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# Is the sum of the prices of the 3 books that Shana bought less than $4 SORT BY: Tags: Show Tags Hide Tags Math Expert Joined: 02 Sep 2009 Posts: 95462 Own Kudos [?]: 657810 [105] Given Kudos: 87247 Most Helpful Reply RC & DI Moderator Joined: 02 Aug 2009 Status:Math and DI Expert Posts: 11512 Own Kudos [?]: 35949 [37] Given Kudos: 333 e-GMAT Representative Joined: 04 Jan 2015 Posts: 3709 Own Kudos [?]: 17735 [22] Given Kudos: 165 General Discussion GMAT Club Legend Joined: 12 Sep 2015 Posts: 6803 Own Kudos [?]: 31276 [5] Given Kudos: 799 Location: Canada Re: Is the sum of the prices of the 3 books that Shana bought less than$4 [#permalink]
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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

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

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

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Re: Is the sum of the prices of the 3 books that Shana bought less than $4 [#permalink] 1 Kudos Top Contributor 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)

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.

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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Re: Is the sum of the prices of the 3 books that Shana bought less than $4 [#permalink] 3 Kudos 2 Bookmarks Expert Reply Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 Target Test Prep Representative Joined: 14 Oct 2015 Status:Founder & CEO Affiliations: Target Test Prep Posts: 19444 Own Kudos [?]: 23196 [2] Given Kudos: 286 Location: United States (CA) Re: Is the sum of the prices of the 3 books that Shana bought less than$4 [#permalink]
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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) 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 GMAT Club Legend Joined: 08 Jul 2010 Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator Posts: 6065 Own Kudos [?]: 14123 [1] Given Kudos: 125 Location: India GMAT: QUANT+DI EXPERT Schools: IIM (A) ISB '24 GMAT 1: 750 Q51 V41 WE:Education (Education) Re: Is the sum of the prices of the 3 books that Shana bought less than$4 [#permalink]
1
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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) Wanna make solving the Official Questions interesting??? Click here and solve 1000+ Official Questions with Video solutions as Timed Sectional Tests and Dedicated Data Sufficiency (DS) Course Answer: Option C Video solution by GMATinsight Get TOPICWISE: Concept Videos | Practice Qns 100+ | Official Qns 50+ | 100% Video solution CLICK HERE. Two MUST join YouTube channels : GMATinsight (1000+ FREE Videos) and GMATclub Intern Joined: 01 Jun 2021 Posts: 2 Own Kudos [?]: 0 [0] Given Kudos: 1 Re: Is the sum of the prices of the 3 books that Shana bought less than$4 [#permalink]
chetan2u
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) Posted from my mobile device Manager Joined: 16 Feb 2017 Posts: 89 Own Kudos [?]: 46 [0] Given Kudos: 56 Location: India Concentration: Finance, Strategy GPA: 3.69 Re: Is the sum of the prices of the 3 books that Shana bought less than$4 [#permalink]
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

BrentGMATPrepNow
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

Cheers,
Brent
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Re: Is the sum of the prices of the 3 books that Shana bought less than $4 [#permalink] 1 Kudos Expert Reply Top Contributor 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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Re: Is the sum of the prices of the 3 books that Shana bought less than $4 [#permalink] 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? BrentGMATPrepNow 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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Re: Is the sum of the prices of the 3 books that Shana bought less than $4 [#permalink] 1 Kudos Expert Reply Top Contributor 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 $$B_2 = B_3$$ Manager Joined: 16 Feb 2017 Posts: 89 Own Kudos [?]: 46 [0] Given Kudos: 56 Location: India Concentration: Finance, Strategy GPA: 3.69 Re: Is the sum of the prices of the 3 books that Shana bought less than$4 [#permalink]
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

BrentGMATPrepNow
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 $$B_2 = B_3$$

Posted from my mobile device
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Re: Is the sum of the prices of the 3 books that Shana bought less than $4 [#permalink] BrentGMATPrepNow 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 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. Re: Is the sum of the prices of the 3 books that Shana bought less than$4 [#permalink]
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