## (OG-12 DS) Joanna...

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### (OG-12 DS) Joanna...

by Elena89 » Fri Dec 23, 2011 6:31 am
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..

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by rijul007 » Fri Dec 23, 2011 7:00 am
No of $0.15 stamps=x No of$0.29 stamps=y
(1) She bought $4.40 worth of stamps. 0.15x + 0.29y = 4.4 Not Sufficient (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 Posts: 35 Joined: 31 Jul 2011 Thanked: 2 times Followed by:1 members by Elena89 » Fri Dec 23, 2011 7:35 am @rijul007 yeah, that's what I did, however that's incorrect! The correct answer is A Legendary Member Posts: 1085 Joined: 15 Apr 2011 Thanked: 158 times Followed by:21 members by pemdas » Fri Dec 23, 2011 8:05 am 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. start with B as prime 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 answer A Last edited by pemdas on Fri Dec 23, 2011 8:11 am, edited 2 times in total. Success doesn't come overnight! Legendary Member Posts: 588 Joined: 16 Oct 2011 Location: New Delhi, India Thanked: 130 times Followed by:9 members GMAT Score:720 by rijul007 » Fri Dec 23, 2011 8:09 am Elena89 wrote:@rijul007 yeah, that's what I did, however that's incorrect! The correct answer is A 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

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by Elena89 » Fri Dec 23, 2011 8:15 am
@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.

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by pemdas » Fri Dec 23, 2011 8:16 am
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 :twisted:
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by pemdas » Fri Dec 23, 2011 8:18 am
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.
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by Elena89 » Fri Dec 23, 2011 8:24 am
yeah, well all that is written in OG too.. but I don't think all that calculation can be done in just 2 minutes..

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by pemdas » Fri Dec 23, 2011 8:37 am
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..
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by Elena89 » Fri Dec 23, 2011 8:52 am
yeah, I get that.. thanks =)

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by LalaB » Fri Dec 23, 2011 10:47 am
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

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by [email protected] » Fri Dec 23, 2011 11:12 am
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: https://www.gmatprepnow.com/module/gmat-data-sufficiency

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com

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