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


(DS13949)
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C
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Is the sum of the prices of the 3 books that Shana bought less than $4 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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Is the sum of the prices of the 3 books that Shana bought less than $4 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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Is the sum of the prices of the 3 books that Shana bought less than $4 23 Jun 2018, 06:39
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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.

Show more

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 08 Nov 2018, 08:49
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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.
Show more

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 Updated on: 22 Dec 2020, 14:47
Originally posted by MHIKER on 23 Sep 2020, 13:13.
Last edited by MHIKER on 22 Dec 2020, 14:47, edited 1 time in total.
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Bunuel
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.



NEW question from GMAT® Official Guide 2019


(DS13949)
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1) The most expensive is B<17 so the total could 48 or less than 48; Insufficient.

2) The most expensive could be any value so insufficient.

Both:
If the most expensive can be maximum 16, the second-highest price can be 15 then the third on will 12; The maximum price will be 43. Even in case of extreme values such as 16.9, 15.9 and 12.9 the less than \(48\). Sufficient.

Ans C.
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Is the sum of the prices of the 3 books that Shana bought less than $4 19 Dec 2020, 16:33
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Video solution from Quant Reasoning:
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Is the sum of the prices of the 3 books that Shana bought less than $4 12 May 2021, 09:06
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Bunuel
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.



NEW question from GMAT® Official Guide 2019


(DS13949)
Show more
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
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Is the sum of the prices of the 3 books that Shana bought less than $4 22 May 2021, 00:51
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Bunuel
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.
Show more


Answer: Option C

Video solution by GMATinsight

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Is the sum of the prices of the 3 books that Shana bought less than $4 02 Sep 2021, 09:21
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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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Is the sum of the prices of the 3 books that Shana bought less than $4 04 May 2022, 21:47
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How do you know B<C? we just know most expensive book costs a certain amount. WHy can't second most expensive book be same price as most expensive? ScottTargetTestPrep BrentGMATPrepNow KarishmaB


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Bunuel
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 05 May 2022, 05:35
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ag153
How do you know B<C? we just know most expensive book costs a certain amount. WHy can't second most expensive book be same price as most expensive? ScottTargetTestPrep BrentGMATPrepNow KarishmaB
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If the prices of books A, B and C were something like $4, $7, and $7 respectively, I suppose we could still say book C is the most expensive book.
Fortunately, the issue doesn't really come into play for this question.
That is, even if we allow for A ≤ B ≤ C, the correct answer is still C.
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Is the sum of the prices of the 3 books that Shana bought less than $4 05 May 2022, 08:16
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I know it will not affect but I am trying to understand what would it be if it were testing us on this concept let's say. Why do we assume that they are necessarily lesser than each other? How does gmat treat the case to be?

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ag153
How do you know B<C? we just know most expensive book costs a certain amount. WHy can't second most expensive book be same price as most expensive? ScottTargetTestPrep BrentGMATPrepNow KarishmaB

If the prices of books A, B and C were something like $4, $7, and $7 respectively, I suppose we could still say book C is the most expensive book.
Fortunately, the issue doesn't really come into play for this question.
That is, even if we allow for A ≤ B ≤ C, the correct answer is still C.
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Is the sum of the prices of the 3 books that Shana bought less than $4 05 May 2022, 08:52
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ag153
I know it will not affect but I am trying to understand what would it be if it were testing us on this concept let's say. Why do we assume that they are necessarily lesser than each other? How does gmat treat the case to be?
Show more

I checked the official solution, and the test makers begin by writing: \(B_1 ≤ B_2 ≤ B_3\).
Later in their solution, when combining both statements, they write the following:


So, it looks like they're allowing for the possibility that \(B_2 = B_3\)
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Is the sum of the prices of the 3 books that Shana bought less than $4 05 May 2022, 12:23
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Awesome thanks for sharing.
Also how would the “second most expensive” in the statement 2 affect the whole situation? I mean it could be that as per statemtn1 they can all be equated but not as per statement 2 since B2 is “second most expensive” which means it has to be lesser expensive than b3. Pls clarify BrentGMATPrepNow


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ag153
I know it will not affect but I am trying to understand what would it be if it were testing us on this concept let's say. Why do we assume that they are necessarily lesser than each other? How does gmat treat the case to be?

I checked the official solution, and the test makers begin by writing: \(B_1 ≤ B_2 ≤ B_3\).
Later in their solution, when combining both statements, they write the following:


So, it looks like they're allowing for the possibility that \(B_2 = B_3\)
Show more

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Is the sum of the prices of the 3 books that Shana bought less than $4 29 Oct 2023, 07:37
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Bunuel
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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Hi,
This solution really helped! Esp the 'maximising' logic in the end.
Btw, I think there is a typo here-
'Since A is $3 less than B, greatest possible value of A = $12.98'
Should be $13.98, thus $47.95
The inferences remain the same though.
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rushimehta
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Is the sum of the prices of the 3 books that Shana bought less than $4 09 Nov 2025, 02:13
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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
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chetan2u karishma Bunuel

I followed the same approach - one quic query - In cases where the question doesn't explictly mention that the values are different, we can take 2 or more values to be the same right ? As in this case we take the cost of second most expensive book to be the same as the most expensive book.
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Is the sum of the prices of the 3 books that Shana bought less than $4 09 Nov 2025, 10:08
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Yes, even if the variables are different say x and y, they can be same. Check them for fractions, negative and positive, zero etc unless specified.
rushimehta


chetan2u karishma Bunuel

I followed the same approach - one quic query - In cases where the question doesn't explictly mention that the values are different, we can take 2 or more values to be the same right ? As in this case we take the cost of second most expensive book to be the same as the most expensive book.
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