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# S99-03

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Math Expert
Joined: 02 Sep 2009
Posts: 55271

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16 Sep 2014, 01:53
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Difficulty:

75% (hard)

Question Stats:

50% (02:53) correct 50% (01:25) wrong based on 52 sessions

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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

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Math Expert
Joined: 02 Sep 2009
Posts: 55271

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16 Sep 2014, 01:53
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

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.

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Intern
Joined: 15 Jul 2018
Posts: 8
GMAT 1: 700 Q47 V39

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15 Sep 2018, 09:39
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.
Intern
Joined: 09 Oct 2018
Posts: 6
Location: India
Schools: Tsinghua (S)
GPA: 3.9

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21 Nov 2018, 16:02
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.

Regards
Re S99-03   [#permalink] 21 Nov 2018, 16:02
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# S99-03

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