Bunuel wrote:

Is the sum of the prices of the 3 books that Shana bought less than $48 ?

(1) The price of the most expensive of the 3 books that Shana bought is less than $17.

(2) The price of the least expensive of the 3 books that Shana bought is exactly $3 less than the price of the second most expensive book.

Target question: Is the sum of the prices of the 3 books less than $48 ?Let A = price of the LEAST expensive book (in dollars)

Let B = price of the mid-priced expensive book (in dollars)

Let C = price of the MOST expensive book (in dollars)So,

A < B < C Statement 1: The price of the most expensive of the 3 books that Shana bought is less than $17. So, C < 17

Let's TEST some values.

There are several cases that satisfy statement 1. Here are two:

Case a: A = $1, B = $2 and C = $3, in which case A + B + C = 1 + 2 + 3 = 6. In this case, the answer to the target question is

YES, the sum of the prices IS less than $48Case b: A = $16.25, B = $16.50 and C = $16.75, in which case A + B + C = 16.25 + 16.50 + 16.75 = 49.50. In this case, the answer to the target question is

NO, the sum of the prices is NOT less than $48Since we cannot answer the

target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The price of the least expensive of the 3 books that Shana bought is exactly $3 less than the price of the second most expensive book.In other words, A = B - 3

Let's TEST some values again.

There are several cases that satisfy statement 1. Here are two:

Case a: A = $1, B = $4 and C = $10, in which case A + B + C = 1 + 4 + 10 = 15. In this case, the answer to the target question is

YES, the sum of the prices IS less than $48Case b: A = $1, B = $4 and C = $100, in which case A + B + C = 1 + 4 + 100 = 105. In this case, the answer to the target question is

NO, the sum of the prices is NOT less than $48Since we cannot answer the

target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined Statement 1 tells us that C < 17

Statement 2 tells us that A = B - 3

Let's MAXIMIZE ALL of the values

If C < $17, then the greatest possible value of C = $16.99

Since B must be less than C, the greatest possible value of B = $16.98

Since A is $3 less than B, greatest possible value of A = $12.98

So, when we MAXIMIZE all 3 values, A + B + C = $16.99 + $16.98 + $12.98 = $46.95, which is less than $48

If if the GREATEST values of A, B and C have a sum that's less than $48, we can conclude that is must be the case that A + B + C < 48

In other words, the answer to the target question is

YES, the sum of the prices IS less than $48Since we can answer the

target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,

Brent

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