Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 20 Sep 2007
Posts: 106

Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
09 Jul 2008, 22:04
2
This post received KUDOS
17
This post was BOOKMARKED
Question Stats:
53% (01:32) correct 47% (01:20) wrong based on 453 sessions
HideShow timer Statistics
Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each. If Juan bought more than 10 paperback books, how many hardcover books did he buy? (1) The total cost of hardcover books that Juan bought was at least $150 (2) The total cost of all books that Juan bought was less than $260
Official Answer and Stats are available only to registered users. Register/ Login.
Last edited by Bunuel on 29 Jun 2013, 06:13, edited 1 time in total.
Edited the question, added the OA and moved to DS forum.



Director
Joined: 27 May 2008
Posts: 539

Re: Juan bought some books ,Gmat prep question [#permalink]
Show Tags
09 Jul 2008, 22:25
It should be E
I dont know if this is thr ight approach
let say Juan baught 11 paperback books = 11*8 = 88
statement 1 : minmium cost of hardcover books = 15088 = 62 x is the number of hardcover books x > 2 . Not suff
statement 2: max cost of hardcover books = 26088 = 172 x < 7 not suff
combine .... 2 < x < 7 ... not suff



VP
Joined: 03 Apr 2007
Posts: 1287

Re: Juan bought some books ,Gmat prep question [#permalink]
Show Tags
09 Jul 2008, 23:49
durgesh79 wrote: It should be E
I dont know if this is thr ight approach
let say Juan baught 11 paperback books = 11*8 = 88
statement 1 : minmium cost of hardcover books = 15088 = 62 x is the number of hardcover books x > 2 . Not suff
statement 2: max cost of hardcover books = 26088 = 172 x < 7 not suff
combine .... 2 < x < 7 ... not suff 1.25h>=150 NS 2.8p+25h<260 NS from 1 and 2 we cannot get exact value for p E



GMAT Instructor
Joined: 04 Jul 2006
Posts: 1254
Location: Madrid

Re: Juan bought some books ,Gmat prep question [#permalink]
Show Tags
10 Jul 2008, 00:27
13
This post received KUDOS
3
This post was BOOKMARKED
Juan bought some paperback books that cost $8 each and some hard cover books that cost $25 each. If Juan bought more than 10 paperback books , how many hardcover books did he buy.
1 The total cost of hardcover books that Juan bought was atleast 150$ He bought more than 6 hardcover books. NOT SUFF 2 The total cost of all the books that Juan bought was less than $260 He spent at least $88 on paperback books, and thus less than 260  88 = $172 on hardcover books. This tells us he bought at most 6 hardover books
Together, we know he bought exactly 6 hardcover books. SUFF



VP
Joined: 03 Apr 2007
Posts: 1287

Re: Juan bought some books ,Gmat prep question [#permalink]
Show Tags
10 Jul 2008, 09:04
1
This post received KUDOS
goalsnr wrote: durgesh79 wrote: It should be E
I dont know if this is thr ight approach
let say Juan baught 11 paperback books = 11*8 = 88
statement 1 : minmium cost of hardcover books = 15088 = 62 x is the number of hardcover books x > 2 . Not suff
statement 2: max cost of hardcover books = 26088 = 172 x < 7 not suff
combine .... 2 < x < 7 ... not suff 1.25h>=150 NS 2.8p+25h<260 NS from 1 and 2 we cannot get exact value for p E We can't find the exact value for P but we can find teh value for H If H >6 and P =11 the total cost exceeds 260 But if we have h =6 but have p= 11 or p=12 we can still remain within the total cost of 260 Agree C .



Senior Manager
Joined: 29 Jan 2011
Posts: 332

Re: Juan bought some books ,Gmat prep question [#permalink]
Show Tags
18 Jul 2011, 02:31
kevincan wrote: Juan bought some paperback books that cost $8 each and some hard cover books that cost $25 each. If Juan bought more than 10 paperback books , how many hardcover books did he buy.
1 The total cost of hardcover books that Juan bought was atleast 150$ He bought more than 6 hardcover books. NOT SUFF 2 The total cost of all the books that Juan bought was less than $260 He spent at least $88 on paperback books, and thus less than 260  88 = $172 on hardcover books. This tells us he bought at most 6 hardover books
Together, we know he bought exactly 6 hardcover books. SUFF I agree with 1 but in stmt 2 : How do we get 88 ? Juan bought atleast 10 paperback books so it has to 80 ...Next the total cost is less than 260 ..Lets say total cost is 100 .. Then 100  80 = 20 ...So juan bought 0 hard cover books... Combined do we get the answer still 6 here ???



