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S99-03

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S99-03  [#permalink]

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New post 16 Sep 2014, 00:53
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Difficulty:

  75% (hard)

Question Stats:

52% (03:04) correct 48% (01:27) wrong based on 46 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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Re S99-03  [#permalink]

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New post 16 Sep 2014, 00:53
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.


Answer: B
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: S99-03  [#permalink]

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New post 15 Sep 2018, 08:39
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.
GMAT Club Bot
Re: S99-03 &nbs [#permalink] 15 Sep 2018, 08:39
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