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# A bag contains red balls that weigh 100 grams each and green balls

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Director
Joined: 18 Feb 2019
Posts: 582
Location: India
GMAT 1: 460 Q42 V13
GPA: 3.6
A bag contains red balls that weigh 100 grams each and green balls  [#permalink]

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29 Mar 2019, 12:07
1
1
00:00

Difficulty:

85% (hard)

Question Stats:

41% (02:42) correct 59% (02:17) wrong based on 22 sessions

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A bag contains red balls that weigh 100 grams each and green balls that weigh 50 grams each. If the number of green balls is 9 more than the number of red balls, how many balls are there in the bag?

I. If two red balls are added to the bag, the number of red balls will be half the number of green balls

II. The total weight of the balls in the bag is between 1.05 kilogram and 1.35 kilogram
Intern
Joined: 12 Jul 2016
Posts: 16
Location: India
GMAT 1: 690 Q50 V32
GPA: 3.74
Re: A bag contains red balls that weigh 100 grams each and green balls  [#permalink]

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29 Mar 2019, 13:15
5
Let number of red balls be x
Then the number of green balls is (x+9)

Statement 1:

If two red balls are added to the bag, the number of red balls will be half the number of green balls.

The new number of red balls is (x +2)
So, (x + 2) = (x + 9)/2
=> 2x + 4 = x + 9
On solving, x = 5.

Statement 1 is sufficient.

Statement 2 :
The total weight of the balls in the bag is between 1.05 kilogram and 1.35 kilogram

Each green ball weight 0.05kg and each red ball weight 0.1kg

Total number of balls :
red + green
= 0.1x + (0.5x + 9[0.5])
= 1.5x + 0.45kg

As per question stem, Weight of the bag can possibly lie between 1.05kg to 1.35kg, so possible options are 1.1 kg, 1.15 Kg, 1.2kg, 1.25kg, 1.30kg.

But for only value which is 1.2kg, the above equation gives solution.( Number of balls cannot be in decimal/fraction. So integer value is considered for x)

=> 1.5x + 0.45 = 1.2
=> 1.5x = 0.75
=> x = 5

Statement 2 is also sufficient.

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Re: A bag contains red balls that weigh 100 grams each and green balls   [#permalink] 29 Mar 2019, 13:15
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