Intern
Joined: 03 Mar 2011
Posts: 17
WE: Sales (Hospitality and Tourism)

Re: Juan bought some books ,Gmat prep question [#permalink]
Show Tags
18 Jul 2011, 11:45
Siddhans, the question states that Juan bought "more than 10 paper books" and not atleast 10. Also didnt quite get how you arrived that the total cost is 100 . Its told that the total cost is less than 260, given your way of working the total cost could also equal to 259, which leads to the right answer



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7997
Location: Pune, India

Re: Juan bought some books ,Gmat prep question [#permalink]
Show Tags
18 Jul 2011, 22:18
siddhans wrote: kevincan wrote: Juan bought some paperback books that cost $8 each and some hard cover books that cost $25 each. If Juan bought more than 10 paperback books , how many hardcover books did he buy.
1 The total cost of hardcover books that Juan bought was atleast 150$ He bought more than 6 hardcover books. NOT SUFF 2 The total cost of all the books that Juan bought was less than $260 He spent at least $88 on paperback books, and thus less than 260  88 = $172 on hardcover books. This tells us he bought at most 6 hardover books
Together, we know he bought exactly 6 hardcover books. SUFF I agree with 1 but in stmt 2 : How do we get 88 ? Juan bought atleast 10 paperback books so it has to 80 ...Next the total cost is less than 260 ..Lets say total cost is 100 .. Then 100  80 = 20 ...So juan bought 0 hard cover books... Combined do we get the answer still 6 here ??? As pointed out by esbee above, Juan bought more than 10 paperback books so he must have bought at least 11 paperbacks. This means he must have spent at least $88 on the paperbacks. Statement 2 alone is not sufficient. All it tells us is that he spent less than $260. This means he spent less than $260  $88 = $172 on hardcover books. He could have spent $88 + $50 = $138 OR $98 + $100 = $198 OR some other combination. We do not know how many hardcover books he bought but we do know that he could not have bought more than 6 since for 7 (or more) hardcover books, he would need $25*7 = $175 (or more). But he spent less than $172 on hardcover books. So he bought at most 6 hardcover books. Using both statements together, statement 1 says that he bought at least 6 hardcover books and statement 2 says he bought at most 6 hardcover books. What does this mean? This means he must have bought exactly 6 hardcover books.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Director
Joined: 29 Nov 2012
Posts: 849

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
29 Jun 2013, 06:05
Great discussion just to point out when combined it can't be 7 books because the cost will be 263 so that's above the the required condition.
_________________
Click +1 Kudos if my post helped...
Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/
GMAT Prep software What if scenarios http://gmatclub.com/forum/gmatprepsoftwareanalysisandwhatifscenarios146146.html



Intern
Joined: 14 Jan 2012
Posts: 14
GMAT 1: 600 Q45 V28 GMAT 2: 700 Q48 V38

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
11 Sep 2013, 06:40
HI CAN SOMEONE PLEASE EXPLAIN WHY ADDING INEQUALITIES DOES NOT WORK IN THIS QUESTION
let the quantity of hardcover books be H and paperback P
Statement 1 25H is greater than or equal to 150 therefore H is greater than or equal to 6 Insufficient.
Statement 2
8(P)+25(H) < 260 AND 10< P
MULTIPLYING BY 8 AND ADDING IF WE SOLVE
H is less than 7.2 insuff
Statement 1 and 2 (H must be an integer)
and greater than or equal to 6,
therefore H can be 6 or 7.
E..I can't wrap around my head how this approach can be wrong? OA: C



