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shrive555
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

We see that 99 pounds is water and 1 pound is cucumber. Letting w = the number of pounds of water that evaporates, we can create the following equation:
(99 - w)/(100 - w) = 98/100

Cross-multiplying, we have:

100(99 - w) = 98(100 - w)

9900 - 100w = 9800 - 98w

100 = 2w

50 = w

The cucumbers have lost 50 pounds of water, so the new weight of the cucumbers is 100 - 50 = 50 pounds.

Answer: B
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My Take:

Generally:
(A1*W1 + A2*W2) / (W1 + W2) = Aavg

In this case:(Water evaporates)
(A1*W1 - A2*W2) / (W1 - W2) = Aavg

=> (99*100 - 100*n) / (100 - n) = 98; Here water concentration = 100% and weight of water = n
=> 99*100 - 100n = 98*100 - 98n
=> 100(99-98) = 100n - 98n
=> 100 = 2n
=> n = 50
Therefore, new weight of cucumber = 100 - 50 = 50 pounds
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This question can pretty much be solved by logical thinking alone:

99% of a cucumber is water and 1% is solid this means 99lb water, 1lb solid

If water evaporates to the point that the 1lb of solid material now accounts for twice as much of the total weight of the cucumber, this means that the cucumber must have lost half its weight. (e.g. 1lb of 50 = 2%)

Hope this helps.

Regards,
Chris
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------------Cmass Water Total
Before % 1/100 99/100 100
--------V 1 99 100

After % 2/100 98/100 100
--------V 1 99-x 100-x


Method1
After Cmass,
(100-x)2/100 = 1 ; x=50

Method2
After water
(100-x)98/100 = 99-x ; x = 50

Method3
Cmass/water
2/98 = 1/(99-x) ; x = 50
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You can determine the new weight by the amount that evaporated.

(99lb water - Xlbs water)/ (100lbs total weight - Xlbs water) = 98/100
9900-100x= 9800-98x
100=2x
x= 50

100lbs total weight - 50lbs water = 50lbs total weight.
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It used to be 99 pounds water and 1 non-water; water changed from 99% to 98%, BUT what didn't change was that 1 pound non-water since it didn't evaporate like water;
So that 1 pound became 2%s of the new weight and 100/2 = 50 pounds.
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Given: 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.

Asked: What is the new weight of the cucumbers, in pounds?

In 100 pounds of cucumber: -
Water = 99 pounds
Other material = 1 pound

Let water evaporated be x pounds
Water = 99-x pounds
Other material = 1 pound
Total = (99-x) + 1 = 100 - x pounds

1/(100-x) = .02
100 - x = 1/.02 = 50
x = 50

New weight of cucumber = 100 - x = 100 -50 = 50 pounds

IMO B
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milanrai78
My approach

Before evaporation by weight

100 pounds of Cucumber = 99 pounds water + 1 pound cucumber matter

After evaporation

lets say the weight of cucumber is x
then by weight

x = (98/100* x is water) + 1 pound of cucumber matter

solving for x gives 50

With the new weight percent 98%, should there be 2 pounds of cucumber matter?
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shrive555
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


100= water(99) + cucmber(1)
After x water evaporates:
1/(99-x) = 2/98 =1/49
--> x=50
the new weight of the cucumbers=100-x=50

B
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Quiter tricky honestly. The main thing is to equate the weights of the cucumbers.

0.01 * Cucumber Qty = 0.02 of New Cucumber Qty

Cucumber Qty = 100

so, 1 = 0.02 of New Cucumber Qty

New Cucumber Qty = 50

B
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shrive555
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


[img]Cucumber Water X
W = 100 99% of 100 = 99 pounds 1 % of 100 = 1 pound
W’ 98% of W’ 2% of W’. = 1 pound[/img]

(because only water evaporates remaining weight remains same)


=> We can infer that weight of X ( portion other than water) remains same
=> 1= (2/100)* W'
=> W' =50

Hence, B
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I solved two such questions in a row, and the only thing that was running in my mind was, does GMAT give such easy questions. I blindly answered 98!
Mirror mirror on the wall, who's the dumbest of them all?
ME!
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100 pound cucumbers are composed of 99% water & 1% rest i.e. 99 pound water & 1 pound rest

Assuming T as new weight of cucumbers post evaporation of water:
T pound cucumbers are composed of 98% water and 2% rest i.e. 0.98T pound water & 1 pound rest

Equating:
T = 0.98T + 1
0.02T = 1
T = 50
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