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Math Expert V
Joined: 02 Sep 2009
Posts: 55802
Between the first day of May and last day in June, the price per kilog  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 57% (02:06) correct 43% (02:33) wrong based on 62 sessions

HideShow timer Statistics Between the first day of May and last day in June, the price per kilogram of Melange, a seasoning mix, first declined by 20 percent and then increased by 50 percent. During this same period, the price per liter of Blue, a spring water, first increased by 20 percent and then declined by 50 percent. If at the end of June, the prices were the same, then, at the beginning of May, the price per kilogram for Blue was what percent of the price per liter of Melange?

A. 2
B. 30
C. 50
D. 100
E. 200

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e-GMAT Representative D
Joined: 04 Jan 2015
Posts: 2904
Re: Between the first day of May and last day in June, the price per kilog  [#permalink]

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Solution

Given:
• The price of Melange first declined by 20% and then increased by 50%
• The price of Blue water first increased by 20% and then declined by 50%
• At the end, both the prices are same

To find:
• At the beginning, price of Blue water was what percent of the price of Melange

Approach and Working:
Assuming the initial price of Melange and Blue water was m and b respectively
• Price of Melange after two changes = m * 0.8 * 1.5 = 1.2 m
• Price of Blue water after two changes = b * 1.2 * 0.5 = 0.6 b

Given that, the end prices were same. Therefore,
• 1.2 m = 0.6 b
Or, $$\frac{b}{m} = \frac{1.2}{0.6} = 2$$
Or, $$\frac{b}{m} * 100 = 2 * 100 = 200%$$

Hence, the correct answer is option E.

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EMPOWERgmat Instructor V
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
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GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: Between the first day of May and last day in June, the price per kilog  [#permalink]

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Hi All,

We're told that a between the first day of May and last day in June, the price per kilogram of Melange, a seasoning mix, first DECLINED by 20 percent and then INCREASED by 50 percent and during this same period, the price per liter of Blue, a spring water, first INCREASED by 20 percent and then DECLINED by 50 percent. We're also told that at the end of June, the prices were the SAME. We're asked, at the beginning of May, the price per kilogram for Blue was what percent of the price per liter of Melange. This question can be solved in a couple of different ways, including by TESTing VALUES and a bit of Arithmetic.

IF... in May...
1 kg of Melange = $100 the 20% decline in price -->$100 - (.2)($100) = 100 - 20 =$80
the 50% increase in price --> $80 + (.5)($80) = 80 + 40 = $120 Using this final price of$120, we can 'work backwards' to figure out the price of Blue in May

Final price of Blue = $120 the 50% decline in price to END at$120 --> (.5)(X) = $120 --> X =$240
the 20% increase to get to $240 --> (1.2Y) =$240 --> Y = $200 In May, the price of 1 kg of Melange =$100 and the price of 1 liter of Blue = $200 200/100 = 2 = 200% the price Final Answer: GMAT assassins aren't born, they're made, Rich _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com *****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***** Rich Cohen Co-Founder & GMAT Assassin Follow Special Offer: Save$75 + GMAT Club Tests Free
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www.empowergmat.com/ Re: Between the first day of May and last day in June, the price per kilog   [#permalink] 27 Nov 2018, 22:58
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