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John purchased large bottles of water for $2 each and small

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John purchased large bottles of water for $2 each and small  [#permalink]

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New post 23 Apr 2012, 05:12
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Question Stats:

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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
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Re: John purchased large bottles of water for $2 each and small  [#permalink]

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New post 23 Apr 2012, 05:29
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 \(\frac{y}{x+y}=\frac{35}{15+35}=\frac{70}{100}\).

Answer: B.
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Re: John purchased large bottles of water for $2 each and small  [#permalink]

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New post 27 Apr 2012, 06:10
1
got B


(A)

2(l) + 1.5(s) = 33

not sufficient

(B)

[2(l) + 1.5(s)] / (l+s) = 1.65

2l + 1.5s = 1.65 (l+s)

2l - 1.65l = 1.65s - 1.5s

0.35(l) = 0.15 (s)

35/15 = s/l


% of small bottles

=35/ (35+15)*100
= 70%

sufficient

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Re: John purchased large bottles of water for $2 each and small  [#permalink]

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New post 11 Sep 2012, 07:16
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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.
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Re: John purchased large bottles of water for $2 each and small  [#permalink]

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New post 11 Sep 2012, 08:38
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 \(y=2\)

Kindly correct me if i am wrong.


Typo edited. Thank you. +1.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: John purchased large bottles of water for $2 each and small  [#permalink]

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New post 11 Sep 2012, 09:43
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

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Re: John purchased large bottles of water for $2 each and small  [#permalink]

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New post 11 Sep 2012, 14:00
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 \(\frac{N_2}{N_1+N_2}\).
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John purchased large bottles of water for $2 each and small  [#permalink]

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New post 31 Dec 2015, 19:16
1. small bottles can be 2, and 15 large or 6 small and 12 large. 1 insufficient.
2. 2L+3S/L+S = 1.65
we are given proportions. thus, we can solve the question.
2L+1.5S=1.65L + 1.65S
0.35L=0.15S.
multiply by 100
35L=15S.
S/L = 35/15

S/S+L = 35/15+35 = 35/50 or 7/10. 70%
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Re: John purchased large bottles of water for $2 each and small  [#permalink]

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New post 19 Jun 2016, 04:03
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


(1)Not suff.
(2) I will use weighted avg. method here
W1/W2=(A2-Avg.)/(Avg.-A2)
W1=No. of large bottles
W2=No. of large bottles
A1=2
A2=1.5
Avg.=1.65
W1/W2=3/7
%age of small bottles= 7/(3+7)------>7/10----70%
Ans B
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Re: John purchased large bottles of water for $2 each and small  [#permalink]

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New post 07 Dec 2017, 11:15
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


We are given that John purchased large bottles of water for $2 each and small bottles of water for $1.50 each. We can let s = the number of small bottles purchased, and b = the number of larger bottles purchased. We need to determine what percentage of the bottles purchased were small bottles, i.e. the value of s/(s+b) x 100.

Statement One Alone:

John spent $33 on the bottles of water.

Using the information in statement one, we can create the following equation:

2b + 1.5s = 33

We can multiply the entire equation by 2 and we have:

4b + 3s = 66

4b = 66 - 3s

4b = 3(22 - s)

b = [3(22 - s)]/4

Since b must be an integer, 3(22 - s) must be a multiple of 4.

3(22 - s) is a multiple of 4 when s = 2, 6, 10, 14, or 18.

Since we have multiple values of s, we will also have multiple values of b, and thus we do not have enough information to answer the question.

Statement Two Alone:

The average price of bottles purchased was $1.65.

Using the information in statement two, we can create the following equation:

1.65 = (2b + 1.5s)/(b + s)

1.65(b + s) = 2b + 1.5s

165(b + s) = 200b + 150s

165b + 165s = 200b + 150s

15s = 35b

3s = 7b

(3/7)s = b

We can now determine the value of s/(s+b) x 100 by substituting (3/7)s for b:

s/[s+(3/7)s] x 100

s/[(10/7)s] x 100

1/(10/7) x 100

7/10 x 100 = 70

So the small bottles account for 70 percent of the bottles purchased. We have answered the question.

Answer: B
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Re: John purchased large bottles of water for $2 each and small &nbs [#permalink] 07 Dec 2017, 11:15
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