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Question Stats: 63% (01:43) correct 37% (01:32) wrong based on 984 sessions

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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.

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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$17.
The price could be 16.99$, then the price of three books could be between 59 and 51..so NO not <48 If the price is 15$ each, total =45, so yes <48
Insufficient

(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. Nothing about the actual cost.. Insufficient.. Combined Let's see the max possible cost.. Least expensive ~17-13 =~14, slightly less than 14 Let the other two be same so ~17.. So total can be just less than 17+17+14=48.. So just less than 48.. Thus always <48 Sufficient C NEW question from GMAT® Official Guide 2019 (DS13949) _________________ e-GMAT Representative V Joined: 04 Jan 2015 Posts: 3230 Re: Is the sum of the prices of the 3 books that Shana bought less than$4  [#permalink]

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Solution

To find:
• Whether the sum of the prices of the 3 books that Shana bought less than $48 Analysing Statement 1 • As per the information given in statement 1, the price of the most expensive book that Shana bought is less than$17

There are 3 possible scenarios in this case:
Case 1: when the sum of the prices is greater than $48 • Example: if the books are priced at$16.x, $16.y, and$16.z, where all x, y, and z are positive integers

Case 2: when the sum of the prices is equal to $48 • Example: if the books are priced at$16.5, $16, and$15.5

Case 3: when the sum of the prices is less than $48 • Example: if all the books are priced at less than$16

As there are multiple possible cases exist, which satisfy the given condition in statement 1, we cannot conclude whether the sum of the prices of 3 books that Shana bought is less than $48 or not Hence, statement 1 is not sufficient to answer the question Analysing Statement 2 • As per the information given in 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
o The two least expensive books can have any price, with a gap of $3 o Moreover, no information was given about the most expensive book’s price Hence, statement 2 is not sufficient to answer the question Combining Both Statements If we combine both the statements, we can say: • The most expensive book costs less than$17
• The least expensive book costs $3 less than the second most expensive book As the most expensive book costs less than$17, we can say
• The second most expensive book will cost less than $17 • The least expensive book will definitely cost less than (17 – 3) =$14

Therefore, the possible sum of prices of all the books = (less than $17 + less than$17 + less than $14) = less than$48

Hence, the correct answer is option C.

_________________
##### General Discussion
GMAT Club Legend  V
Joined: 12 Sep 2015
Posts: 4228
Re: Is the sum of the prices of the 3 books that Shana bought less than $4 [#permalink] ### Show Tags 1 Top Contributor 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$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 _________________ Manager  P Joined: 14 Apr 2017 Posts: 70 Location: Hungary GMAT 1: 760 Q50 V42 WE: Education (Education) Is the sum of the prices of the 3 books that Shana bought less than$4  [#permalink]

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1
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. Let $$x_1, x_2, x_3$$ be the prices in increasing order and let $$S$$ be the sum of the prices. The original question: Is $$S<48$$ ? 1) Using that $$x_3<17$$, we can determine an upper bound for $$S$$. $$S\leq 3x_3<51$$ $$S<51$$ We can't get a definite answer to the original question. $$\implies$$ Insufficient 2) We know that $$x_1=x_2-3$$, but no information is given about $$x_3$$. Thus, we can't get a definite answer to the original question. $$\implies$$ Insufficient 1&2) Using all statement information, we can determine an upper bound for $$S$$. $$S\leq x_3-3+x_3+x_3$$ $$S\leq 3x_3-3<48$$ $$S<48$$ Thus, the answer to the original question is a definite Yes. $$\implies$$ Sufficient Answer: C _________________ My book with my solutions to all 230 PS questions in OG2018: Zoltan's solutions to OG2018 PS Non-Human User Joined: 09 Sep 2013 Posts: 14012 Re: Is the sum of the prices of the 3 books that Shana bought less than$4  [#permalink]

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_________________ Re: Is the sum of the prices of the 3 books that Shana bought less than $4 [#permalink] 20 Nov 2019, 00:39 Display posts from previous: Sort by # Is the sum of the prices of the 3 books that Shana bought less than$4  