(OG-12 DS) Joanna...

This topic has expert replies
User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: 31 Jul 2011
Thanked: 2 times
Followed by:1 members

(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..

User avatar
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 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

User avatar
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!

User avatar
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
:D

User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: 31 Jul 2011
Thanked: 2 times
Followed by:1 members

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.

Legendary Member
Posts: 1085
Joined: 15 Apr 2011
Thanked: 158 times
Followed by:21 members

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:
Success doesn't come overnight!

Legendary Member
Posts: 1085
Joined: 15 Apr 2011
Thanked: 158 times
Followed by:21 members

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.
Success doesn't come overnight!

User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: 31 Jul 2011
Thanked: 2 times
Followed by:1 members

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.. :?

Legendary Member
Posts: 1085
Joined: 15 Apr 2011
Thanked: 158 times
Followed by:21 members

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.. :?
Success doesn't come overnight!

User avatar
Senior | Next Rank: 100 Posts
Posts: 35
Joined: 31 Jul 2011
Thanked: 2 times
Followed by:1 members

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

User avatar
Master | Next Rank: 500 Posts
Posts: 425
Joined: 08 Dec 2010
Thanked: 56 times
Followed by:7 members
GMAT Score:690

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

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 15948
Joined: 08 Dec 2008
Location: Vancouver, BC
Thanked: 5254 times
Followed by:1267 members
GMAT Score:770

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
Image