Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: John purchased large bottles of water for $2 each and small [#permalink]
23 Apr 2012, 04:29

Expert's post

John purchased large bottles of water for $2 each and small bottles of water for $1.50 each. What percent of the bottles purchased were small bottles?

Say John purchased x large bottles and y small bottles.

(1) John spent $33 on the bottles of water --> 2x+1.5y=33 --> 4x+3y=66. Several integer solutions possible to satisfy this equation, for example x=15 and y=2 OR x=12 and y=6. Not sufficient.

(2) The average price of bottles purchased was $1.65 --> \frac{2x+1.5y}{x+y}=1.65 --> 2x+1.5y=1.65x+1.65y --> 0.35x=0.15y --> \frac{y}{x}=\frac{35}{15}, we have the ratio, which is sufficient to get the percentage.

Just to illustrate \frac{y}{x+y}=\frac{35}{15+35}=\frac{70}{100}.

Re: John purchased large bottles of water for $2 each and small [#permalink]
11 Sep 2012, 06:16

1

This post received KUDOS

Bunuel wrote:

John purchased large bottles of water for $2 each and small bottles of water for $1.50 each. What percent of the bottles purchased were small bottles?

Say John purchased x large bottles and y small bottles.

(1) John spent $33 on the bottles of water --> 2x+1.5y=33 --> 4x+3y=66. Several integer solutions possible to satisfy this equation, for example x=15 and y=3 OR x=12 and y=6. Not sufficient.

(2) The average price of bottles purchased was $1.65 --> \frac{2x+1.5y}{x+y}=1.65 --> 2x+1.5y=1.65x+1.65y --> 0.35x=0.15y --> \frac{y}{x}=\frac{35}{15}, we have the ratio, which is sufficient to get the percentage.

Just to illustrate \frac{y}{x+y}=\frac{35}{15+35}=\frac{70}{100}.

Answer: B.

Hi Bunuel,

There is small error in one of the calculations. x=15 and y=3 should be x=15 and y=2

Kindly correct me if i am wrong. _________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Re: John purchased large bottles of water for $2 each and small [#permalink]
11 Sep 2012, 07:38

Expert's post

fameatop wrote:

Bunuel wrote:

John purchased large bottles of water for $2 each and small bottles of water for $1.50 each. What percent of the bottles purchased were small bottles?

Say John purchased x large bottles and y small bottles.

(1) John spent $33 on the bottles of water --> 2x+1.5y=33 --> 4x+3y=66. Several integer solutions possible to satisfy this equation, for example x=15 and y=3 OR x=12 and y=6. Not sufficient.

(2) The average price of bottles purchased was $1.65 --> \frac{2x+1.5y}{x+y}=1.65 --> 2x+1.5y=1.65x+1.65y --> 0.35x=0.15y --> \frac{y}{x}=\frac{35}{15}, we have the ratio, which is sufficient to get the percentage.

Just to illustrate \frac{y}{x+y}=\frac{35}{15+35}=\frac{70}{100}.

Answer: B.

Hi Bunuel,

There is small error in one of the calculations. x=15 and y=3 should be x=15 and y=2

Re: John purchased large bottles of water for $2 each and small [#permalink]
11 Sep 2012, 08:43

Let x be the number of large bottles of water and y be the number of small bottles of water, from the question stem we get: 2*x+1.5*y=33, thus 1 is INSUFFICIENT. Mowing to 2 condition: (2*x+1.5*y)/(x+y) = 1.65 ------>>>> 2x+1.5y = 1.65x+1.65y, from here we easily get that 7x=3y, OR x = 3y/7 now we now x we can easily find the ratio of y in total of bottles: y/(y+3y/7) = 7/10 or 70%

Please correct me, if I went awry. Actually we do not need the solution, as it is data sufficiency so 2 is SUFFICIENT

dzodzo85 wrote:

John purchased large bottles of water for $2 each and small bottles of water for $1.50 each. What percent of the bottles purchased were small bottles?

(1) John spent $33 on the bottles of water (2) The average price of bottles purchased was $1.65

Re: John purchased large bottles of water for $2 each and small [#permalink]
11 Sep 2012, 13:00

dzodzo85 wrote:

John purchased large bottles of water for $2 each and small bottles of water for $1.50 each. What percent of the bottles purchased were small bottles?

(1) John spent $33 on the bottles of water (2) The average price of bottles purchased was $1.65

Dealing with Statement (2): remember weighted average (also used when dealing with mixture problems).

If we have N_1 numbers with average A_1, and N_2 numbers with average A_2, the final average being A, then the differences between the final average and the initial averages are inversely proportional to the two numbers of numbers (assume A_1>A_2):

(A_1-A)N_1=(A-A_2)N_2 or \frac{A_1-A}{A-A_2}=\frac{N_2}{N_1}.

This follows from the equality \frac{N_1A_1+N_2A_2}{N_1+N_2}=A.

In our case we know A, A_1,A_2 so we can find the ratio \frac{N_2}{N_1} and then, obviously \frac{N_2}{N_1+N_2}. _________________

PhD in Applied Mathematics Love GMAT Quant questions and running.

Re: John purchased large bottles of water for $2 each and small [#permalink]
19 Jun 2014, 03:33

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________