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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## (OG-12 DS) Joanna... tagged by: Brent@GMATPrepNow ##### This topic has 1 expert reply and 11 member replies Joanna bought only$0.15 stamps and $0.29 stamps.How many$0.15 stamps did she buy?

(1) She bought $4.40 worth of stamps. (2) She bought an equal number of$0.15 stamps and $0.29 stamps. OG has a weird explanation for this one. Can someone give a simpler one? Thanks.. Legendary Member Joined 16 Oct 2011 Posted: 588 messages Followed by: 9 members Upvotes: 130 Test Date: 3rd May '12 Target GMAT Score: 750+ GMAT Score: 720 No of$0.15 stamps=x
No of $0.29 stamps=y Quote: (1) She bought$4.40 worth of stamps.
0.15x + 0.29y = 4.4

Not Sufficient

Quote:
(2) She bought an equal number of $0.15 stamps and$0.29 stamps.
x = y

still not sufficient

Combining the two statements

0.15x + 0.29x = 4.4

Find the value of x

Option C

Senior | Next Rank: 100 Posts Joined
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2 @rijul007

yeah, that's what I did, however that's incorrect!

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opss in st(2) there's a small nuance

though found in OG-12 it comes from old OGs till now

the question to find integer value of quantity for $0.15 priced stamps bought. let$0.15 priced stamps' quantity be A and $0.29 priced ones' be B, then 0.15A+0.29B=Cost of stamps and we need to find A? st(1) implies Cost Joanna paid was 4.40 and we assume buying B number of$0.29 priced stamps - we must find the possible integer value of B, if any. For this we assign two binomials 0.29B+0.15A=4.40 and assess the values of A and B. If we succeed to find the unique values for A and B, then st(1) is Sufficient, otherwise Not.
B=1 -> 29+15A=440 AND A=(440-29)/15 Not Integer(NI)
B=2 -> 58+15A=440 AND A=(440-58)/15 NI
...
we can use common sense as a number is divisible by 5 if it ends by 0 or 5, and (440-29B) will end in 5 or 0 only if B=5,10,15
B=5, 145+15A=440, A=295/15 NI
B=10, 290+15A=440, A=150/15 good choice
B=15, 435+15A=440, A=5/15 NI

hence we have one unique set when A=10 and B=10 and can answer the question, Sufficient.
check: 0.29*10+0.15*10=4.40

st(2) A=B and we need to know the Cost which is in st(1) only (15A+29B=440 OR 44A=440, A=10) therefore st(2) Alone is Not Sufficient

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Last edited by pemdas on Fri Dec 23, 2011 8:11 am; edited 2 times in total

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Elena89 wrote:
@rijul007

yeah, that's what I did, however that's incorrect!
ok so its not as easy as it seemed

Statement 1

0.15x + 0.29y = 4.4
or
15x + 29y = 440

Y = 1
15x = 440-29 (not divisible by 15)

y = 5
15x = 440 - 145 (ot divisible by 15)

y = 10

15x = 450 - 290 = 150
x = 10

y = 15 = 145 + 290 = 435

15x = 440 - 29*15 = 440-435
[not divisible by 15]

so no of $0.15 stamps = 10 Sufficient Option A Senior | Next Rank: 100 Posts Joined 31 Jul 2011 Posted: 35 messages Followed by: 1 members Upvotes: 2 @pemdas Wrong! The OA is 'A' What I do not understand is how we can find the value of one unknown from only one equation. What I do understand from OG's explanation is that since both unknowns are 'integers'(whole numbers) therefore from the properties of integer constraints, only one value of any of the 2 unknowns is obtainable! and so the first is sufficient. Legendary Member Joined 15 Apr 2011 Posted: 1085 messages Followed by: 21 members Upvotes: 158 this q. shows how stupid mistakes may turn our GMAT lives into nightmares, I've mistakenly assumed that the Cost is given following st(1) Sufficient and turned D firstly. Afterwards, seen no word speaks about 4.40 Cost in st(2). Phew _________________ Success doesn't come overnight! Legendary Member Joined 15 Apr 2011 Posted: 1085 messages Followed by: 21 members Upvotes: 158 yea, just turned back and seen/corrected/explained in previous post Elena89 wrote: @pemdas Wrong! The OA is 'A' What I do not understand is how we can find the value of one unknown from only one equation. What I do understand from OG's explanation is that since both unknowns are 'integers'(whole numbers) therefore from the properties of integer constraints, only one value of any of the 2 unknowns is obtainable! and so the first is sufficient. _________________ Success doesn't come overnight! Senior | Next Rank: 100 Posts Joined 31 Jul 2011 Posted: 35 messages Followed by: 1 members Upvotes: 2 yeah, well all that is written in OG too.. but I don't think all that calculation can be done in just 2 minutes.. Legendary Member Joined 15 Apr 2011 Posted: 1085 messages Followed by: 21 members Upvotes: 158 listen, to calculate you need preset values, correct? The complexity and timeliness of your calculation depends on your values. If you start as I and riju from the detail consideration and move onto testing numbers, then yes it's over 2 mins? However, if you use your number property theory knowledge and apply divisibility by 5 for (440-29B)/15 as I put in my solution, then it's only scratch paper work you do - max. four operations to test st(1) and st(2) is automatically Not Sufficient, unless you as I stupidly follow auto-pilot approach and decide the Cost is given. Elena89 wrote: yeah, well all that is written in OG too.. but I don't think all that calculation can be done in just 2 minutes.. _________________ Success doesn't come overnight! Senior | Next Rank: 100 Posts Joined 31 Jul 2011 Posted: 35 messages Followed by: 1 members Upvotes: 2 yeah, I get that.. thanks =) Master | Next Rank: 500 Posts Joined 08 Dec 2010 Posted: 425 messages Followed by: 7 members Upvotes: 56 GMAT Score: 690 Elena89 wrote: What I do not understand is how we can find the value of one unknown from only one equation. 15x+29y=44 please pay attention to the fact, that x and y must be integers. since the result is too small (44), u should think first about 0, then about 1. so only if x=1 and y=1 we will get 44 stmnt2 is insuf. no info about the sum. all we know that x=y . so (2) is insuf ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13038 messages Followed by: 1251 members Upvotes: 5254 GMAT Score: 770 LalaB wrote: Elena89 wrote: What I do not understand is how we can find the value of one unknown from only one equation. 15x+29y=44 please pay attention to the fact, that x and y must be integers. since the result is too small (44), u should think first about 0, then about 1. so only if x=1 and y=1 we will get 44 stmnt2 is insuf. no info about the sum. all we know that x=y . so (2) is insuf This is a common trap on the GMAT. In high school, we learned that we cannot find the value of a variable if we're given 1 equation with 2 variables. However, if we restrict the variables to positive integers, then there are times when we can find the value of a variable if we're given 1 equation with 2 variables. In this question, the number of each stamp denomination must be a positive integer. I cover this common GMAT trap (and other common GMAT traps) in video #11 "Avoiding Common Mistakes - Part II." This is a free video you can find at: http://www.gmatprepnow.com/module/gmat-data-sufficiency Cheers, Brent _________________ Brent Hanneson – Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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