Mixture 2

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Mon Dec 26, 2011 3:16 am

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?

7/30
7/21
2/5
12/29
4/7

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Source: Beat The GMAT — Problem Solving | Mon Dec 26, 2011 3:16 am

rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Mon Dec 26, 2011 4:05 am

Lets say the total amount of drink was 21 litres

Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya.

Soda water = 12 lt
Lemon Juice = 7 lt

The amounts of sugar and papaya puree in Papayaya are equal.

Amount of sugar = Amount of Papaya puree = [21 - (12+7)]/2 = 1 lt

Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree.

Amount of lemon juice = 14 lt
Amount of papaya puree = 3 lt

Total amount of Papayaya = 14+12+1+3 = 30 lt

fracional portion of soda water = 12/30 = 2/5

Option C

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Mon Dec 26, 2011 5:54 am

@Riju

This problem is to be done with the assumptions of a VALUE.

How to determine / decide in any problem to assume a Value. Is there a strategy?

rijul007 wrote:Lets say the total amount of drink was 21 litres

Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya.
Soda water = 12 lt
Lemon Juice = 7 lt

The amounts of sugar and papaya puree in Papayaya are equal.
Amount of sugar = Amount of Papaya puree = [21 - (12+7)]/2 = 1 lt

Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree.
Amount of lemon juice = 14 lt
Amount of papaya puree = 3 lt

Total amount of Papayaya = 14+12+1+3 = 30 lt

fracional portion of soda water = 12/30 = 2/5

Option C

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rijul007: Legendary Member; Posts: 588; Joined: Sun Oct 16, 2011 9:42 amFollowed by: 9 members; Location: New Delhi, India; Thanked: 130 times; GMAT Score:720

by rijul007 » Mon Dec 26, 2011 8:50 am

karthikpandian19 wrote:@Riju

This problem is to be done with the assumptions of a VALUE.

How to determine / decide in any problem to assume a Value. Is there a strategy?
rijul007 wrote:Lets say the total amount of drink was 21 litres

Soda water comprise 4/7 of Papayaya and natural lemon juice makes 1/3 of Papayaya.
Soda water = 12 lt
Lemon Juice = 7 lt

The amounts of sugar and papaya puree in Papayaya are equal.
Amount of sugar = Amount of Papaya puree = [21 - (12+7)]/2 = 1 lt

Due to a malfunction, the mixing machine mixes double the regular amount of lemon juice and three times the regular amount of papaya puree.
Amount of lemon juice = 14 lt
Amount of papaya puree = 3 lt

Total amount of Papayaya = 14+12+1+3 = 30 lt

fracional portion of soda water = 12/30 = 2/5

Option C

In such questions we assume integer numbers to avoid messy calculations among fractions..

when we are given a fraction, for example in this ques, 4/7 and 1/3
one can assume the total number to be 21 which is the LCM of the denominators
multiply the fractions with the LCM and you'll get Integer numbers corresponding to those fractions

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ronnie1985: Legendary Member; Posts: 626; Joined: Fri Dec 23, 2011 2:50 amFollowed by: 10 members; Location: Ahmedabad; Thanked: 31 times

by ronnie1985 » Mon Dec 26, 2011 8:06 pm

Soda Water = 4/7
Lemon Juice = 1/3
Sugar =1/21
Papaya = 1/21
Change,
Soda Water = 4/7
Lemon Juice = 2/3
Sugar = 1/21
Papaya = 3/21
New Ration of Soda Water = (4/7) / (2/3 + 3/21 + 1/21 + 4/7) = 2/5

Follow your passion, Success as perceived by others shall follow you

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karthikpandian19: Legendary Member; Posts: 1665; Joined: Thu Nov 03, 2011 7:04 pmFollowed by: 70 members; Thanked: 165 times

by karthikpandian19 » Tue Dec 27, 2011 9:42 pm

OA is 2/5

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