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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