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If Pei ordered a total of 63 bottles of cola, root beer, and ginger

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NoHalfMeasures
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If Pei ordered a total of 63 bottles of cola, root beer, and ginger [#permalink] New post   04 Jun 2014, 23:30
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If Pei ordered a total of 63 bottles of cola, root beer, and ginger ale for a party, how many bottles of cola did she order?

(1) The number of bottles of root beer that Pei ordered was 80 percent of the number of bottles of ginger ale that she ordered.

(2) The number of bottles of cola that Pei ordered was 75 percent of the total number of bottles of root beer and ginger ale that she ordered.


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Bunuel
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Re: If Pei ordered a total of 63 bottles of cola, root beer, and ginger [#permalink] New post   05 Jun 2014, 01:06
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If Pei ordered a total of 63 bottles of Cola, Root Beer and Ginger Ale for a part. How many Cola bottles did she order?

Given: {Cola} + {Beer} + {Ale} = 63.
Question: {Cola} = ?

(1) The no of bottles of root beer Pei order was 80% of bottles of ginger ale that she ordered --> {Beer} = 0.8{Ale} --> 5*{Beer} = 4*{Ale} ({Beer} is a multiple of 4 and {Ale} is a multiple of 5). If {Beer} = 4 and {Ale} = 5, then {Cola} = 54 but if {Beer} = 8 and {Ale} = 10, then {Cola} = 45. Not sufficient.

(2) The no of bottles of cola Pei order was 75% of total no. of bottles of ginger ale and root beer that she ordered --> {Cola} = 0.75*({Beer} + {Ale}) --> {Beer} + {Ale} = 4/3*{Cola} --> {Cola} + 4/3*{Cola} = 63. We can solve for C. Sufficient.

Answer: B.
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Re: If Pei ordered a total of 63 bottles of cola, root beer, and ginger [#permalink] New post   27 Nov 2015, 10:17
Bunuel wrote:
If Pei ordered a total of 63 bottles of Cola, Root Beer and Ginger Ale for a part. How many Cola bottles did she order?

Given: {Cola} + {Beer} + {Ale} = 63.
Question: {Cola} = ?

(1) The no of bottles of root beer Pei order was 80% of bottles of ginger ale that she ordered --> {Beer} = 0.8{Ale} --> 5*{Beer} = 4*{Ale} ({Beer} is a multiple of 4 and {Ale} is a multiple of 5). If {Beer} = 4 and {Ale} = 5, then {Cola} = 54 but if {Beer} = 8 and {Ale} = 10, then {Cola} = 45. Not sufficient.

(2) The no of bottles of cola Pei order was 75% of total no. of bottles of ginger ale and root beer that she ordered --> {Cola} = 0.75*({Beer} + {Ale}) --> {Beer} + {Ale} = 4/3*{Cola} --> {Cola} + 4/3*{Cola} = 63. We can solve for C. Sufficient.

Answer: B.


Question : How did you get from 0.8 Ale to 5 Beer , and then to the 4 ale, beer ? Also, how did you get from 0,75 beer ale to 4/3 cola?
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Re: If Pei ordered a total of 63 bottles of cola, root beer, and ginger [#permalink] New post   05 Dec 2015, 17:54
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sagnik242 wrote:
Bunuel wrote:
If Pei ordered a total of 63 bottles of Cola, Root Beer and Ginger Ale for a part. How many Cola bottles did she order?

Given: {Cola} + {Beer} + {Ale} = 63.
Question: {Cola} = ?

(1) The no of bottles of root beer Pei order was 80% of bottles of ginger ale that she ordered --> {Beer} = 0.8{Ale} --> 5*{Beer} = 4*{Ale} ({Beer} is a multiple of 4 and {Ale} is a multiple of 5). If {Beer} = 4 and {Ale} = 5, then {Cola} = 54 but if {Beer} = 8 and {Ale} = 10, then {Cola} = 45. Not sufficient.

(2) The no of bottles of cola Pei order was 75% of total no. of bottles of ginger ale and root beer that she ordered --> {Cola} = 0.75*({Beer} + {Ale}) --> {Beer} + {Ale} = 4/3*{Cola} --> {Cola} + 4/3*{Cola} = 63. We can solve for C. Sufficient.

Answer: B.


Question : How did you get from 0.8 Ale to 5 Beer , and then to the 4 ale, beer ? Also, how did you get from 0,75 beer ale to 4/3 cola?


Hi sagnik242,

let me try to help.
Beer = 0.8 Ale
Beer = \(\frac{8}{10}\) Ale
10 Beer = 8 Ale (multiply the entire expression with 10)
5 Beer = 4 Ale (simplify by dividing the entire expression with 2)

same goes with 0,75 beer ale to 4/3 cola. hope that was helpful :D
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Re: If Pei ordered a total of 63 bottles of cola, root beer, and ginger [#permalink] New post   21 Dec 2017, 07:47
This question could be very tricky if total number of bottles bought was between 10 and 17. A could be sufficient.


When I solved A, I didn't use any equation. I tried to think logically that Number of cola bottle could be any number if I different number of Ginger ale bottles.

But after looking the official solution, I realized that my thought process for A could be dangerous. I have to actually form equation in this type of situation.
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Re: If Pei ordered a total of 63 bottles of cola, root beer, and ginger [#permalink] New post   14 Oct 2021, 22:47
NoHalfMeasures wrote:
If Pei ordered a total of 63 bottles of Cola, Root Beer and Ginger Ale for a part. How many Cola bottles did she order?

(1) The no of bottles of root beer Pei order was 80% of bottles of ginger ale that she ordered
(2) The no of bottles of cola Pei order was 75% of total no. of bottles of ginger ale and root beer that she ordered


Take into consideration the av.time taken by participants, I have doubt that the first statement was fully tested. Or I do it too slowly :-)

C + RB + GA = 63

Statement 1
RB = 8/10 of GA = 4/5 of GA

C + 4/5GA + GA = 63
5C + 9GA = 315
C = 9(35-GA)/5

Hence, C is a multiple of 9, yet it can by any number within aforementioned restrictions.
The quibble here is if those numbers were primes, the probability that we can get correct answer is very high.

Statement 2
is indeed sufficient, we get sum of RB + GA, and, thus, we can deduct it from total and get the result.
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Re: If Pei ordered a total of 63 bottles of cola, root beer, and ginger [#permalink] New post   28 Feb 2024, 14:41
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Re: If Pei ordered a total of 63 bottles of cola, root beer, and ginger [#permalink]
28 Feb 2024, 14:41
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