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7997
Location: Pune, India

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
11 Sep 2013, 21:43
GMAT98 wrote: HI CAN SOMEONE PLEASE EXPLAIN WHY ADDING INEQUALITIES DOES NOT WORK IN THIS QUESTION
let the quantity of hardcover books be H and paperback P
Statement 1 25H is greater than or equal to 150 therefore H is greater than or equal to 6 Insufficient.
Statement 2
8(P)+25(H) < 260 AND 10< P
MULTIPLYING BY 8 AND ADDING IF WE SOLVE
H is less than 7.2 insuff
Statement 1 and 2 (H must be an integer)
and greater than or equal to 6,
therefore H can be 6 or 7.
E..I can't wrap around my head how this approach can be wrong? OA: C Because the inequality 10 < P does not include all the information you have available. You know that P cannot be 10.5 i.e. a decimal. It must be an integer since it represents the number of paperbacks. So you might want to use 11<= P to get a tighter value for H. 8P + 25H < 260 88 <= 8P When you add, you get 25H < 172 i.e. H < 6.9 All in all, algebra will always give you the correct result; but it may not be sufficient if you don't use reasoning as well. You got that H is less than 7.2 which is correct but it was not enough.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 14 Jan 2012
Posts: 14
GMAT 1: 600 Q45 V28 GMAT 2: 700 Q48 V38

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
11 Sep 2013, 21:54
VeritasPrepKarishma wrote: GMAT98 wrote: HI CAN SOMEONE PLEASE EXPLAIN WHY ADDING INEQUALITIES DOES NOT WORK IN THIS QUESTION
let the quantity of hardcover books be H and paperback P
Statement 1 25H is greater than or equal to 150 therefore H is greater than or equal to 6 Insufficient.
Statement 2
8(P)+25(H) < 260 AND 10< P
MULTIPLYING BY 8 AND ADDING IF WE SOLVE
H is less than 7.2 insuff
Statement 1 and 2 (H must be an integer)
and greater than or equal to 6,
therefore H can be 6 or 7.
E..I can't wrap around my head how this approach can be wrong? OA: C Because the inequality 10 < P does not include all the information you have available. You know that P cannot be 10.5 i.e. a decimal. It must be an integer since it represents the number of paperbacks. So you might want to use 11<= P to get a tighter value for H. 8P + 25H < 260 88 <= 8P When you add, you get 25H < 172 i.e. H < 6.9 All in all, algebra will always give you the correct result; but it may not be sufficient if you don't use reasoning as well. You got that H is less than 7.2 which is correct but it was not enough. ok..i got it. I should have applied hidden constraint. Thanks for prompt reply.



Current Student
Joined: 06 Sep 2013
Posts: 1948
Concentration: Finance

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
18 Feb 2014, 18:06
Statement 1 alone only tells us that H>=6.
Statement 2 tells us that the total cost that is 25H + 8P<260, which together with P>=11 is not sufficient.
Both statements together tell us that H has to be 6. Given that P is the minimum possible value = 11, if H were 7 then total cost >260 and violate statement 2. Therefore C stands.
Hope this helps Cheers J



Manager
Joined: 18 May 2014
Posts: 61
Location: United States
Concentration: General Management, Other
GMAT Date: 07312014
GPA: 3.99
WE: Analyst (Consulting)

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
18 May 2014, 10:40
1
This post received KUDOS
Statement 1: Juan spent at least $150 on Hardcovers. So that means he bought at least 6 harcovers. We have no upside limit though.
Insufficient.
Statement 2: Juan spent less than $260 total on books. This tells us at most that Juan spent $259  $88 (minimum amount possible spent on paperbacks) = $171 maximum on hardcovers. 171 divided by 25 is 6 and change. So round down. The maximum number of harcovers that could be purchased is 6. This statement could also be true with any number of hardcovers below six being purchased. For example, 0 hardcovers + 12 paperbacks = $96, which is less than $260.
Insufficient.
Together:
Looking at Statement 1, we know that at least 6 hardcovers had to be purchased. Looking at Statement 2, we know that no more than 6 hardcovers could be purchased. So Juan must have purchased 6 hardcovers.



