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..

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

##### This topic has expert replies

- rijul007
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No of $0.29 stamps=y

0.15x + 0.29y = 4.4(1) She bought $4.40 worth of stamps.

Not Sufficient

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

still not sufficient

**Combining the two statements**

0.15x + 0.29x = 4.4

Find the value of x

Option C

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=

and we need to find A?

st(1) implies

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

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 stampsand 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!

- rijul007
- Legendary Member
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ok so its not as easy as it seemedElena89 wrote:@rijul007

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

The correct answer is A

**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
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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:

Success doesn't come overnight!

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 onevalue of any of the 2 unknowns is obtainable! and so the first is sufficient.

Success doesn't come overnight!

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

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!

- LalaB
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15x+29y=44Elena89 wrote:

What I do not understand is how we can find the value of one unknown from only one equation.

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

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This is a common trap on the GMAT.LalaB wrote:15x+29y=44Elena89 wrote:

What I do not understand is how we can find the value of one unknown from only one equation.

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

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