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Is the sum of the prices of the 3 books that Shana bought less than $4

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Is the sum of the prices of the 3 books that Shana bought less than $4  [#permalink]

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New post 22 Jun 2018, 02:04
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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.
(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.



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Re: Is the sum of the prices of the 3 books that Shana bought less than $4  [#permalink]

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New post 22 Jun 2018, 03:20
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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


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Re: Is the sum of the prices of the 3 books that Shana bought less than $4  [#permalink]

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New post 22 Jun 2018, 06:30
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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.

Answer: C
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Re: Is the sum of the prices of the 3 books that Shana bought less than $4  [#permalink]

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New post 23 Jun 2018, 06:39
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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
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Is the sum of the prices of the 3 books that Shana bought less than $4  [#permalink]

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New post 08 Nov 2018, 08:49
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
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Is the sum of the prices of the 3 books that Shana bought less than $4   [#permalink] 08 Nov 2018, 08:49
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