(OG-12 DS) Joanna...

[Elena89]

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..

[rijul007]

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

[Elena89]

@rijul007

yeah, that's what I did, however that's incorrect!
The correct answer is A

[pemdas]

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

[rijul007]

@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

[Elena89]

@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.

[pemdas]

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:

[pemdas]

yea, just turned back and seen/corrected/explained in previous post

@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.

[Elena89]

yeah, well all that is written in OG too.. but I don't think all that calculation can be done in just 2 minutes..

[pemdas]

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.

yeah, well all that is written in OG too.. but I don't think all that calculation can be done in just 2 minutes..

[Elena89]

yeah, I get that.. thanks =)

[LalaB]

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

[Brent@GMATPrepNow]

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