Between the first day of May and last day in June, the price

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BTGmoderatorLU: Moderator; Posts: 2505; Joined: Sun Oct 15, 2017 1:50 pm; Followed by:6 members

Between the first day of May and last day in June, the price

by BTGmoderatorLU » Thu Jul 11, 2019 3:51 pm

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Source: Princeton Review

Between the first day of May and the 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

The OA is E

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Source: Beat The GMAT — Problem Solving | Thu Jul 11, 2019 3:51 pm

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by GMATGuruNY » Thu Jul 11, 2019 4:19 pm

BTGmoderatorLU wrote:Source: Princeton Review

Between the first day of May and the 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

We can PLUG IN THE ANSWERS.
When the correct answer is plugged in, Blue's resulting price and Melange's resulting price will be EQUAL.

D: 100
Here, Blue's initial price is 100% of Melange's initial price, implying that the two initial prices are equal.
Let Blue = May = $100.
From May to June:
Blue's $100 initial price increases by 20% to $120 and then decreases by 50% to $60.
Melange's $100 initial price increases by 50% to $150 and then decreases by 20% to $120.
In this case, Blue's resulting price is LESS THAN Melange's resulting price.
Implication:
For the two resulting prices to be equal, Blue's initial price must be a higher percentage of Melange's initial price.

The correct answer is E.

Algebra:

Blue increased by 20 percent and then declined by 50 percent.
B * 120/100 * 50/100 = B * 6/5 * 1/2 = (3/5)B.
Melange declined by 20 percent and then increased by 50 percent.
M * 80/100 * 150/100 = M * 4/5 * 3/2 = (6/5)M.
Since the two resulting prices are equal, we get:
(3/5)B = (6/5)M
3B = 6M
B = 2M
Since B is twice the value of M, Blue's initial price is equal to 200% of Melange's initial price.

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by Scott@TargetTestPrep » Fri Jul 12, 2019 5:54 pm

BTGmoderatorLU wrote:Source: Princeton Review

Between the first day of May and the 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

The OA is E

We can let the price per kilogram of Melange and price per liter of Blue at the beginning of May be m and b, respectively. We can create the equation:

w x 0.8 x 1.5 = b x 1.2 x 0.5

1.2w = 0.6b

2w = b

Since b = 2w, b is 200% of w.

Answer: E

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