3 books at a book fair. What was the median price of the 3 books?

(1) The average (arithmetic mean) price of the 3 books was $1.5

(2) The price of one of the 3 books was $1.5

Sasindran · Answer

C

Let the cost of books be x y and z.

1: x+y+z=4.5. Clearly insufficient. 
2: no info about the other two books.

Combining,
We get x=1 or 1.2 or 1.5, y=1.5, and z=2 or 1.8 or 1.5. x and z can be any value. But the median is always 1.5. Hence C

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Manishcfc8 · Answer

Median means the entry needs to be present in the list. Having the average isn't enough. So, 1 is not sufficient

2 is not sufficient as it doesn't mention the price of the other two books.

Combining both the statements: The average is 3 and one of the entry is 1.5

Since one of the entry is 1.5, we are left with 3 as the price of two other books combined. Any combination of 2 numbers adding to 3 will follow two pattern:
--> either both are 1.5 each
--> one is smaller and the other is greater than 1.5. both simultaneously can't be smaller or bigger than 1.5

In both the patterns above, 1.5 will lie in the middle of the list, Nd hence, 1.5 is the median

Answer is C

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egmat · Answer

Statement 1:  Average price = $1.5
This tells us the sum of all 3 prices =  $4.5

Case 1:  $0.50, $1.50, $2.50 → Median =  $1.50 
 Case 2:  $1.00, $1.00, $2.50 → Median =  $1.00

Both satisfy the average, but give different medians.
→  Not Sufficient

Statement 2:  One book costs $1.5
We don't know if $1.5 is the smallest, middle, or largest price.

Case 1:  $1.00, $1.50, $2.00 → Median =  $1.50 
 Case 2:  $1.50, $2.00, $3.00 → Median =  $2.00

Different medians possible.
→  Not Sufficient

Both Statements Together: 
Sum = $4.5 and one book costs $1.5
So the other two books sum to: $4.5 - $1.5 =  $3.00

If two numbers sum to $3.00, can both be greater than $1.50? No! (That would make sum > $3). Can both be less than $1.50? No! (That would make sum < $3).

So one book must be ≤ $1.50 and one must be ≥ $1.50.
This means $1.50 is  always  the middle value.

→  Median = $1.50  →  Sufficient

Answer: C

Linda purchased 3 books at a book fair. What was the median price of

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GMAT Data Sufficiency (DS) Questions

Linda purchased 3 books at a book fair. What was the median price of

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