Problem Solving

Papayaya, a popular soft drink, contains only four ingredients. Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya. The amounts of sugar and papaya puree in Papayaya are equal. Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree. If no other changes were made to the relative quantities of the ingredients, what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine?

A) 7/30
B) 7/21
C) 2/5
D) 12/29
E) 4/7

Sugar = Purie = [ 1- (4/7+1/3) ]/2 = 1/21
New Conc:-
Soda : 12/21
Lemon : 14/21 (Double)
Sugar : 1/21
Purie : 3/21 (Triples)
New Conc of Soda = 12 / (14+12+1+3) = 12/30 = 2/5

Anurag@Gurome wrote: In the original papayaya drink, soda water = 4/7, natural lemon juice = 1/3, remaining ingredients = 1 - (4/7 + 1/3) = 1 - 19/21 = 2/21
Since, amounts of sugar and papaya puree in Papayaya are equal, so sugar = 1/21 and papaya puree = 1/21
After malfunctioning, soda water = 4/7, natural lemon juice = 2/3, sugar = 1/21 and papaya puree = 3/21 = 1/7
Therefore, fractional portion of soda water in the drink that comes out of the malfunctioning machine = 4/7 / (4/7 + 2/3 + 1/21 + 3/21) = 4/7 / 30/21 = [spoiler]2/5[/spoiler]

The correct answer is C.

Hi, thanks

What does 'If no other changes were made to the relative quantities of the ingredients' mean? Why 'relative' is mentioned?

patanjali.purpose wrote:Papayaya, a popular soft drink, contains only four ingredients. Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya. The amounts of sugar and papaya puree in Papayaya are equal. Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree. If no other changes were made to the relative quantities of the ingredients, what is the fractional portion of soda water in the drink that comes out of the malfunctioning machine?

A) 7/30
B) 7/21
C) 2/5
D) 12/29
E) 4/7

Before the malfunction:
Let the total = 42 units.
Soda = (4/7)42 = 24 units.
Lemon juice = (1/3)42 = 14 units.
Remaining units = 42-24-14 = 4 units.
Dividing the remaining units equally between the sugar and the papaya:
Sugar = 2 units.
Papaya = 2 units.

After the malfunction:
Lemon juice doubled = 2*14 = 28 units.
Papaya tripled = 3*2 = 6 units.
New total = soda + new lemon + sugar + new papaya = 24+28+2+6 = 60 units.
Soda/total = 24/60 = 2/5.

The correct answer is C.

GMATGuruNY wrote:
Before the malfunction:
Let the total = 42 units.
Soda = (4/7)42 = 24 units.
Lemon juice = (1/3)42 = 14 units.
Remaining units = 42-24-14 = 4 units.
Dividing the remaining units equally between the sugar and the papaya:
Sugar = 2 units.
Papaya = 2 units.

After the malfunction:
Lemon juice doubled = 2*14 = 28 units.
Papaya tripled = 3*2 = 6 units.
New total = soda + new lemon + sugar + new papaya = 24+28+2+6 = 60 units.
Soda/total = 24/60 = 2/5.

The correct answer is C.

Hi Mitch,

I attempted the question same way but all along I was wondering whether overall quantity of juice before and after will change - could not find an appropriate indication in question for this. Does 'the relative quanitities' give this impression - what does it mean. Could you pls explain.

regards