Data Sufficiency

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.

Can you please provide you logic in reaching the answer. Thanks.

I think the answer is A.

Statement I.

Total is $4.40.

Therefore, 15x+29y=440

Try pluggin in any value for x so that y's value is an integer.
There is only one value for x and y that can satisfy above equation i.e. x=10 or y=10.
Sufficient.

Statement II.

Both the stamps are of same number. We cannot find the specific value of the stamps since they could be any number in multiples of 10.
Insufficient.

Hence A

Whats the OA?

Initially I thought C, but parallel_chase made a very smart observation.

Can you please explain though, how you're sure that the only combination of numbers (10,10) works? How can you verify that there is no other combination given such little time?

If what you said is true, then can't we choose D? Statements 1 and 2 combined are pretty much involved the same work that done by parallel_chase in statement 1.

Thx!

(1)
The total value of the $0.15 stamps must be a dollar amount that ends in 5 or 0 (in the units cents position). In order for the total value of both stamps to equal $4.40, therefore, the total value of the $0.29 stamps must also be a dollar amount that ends in 5 or 0.

That would only occur if a multiple of 5 $0.29 stamps are purchased.

5 $0.29 stamps = $1.45, leaving $2.95 to make $4.40. But $2.95 is not a multiple of $0.15 -- no good.
10 $0.29 stamps = $2.90, leaving $1.50 to make $4.40. So 10 $0.15 would be purchased.
15 $0.29 stamps = $4.35, leaving $0.05 to make $4.40. Clearly not a multiple of $0.15 -- no good.

The only possibility is that 10 of each stamp are purchased. SUFFICIENT.

(2)
Any number of stamps could be purchased. INSUFFICIENT.

The correct answer is A.

440=15x+29y
29y must have a unit which is 0 or 5
and (440-29y) must be a multiple of 15

You can fastly find the one which have a last unit digit of 0 or 5
29*5=145
29*10=290
29*15=335
(29*20>440)

And check which one have (440-29y) which is a multiple of 15

It is true when you see 2 unknows in one equation you often tell you it's impossible, sometimes it is better to search a little.
Chase how did you do to fastly find there is only one solution?

Here is step by step process of how I dismantled the question.

Only $0.15 stamps and only $0.29 stamps

I read both the statements

total amt. = 4.40

I added both o.15+0.29=0.44
0.44*10 =$4.40

I looked at the second statement, and some how I knew i was inside the question maker's head.

I calculated for 20 stamps of 0.15 and 0.29, the answer is $8.80

So I stressed on proving statement A incorrect.

I simplified the equation, because I find it easier to work with whole numbers rather than decimals.

15x+29y=440
only way a units digit of two numbers can result in 0, if units digit of either number is 5 or 0.

Hence A is the correct answer.

This entire process took me less than 1 minute. Let me know if you still have any doubts.

Some good input here folks ! The correct answer is A.

So what is this question really trying to test here ?
- Ability to translation words into algebra
- Ability to work with equations
- Knowledge of divisibility (divisibility rules for number 5 and 10)
- Knowlegde of DIGITS and PLACE VALUE

I initially fell into the trap of choosing answer C.

The easy statement here is statement 2 ... which is clearly not sufficient, since there is no way of determining how many of each type of stamp was purchased.

With statement 1, I had the following equation:
0.15x + 0.29y = 4.40
Under strict time conditions in an exam situation, I looked at this and thought ... 2 unknowns and 1 equation, hence we have INSUFFICIENT information to solve for x.

How did you guys look at this problem and identify that you had to use knowledge of digits and divisibility rules ?
In other words, what signalled you to go down and use the approach of working with the units digit ?

Thanks in advance.

I think the question is really trying to test the algebra and divisibility rules.

Especially in data sufficiency I find that when ever there is an algebric equation with 2 unknowns make sure that you negate the possibility of having only more than one value for both the variables.

The other questions you are asking about what triggered to use divisibility or digit rules are more psychological and relative to the question.

parallel_chase wrote:I think the question is really trying to test the algebra and divisibility rules.

Especially in data sufficiency I find that when ever there is an algebric equation with 2 unknowns make sure that you negate the possibility of having only more than one value for both the variables.

The other questions you are asking about what triggered to use divisibility or digit rules are more psychological and relative to the question.

I dont understand what you mean by "psycjological and relative to the question".
ON THIS QUESTION what would make you think ... right I have to use divisibility rules here ... and use my knowledge of digits (last digit). What signals from this question would point you to think about divisibility rules and digits ?
As I mentioned ... I fell into the trap of looking at this as 0.15x + 0.29y = 4.40 and thought about 1 equation and 2 variables, hence thought it was insufficient. What should I do in the future to avoid falling into this trap.

Thanks.

I dont understand what you mean by "psycjological and relative to the question".

What I mean is that everyone has their own strategy or rather a mindset to solve a question. And it goes same for this question as well. If you look at above posts everyone of us started with a different approach. Thats why I said it is psychological and relative to the question. Every GMAT question can be done in two or more ways.

ON THIS QUESTION what would make you think ... right I have to use divisibility rules here ... and use my knowledge of digits (last digit). What signals from this question would point you to think about divisibility rules and digits ?
As I mentioned ... I fell into the trap of looking at this as 0.15x + 0.29y = 4.40 and thought about 1 equation and 2 variables, hence thought it was insufficient. What should I do in the future to avoid falling into this trap.

Thanks.

Here is the entire process and some suggestions which i had mentioned before in same topic.

Here is step by step process of how I dismantled the question.
Only $0.15 stamps and only $0.29 stamps
I read both the statements
total amt. = 4.40
I added both o.15+0.29=0.44
0.44*10 =$4.40
I looked at the second statement, and some how I knew i was inside the question maker's head.
I calculated for 20 stamps of 0.15 and 0.29, the answer is $8.80
So I stressed on proving statement A incorrect.
I simplified the equation, because I find it easier to work with whole numbers rather than decimals.
15x+29y=440
only way a units digit of two numbers can result in 0, if units digit of either number is 5 or 0.

Especially in data sufficiency I find that when ever there is an algebric equation with 2 unknowns make sure that you negate the possibility of having more than one value for both the variables.


Hope it helps.

thanks !

I think that the best way to crack this one is:

1° found de MCM of 0.29 and 0.15 (it is better to use 29 and 15)
2° then if the MCM of 29 and 15 is less than 440 there is only one solution...

MCM (29x5x3) = 435 < 440 . So A is the correct answer.

I think that this is the best way to crack this kind of exercise

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



.29 Y = 4.40 - .15X


Now since right side is always end in either 5 or 0

lets find out the multiple of .29 ending with the same

.29*5 = 1.45 out

.29*10 = 2.9 in

.29*15 = 4.45 out



2) We can always find that!


choose D

ronniecoleman wrote: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



.29 Y = 4.40 - .15X


Now since right side is always end in either 5 or 0

lets find out the multiple of .29 ending with the same

.29*5 = 1.45 out

.29*10 = 2.9 in

.29*15 = 4.45 out



2) We can always find that!


choose D

Ronnie,

You should not do this kind of mistake 22 days before your test. WARNING SIGN! And try to read this LONG post before jumping into in it...Just for a little hint, check what I wrote in my post for this question.