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

@rijul007

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

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

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

@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.

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:

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.

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

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..

yeah, I get that.. thanks =)

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