GMAT Official Guide 2019 Is the sum of the prices of the

[BTGmoderatorDC]

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.

[Brent@GMATPrepNow]

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 $48
Case 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 $48
Since 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 $48
Case 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 $48
Since 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 $48
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer: C

Cheers,
Brent

[Scott@TargetTestPrep]

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.

Solution:

Question Stem Analysis:

We need to determine whether the total amount spent on the 3 books is less than $48.

Statement One Alone:

Since the most expensive of the 3 books Shana bought is less than $17, the total she has spent is less than 17 x 3 = $51. Since it’s less than $51, it could be less than $48 (e.g., $47), or it could be more than $48 (e.g., $50). Statement one alone is not sufficient.

Statement Two Alone:

Since we don’t know the actual amount spent on any of the 3 books, statement two alone does not allow us to determine whether the total amount spent is less than $48 or not.

Statements One and Two Alone:

With the two statements, let’s assume that the most expensive book is $17 (even though we know it’s less than $17). Let’s also assume the second most expensive book is also $17 and hence the least expensive book is $14. If this is the case, the total amount spent on the 3 books would be exactly 17 + 17 + 14 = $48. However, since we know the prices of the 3 books must be actually less than $17, $17, and $14, respectively, then the total spent is indeed less than $48.

Answer: C