S99-03

Question

Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 98% water by weight. What is the new weight of the cucumbers, in pounds?

A. 2
B. 50
C. 92
D. 96
E. 98

A. 2
B. 50
C. 92
D. 96
E. 98

Bunuel · Answer

Official Solution:

Each of the cucumbers in 100 pounds of cucumbers is composed of 99% water, by weight. After some of the water evaporates, the cucumbers are now 98% water by weight. What is the new weight of the cucumbers, in pounds?

A. 2
B. 50
C. 92
D. 96
E. 98

A. 2
B. 50
C. 92
D. 96
E. 98

Since each cucumber is 99% water by weight, each one is also 1% something else (say, "mush.") So each cucumber is 99% water and 1% mush. That means that all the cucumbers together are 99% water and 1% mush. Since the total weight is 100 pounds, the weight of the mush is equal to  0.01(100) = 1  pound, and the weight of the water is 99 pounds.
 
After the water evaporates, each cucumber is 98% water. Therefore, we know that all the cucumbers together are 2% mush and 98% water. The key point is that the amount of water changed, but the amount of mush has not. Thus, we should equate the amount of mush BEFORE with the amount of mush AFTER.
 
If we call the new, unknown weight of the cucumbers  x , then the weight of the mush after evaporation is 2% of  x , or  0.02x .
 
Now, we can equate the weight of the mush before and after:
 
1 pound  = 0.02x 
 
  \frac{1}{0.02} = x  
 
  x = 50  
 
The new weight of the bag is 50 pounds.

Answer: B

Gayluk · Answer

another possible explanation:

100*99/100 - X*100/100=(100-X)*98/100, where X is the amout of evaporated water

When solve we get X = 50, thus 100 - 50 = 50.

Please correct me if I am wrong.

bks170882 · Answer

I think this the explanation isn't clear enough, please elaborate. 99% of water by WEIGHT contributed to 99 pounds.

98% of water by WEIGHT contributed to 50 pounds?
Before extra matter was 1% i.e. 1 pound.
After that there is no information whether extra matter increased or changed? Only change in water component is mentioned.

Can you please help with it.

Regards

Tlo19 · Answer

Hi Bunuel,

Would X be referring to the new total weight? Since 1lbs (Mush) = 0.02 (% of total weight that is mush) x 'X' (Total weight) and as such, the weight of the water would be 98% of X, which would be 0.98*50 = 49?

I am still unsure of how you got to your answer and would like to know what you and others think

Bunuel · Answer

Hope my solution helps: https://gmatclub.com/forum/each-of-the- ... ml#p795199

Archit3110 · Answer

99% water leaves with 1% weight of the cucumbers but we dont know what exactly is the 1% of weight is or say .01 1lbs
and later new weight of cucumber is 98% water and 2 lbs 
we can equate 1=.02x
x= 50
IMO B

AShahh4400 · Answer

we know that in the 100 pounds cucumber, 1 pound is mush and 99 is water. 
Assuming that the x pounds of water evaporated from the cucumbers with mush staying the same, the total water in the cucumber = 99-x and total weight of cucumbers is 100-x

since the percentage of water in cucumbers after evaporation is 98%, hence, (99-x)/(110-x)=98/100 
From this equation we get x = 50 and new weight of cucumbers is 100-50 = 50

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