Senior Manager
Joined: 15 Aug 2013
Posts: 288

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
30 Aug 2014, 10:22
VeritasPrepKarishma wrote: siddhans wrote: kevincan wrote: Juan bought some paperback books that cost $8 each and some hard cover books that cost $25 each. If Juan bought more than 10 paperback books , how many hardcover books did he buy.
1 The total cost of hardcover books that Juan bought was atleast 150$ He bought more than 6 hardcover books. NOT SUFF 2 The total cost of all the books that Juan bought was less than $260 He spent at least $88 on paperback books, and thus less than 260  88 = $172 on hardcover books. This tells us he bought at most 6 hardover books
Together, we know he bought exactly 6 hardcover books. SUFF I agree with 1 but in stmt 2 : How do we get 88 ? Juan bought atleast 10 paperback books so it has to 80 ...Next the total cost is less than 260 ..Lets say total cost is 100 .. Then 100  80 = 20 ...So juan bought 0 hard cover books... Combined do we get the answer still 6 here ??? As pointed out by esbee above, Juan bought more than 10 paperback books so he must have bought at least 11 paperbacks. This means he must have spent at least $88 on the paperbacks. Statement 2 alone is not sufficient. All it tells us is that he spent less than $260. This means he spent less than $260  $88 = $172 on hardcover books. He could have spent $88 + $50 = $138 OR $98 + $100 = $198 OR some other combination. We do not know how many hardcover books he bought but we do know that he could not have bought more than 6 since for 7 (or more) hardcover books, he would need $25*7 = $175 (or more). But he spent less than $172 on hardcover books. So he bought at most 6 hardcover books. Using both statements together, statement 1 says that he bought at least 6 hardcover books and statement 2 says he bought at most 6 hardcover books. What does this mean? This means he must have bought exactly 6 hardcover books. Hi Karishma, These exact type of problems give me a lot of trouble but I'm definitely getting better at them. I just get overwhelmed with information despite making charts etc and before I know it, it's 3+ minutes in and i'm stuck! What a complete waste of time. Do you have a post that tackles on how to deal with these problems, perhaps algebraically. Looking at the solution posted above, I can see how you came to the actual answer. That's never my problem. I can always FOLLOW the work, but for some reason, I can't start it myself. How do I fix this? For this problem, I created a table but it ended up in shambles. Would really appreciate your help here. Statement 1/2 insufficient solo. I'm always skeptical of C so I guessed E at the end of 3 minutes, like I said, horrible waste of time. My equations were as such. Statement 1: (x=# of hc books)(25) < 150 Statement 2: (x)(25) + (11)(8)<260 I tried to see what value will make statement 2 valid. I noticed that 8(whatever number) has to end in a 0 to make this valid and it has to be greater than 88, so I had 120 and 160. That made x only valid if the other value was 160, therefore, x had to 4. This is completely off than the explanation above. Where did I go wrong?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7997
Location: Pune, India

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
03 Sep 2014, 01:26
russ9 wrote: Hi Karishma,
These exact type of problems give me a lot of trouble but I'm definitely getting better at them. I just get overwhelmed with information despite making charts etc and before I know it, it's 3+ minutes in and i'm stuck! What a complete waste of time.
Do you have a post that tackles on how to deal with these problems, perhaps algebraically.
Looking at the solution posted above, I can see how you came to the actual answer. That's never my problem. I can always FOLLOW the work, but for some reason, I can't start it myself. How do I fix this?
For this problem, I created a table but it ended up in shambles. Would really appreciate your help here.
Statement 1/2 insufficient solo. I'm always skeptical of C so I guessed E at the end of 3 minutes, like I said, horrible waste of time. My equations were as such.
Statement 1: (x=# of hc books)(25) < 150 Statement 2: (x)(25) + (11)(8)<260
I tried to see what value will make statement 2 valid. I noticed that 8(whatever number) has to end in a 0 to make this valid and it has to be greater than 88, so I had 120 and 160.
That made x only valid if the other value was 160, therefore, x had to 4. This is completely off than the explanation above. Where did I go wrong? I have discussed this here: http://www.veritasprep.com/blog/2013/09 ... ctanswer/
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Status: preparing
Joined: 30 Dec 2013
Posts: 41
Location: United Arab Emirates
Concentration: Technology, Entrepreneurship
GMAT 1: 660 Q45 V35 GMAT 2: 640 Q49 V28 GMAT 3: 640 Q49 V28 GMAT 4: 640 Q49 V28 GMAT 5: 640 Q49 V28
GPA: 2.84
WE: General Management (Consumer Products)

Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
19 Sep 2014, 02:54
1
This post received KUDOS
neeraj.kaushal wrote: Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each. If Juan bought more than 10 paperback books, how many hardcover books did he buy?
(1) The total cost of hardcover books that Juan bought was at least $150 (2) The total cost of all books that Juan bought was less than $260 1) 25h>=150 Sol : h>=150/25 => h>=6 it can be from 6 to +infinite. not a definite answer. so, NOT SUFFICIENT ALONE. 2) 8 p + 25 h < 260 sol: its been mentioned that p>10. lets say that she bought only one hardcover, h=1, makes p=29 but "p" can be any number from 11 to 29 (price of p=8*11=88 to 8*29=232) : (lets say that she bought only one hardcover, h=1, makes p=29) depending upon "p", value of "h" can vary from 1>6 (since p>10, so if p=11, h=6) so this again is NOT SUFFICIENT ALONE. NOW LETS TAKE BOTH statements 1 and 2: 1) h>=6 2)1<= h <=6 so h=6." C " is the answer



Manager
Joined: 01 Aug 2014
Posts: 54

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
18 Feb 2016, 08:33
8$/Pb; 25$/Hb. Juan bought > 10*8 & Hb = ? 1) 25*Hb >= 150 Hb >= 6 Not sufficient. 2) (10+n)*8 + 25*Hb < 260 Not sufficient. 1) & 2) Hb = 6 <=>n = 13 Yes; Hb = 7 <> n = 0 No Answer C.



Director
Joined: 26 Oct 2016
Posts: 682
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
05 Feb 2017, 00:44
From Stem : Price Paperback = $ 8 Price Hardcover = $ 25 , Number paperback >10 , P = { 11, 12, ....} P and H are integers St1> 25* Number Hardcover >=150 Number Hardcover > =6 Then , H = { 6, 7, ....} Since question requires a unique value, INSUFFICIENT St2> 8P + 25H < 260 Since Greatest Common Factor of { 8, 25, 260} is different from 1, More than one solution , INSUFFICIENT From St1 and St2 > While P and H can only be integers Plug the minimmum values for H and P at 8P + 25H < 260, Eg. ( P, H ) at 8P + 25H < 260, ( 11, 6 ) , 238 < 260, VALID ( 11, 7 ) 263 < 260, WRONG ( 12, 7 ) 271 < 260, WRONG From this point, all other combinations will NOT comply the inequality. Then , there is a unique value for H = 6 answer = C To find the GCF of two numbers: 1) List the prime factors of each number. 2) Multiply those factors both numbers have in common. If there are no common prime factors, the GCF is 1.
_________________
Thanks & Regards, Anaira Mitch



Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 2319
Location: United States (CA)

Re: Juan bought some paperback books that cost $8 each and some [#permalink]
Show Tags
05 Dec 2017, 19:22
neeraj.kaushal wrote: Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each. If Juan bought more than 10 paperback books, how many hardcover books did he buy?
(1) The total cost of hardcover books that Juan bought was at least $150 (2) The total cost of all books that Juan bought was less than $260 We are given that Juan bought some paperback books that cost $8 each and some hardcover books that cost $25 each, and that he bought more than 10 paperback books. If we let p = the number of paperback books Juan bought and h = the number of hardcover books, the total cost of the paperback books is 8p, the total cost of the hardcover books is 25h, and the total cost of all books is 8p + 25h. We need to determine the value of h, the number of hardcover books purchased by Juan. Statement One Alone: The total cost of the hardcover books that Juan bought was at least $150. Using the information in statement one, we can create the following inequality: 25h ≥ 150 h ≥ 6 Thus, at least 6 hardcover books were purchased. However, we cannot determine the exact number of hardcover books purchased by Juan. Statement one alone is not sufficient to answer the question. We can eliminate answer choices A and D. Statement Two Alone: The total cost of all the books that Juan bought was less than $260. Using the information in statement two, we can create the following inequality: 8p + 25h ≤ 260 We still do not have enough information to determine how many hardcover books were purchased by Juan. Statements One and Two Together: From the given information as well as our two statements, we know that p > 10, h ≥ 6, and that 8p + 25h ≤ 260. Since p > 10, Juan, at minimum, purchased 11 paperback books. If we use 11 for p in the inequality 8p + 25h ≤ 260, then we have: 88 + 25h ≤ 260 25h ≤ 172 h ≤ 6 22/25 Recall that h ≥ 6, and since h has to be a whole number, Juan must have purchased 6 hardcover books. Answer: C
_________________
Scott WoodburyStewart
Founder and CEO
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions




Re: Juan bought some paperback books that cost $8 each and some
[#permalink]
05 Dec 2017, 19:22






