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A store calls the original price of an item the X-level pric [#permalink]
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Carcass wrote:
A store calls the original price of an item the X-level price. The store reduces the X-level price of an item by 30%, resulting in what the store calls the Y-level price of the item. The store then reduces the Y-level price of the item by 20%, resulting in what the store calls the Z-level price of the item. The Z-level price of the item is less than $ 49. Which of the following statements must be true?

Indicate all such statements.

A. The X-level price of the item is less than $ 86.00.

B. When the Z-level price of the item is subtracted from the Y-level price of the item, the result is less than $ 16.00.

C. The Y-level price of the item is a percent greater than the Z-level price of the item, where \(0 < a < 30\)


X-level price = \(x\)
Y-level price = \(0.7x\)
Z-level price = \((0.8)(0.7x) = 0.56x\)

Now,
\(0.56x < 49\)
\(x < 87.5\)

A. The X-level price of the item is less than $ 86.00 - NO
It is less than $87.50, but how much - we have no idea!
It might be $87 or $80

B. When the Z-level price of the item is subtracted from the Y-level price of the item, the result is less than $ 16.00 - YES
\(0.70x - 0.56x = 0.14x = 0.14(87.50) =\) $12.25

C. The Y-level price of the item is \(a\) percent greater than the Z-level price of the item, where \(0 < a < 30\) - YES
\(\frac{Y}{Z} = \frac{(0.70x)}{(0.56x)} = 1.25\), which means it is \(25\)% greater

Hence, option B and C
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Re: A store calls the original price of an item the X-level pric [#permalink]
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Why would this be equal?

Now,
0.56x=49 0.56x=49
x=87.5x=87.5


Shouldnt it be 0.56x<$49?
Therefore x<$87.5? And this statement 1 is correct?
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Re: A store calls the original price of an item the X-level pric [#permalink]
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GJSKGJ wrote:
Why would this be equal?

Now,
0.56x=49 0.56x=49
x=87.5x=87.5


Shouldnt it be 0.56x<$49?
Therefore x<$87.5? And this statement 1 is correct?


GJSKGJ
Thank you for pointing out the mistake.
I have made the necessary changes in the explanation as well. Let me know If you still have any doubt
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A store calls the original price of an item the X-level pric [#permalink]
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The following is the EASIEST way to solve this problem.

Option-1:
28 ≡ 49
50 ≡ 87.5 Thus False.

Option-2:
28 ≡ 7
49 ≡ 12.25 Thus True.

Option-3: [Applying the most popular percent change fomula]
(35-28)/28 *100% = 25% Thus True.

To see my other solutions click here: https://gre.myprepclub.com/forum/member ... 37770.html
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