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# All of the tickets for 2 music concerts, X and Y, were either purchase

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Math Expert
Joined: 02 Sep 2009
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All of the tickets for 2 music concerts, X and Y, were either purchase  [#permalink]

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02 Nov 2015, 08:33
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Difficulty:

45% (medium)

Question Stats:

57% (01:47) correct 43% (01:31) wrong based on 90 sessions

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All of the tickets for 2 music concerts, X and Y, were either purchased or given away, and the ratio of X tickets to Y was 2 to 1. Of the total number of X tickets and Y tickets, what percentage was purchased?

(1) The total number of X tickets and Y tickets, is 240.

(2) Of the X tickets, exactly 60% were purchased, and of the Y tickets, exactly 80% were purchased.

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Re: All of the tickets for 2 music concerts, X and Y, were either purchase  [#permalink]

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02 Nov 2015, 11:39
All of the tickets for 2 music concerts, X and Y, were either purchased or given away, and the ratio of X tickets to Y was 2 to 1. Of the total number of X tickets and Y tickets, what percentage was purchased?

(1) The total number of X tickets and Y tickets, is 240.

(2) Of the X tickets, exactly 60% were purchased, and of the Y tickets, exactly 80% were purchased.

x/y = 2/1 => x=2y

St 1:

The total number of X tickets and Y tickets, is 240.

x + y = 240; 2y + y = 240

=> y=80 and x=160. But no relevant info about how many tickets were purchased from both.

This is not sufficient.

St2 :

Of the X tickets, exactly 60% were purchased, and of the Y tickets, exactly 80% were purchased.

No of tickets purchased by X = 60% of 2y = 1.2y

No of tickets purchased by Y = 80% of y = 0.8y

Total tickets sold is 2y out of 3y, which gives 66.66%

Another method :
Plugging in numbers, Let x=200 and y=100
60% of 200 is 120, 80% of 100 is 80
Total sales 120+80 = 200 out of 300, which gives the same 66.66%. (same happens with 1st stmt data).

This is sufficient.

Ans B.
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Re: All of the tickets for 2 music concerts, X and Y, were either purchase  [#permalink]

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02 Nov 2015, 22:28
Hi,

Using statement 1 along with Premise, we arrive at Tx = 160 and Ty =80 but we can not arrive at the ratio of Px and Py. So Statement 1 is insufficient

Using statement 2 along with Premise,
Px:Py = 3/5Tx / (4/5Ty) = 3/5 * 5/4 * 2/1 = 3/2 (We know from the premise that Tx/Ty = 2:1)

Hence Option B.

Tx = Total tickets of X concert (Purchase plus given)
Ty= Total tickets of Y
Px and Py = Purchase tickets of X and Y
Gx and Gy = Given tickets of X and Y
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Re: All of the tickets for 2 music concerts, X and Y, were either purchase  [#permalink]

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04 Nov 2015, 20:03
Bunuel wrote:
All of the tickets for 2 music concerts, X and Y, were either purchased or given away, and the ratio of X tickets to Y was 2 to 1. Of the total number of X tickets and Y tickets, what percentage was purchased?

(1) The total number of X tickets and Y tickets, is 240.

(2) Of the X tickets, exactly 60% were purchased, and of the Y tickets, exactly 80% were purchased.

Ans: B

Solution: question stem tells us that x:y = 2:1 means x=2n and y=n total 3n tickets.
1) this gives is number of tickets total and in x and y but no info is given to get to the purchased or give away [Not Sufficient]
2) this says 60*2n/100 and 80*n/100 are purchased = 2n are purchased
here we know total tickets = 3n and purchsed are 2n we can get the required percentage from this [Sufficient]

Ans:B
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Re: All of the tickets for 2 music concerts, X and Y, were either purchase  [#permalink]

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04 Nov 2015, 21:12
Bunuel wrote:
All of the tickets for 2 music concerts, X and Y, were either purchased or given away, and the ratio of X tickets to Y was 2 to 1. Of the total number of X tickets and Y tickets, what percentage was purchased?

(1) The total number of X tickets and Y tickets, is 240.

(2) Of the X tickets, exactly 60% were purchased, and of the Y tickets, exactly 80% were purchased.

hello,
since the question is asking in % and the ratio of two things is given, we can find the answer even without actual numbers..
1) stat 1 does not help in any way..
2) stat 2 gives the % of purchased and given.. suff to answer
B
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Re: All of the tickets for 2 music concerts, X and Y, were either purchase  [#permalink]

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08 Nov 2015, 05:50
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

All of the tickets for 2 music concerts, X and Y, were either purchased or given away, and the ratio of X tickets to Y was 2 to 1. Of the total number of X tickets and Y tickets, what percentage was purchased?

(1) The total number of X tickets and Y tickets, is 240.

(2) Of the X tickets, exactly 60% were purchased, and of the Y tickets, exactly 80% were purchased.

In a 2 by 2 question as above, if a condition has 3 values of percentages when the question is asking for percentages, the condition becomes sufficient.

Attachment:

GC DS Bunuel All of the tickets for (20151104).jpg [ 29.84 KiB | Viewed 2107 times ]

There are 2 variables (x,y) and 2 equations regarding percentages are given from the 2 conditions, (especially condition 2 has 2 values of percentages), so the condition is sufficient.
x=36, y=24. The answer becomes (B).

from con 1) and con 2), if one of the conditions is given by numbers and the other is given by ratio (percent,fraction), then the condition with ratio (percent,fraction) value has higher chance of being the answer.
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Re: All of the tickets for 2 music concerts, X and Y, were either purchase  [#permalink]

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31 Jul 2017, 11:13
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Re: All of the tickets for 2 music concerts, X and Y, were either purchase   [#permalink] 31 Jul 2017, 11:13
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