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Each of the cucumbers in 100 pounds of cucumbers is composed

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etdenlinger

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08 Mar 2016, 06:28

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Let w equal the amount of water in pounds
(98 / 100) = w / (1+w) where (1+w) is the weight of the cucumber in pounds
Solve for w.
w = 49 pounds of water
49 pounds of water + 1 pounds of non-water = 50 pounds of cucumber

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13 Mar 2016, 20:58

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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

Let w1 pounds of water evaporate.

New weight of water = 99-w1 --- (1)
New weight of water is also= 98% of (100-w1) -- (2)

Equating 1 and 2, w1=50 pounds. New weight of cucumber = 100-50=50 pounds

Mathivanan Palraj

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13 Mar 2016, 21:15

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shrive555

In 100 pounds, 99 pounds are water that makes 99% water content; the ratio is 99:1
To get 98% water content, the ratio has to be 98:2; that is possible only if it is reduced to 49:1
That implies 50 pounds are evaporated.

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09 Apr 2018, 16:33

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shrive555

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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16 Mar 2019, 08:35

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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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16 Mar 2019, 08:45

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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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22 Jun 2019, 22:59

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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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09 Aug 2019, 20:16

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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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29 Jan 2020, 03:27

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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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27 Feb 2022, 23:18

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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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21 May 2022, 04:21

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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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23 May 2022, 09:09

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shrive555

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

RastogiSarthak99

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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

[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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04 Jun 2024, 11:28

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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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