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Bunuel
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A store calls the original price of an item the X-level price.   24 Jan 2023, 02:30
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

85% (hard)

Question Stats:

57% (03:21) correct 43% (03:43) wrong based on 81 sessions

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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?

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

II. 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.

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

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III




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D
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A store calls the original price of an item the X-level price.   24 Jan 2023, 07:09
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Option D it seems

Statement 1 is clearly incorrect
Statement 2 is true as difference ~ $12
Statement 3 is true by % change formula ~ 25% < 30.

Thus option D.

Posted from my mobile device
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A store calls the original price of an item the X-level price.   10 Mar 2023, 01:13
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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?
I. The X-level price of the item is less than $86.00.
II. 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.
III. The Y-level price of the item is a percent greater than the Z-level price of the item, where \(0 < a < 30\).
A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III
Solution:

  • let the X level price be \(p\)
  • So, Y level price \(=0.7p\)
  • And Z level price \(=0.8\times 0.7p=0.56p\)
  • According to the question, \(0.56p<49\) or \(p<87.5\)

    I. The X-level price of the item is less than $86.00
  • We know \(p<87.5\) so the value of p can be 87
  • Thus this must not be true

    II. 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
  • \(0.7p-0.56p<16\)
    \(⇒0.14p<16\)
    \(⇒p<114.xx\)
  • We know \(p<87.5\)
  • Thus this must be true

    III. The Y-level price of the item is a percent greater than the Z-level price of the item, where \(0 < a < 30\)
  • \(\frac{0.7p-0.56p}{0.7p}\times 100=a\)
    \(⇒\frac{0.14}{0.7}\times 100\)
    \(⇒20\%\) which is in between 0 and 30
  • Thus this must be true

Hence the right answer is Option D
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A store calls the original price of an item the X-level price.   04 Aug 2024, 10:53
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Bunuel
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?
I. The X-level price of the item is less than $86.00.
II. 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.
III. The Y-level price of the item is a percent greater than the Z-level price of the item, where \(0 < a < 30\).
A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III
Solution:

  • let the X level price be \(p\)
  • So, Y level price \(=0.7p\)
  • And Z level price \(=0.8\times 0.7p=0.56p\)
  • According to the question, \(0.56p<49\) or \(p<87.5\)

    I. The X-level price of the item is less than $86.00
  • We know \(p<87.5\) so the value of p can be 87
  • Thus this must not be true

    II. 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
  • \(0.7p-0.56p<16\)
    \(⇒0.14p<16\)
    \(⇒p<114.xx\)
  • We know \(p<87.5\)
  • Thus this must be true

    III. The Y-level price of the item is a percent greater than the Z-level price of the item, where \(0 < a < 30\)
  • \(\frac{0.7p-0.56p}{0.7p}\times 100=a\)
    \(⇒\frac{0.14}{0.7}\times 100\)
    \(⇒20\%\) which is in between 0 and 30
  • Thus this must be true

Hence the right answer is Option D
­
even though it doesnt change the answer, isn't the III. 0.7p-0.56p/0.56p = 25% instead of 0.7p-0.56p/0.7p = 20%?­
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A store calls the original price of an item the X-level price.   04 Aug 2024, 23:10
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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?

Y = (100%-30%)X = .7X
Z = (100%-20%)Y = .8Y = .8*.7X = .56X
Z = .8Y = .56X < $49
.8Y < 49; Y< 49/.8 = 61.2; Y < $61.2
.56X < 49; X < $87.5

I. The X-level price of the item is less than $86.00.
X-level price of the item can be $87 < $87.5
NOT NECESSARILY TRUE

II. 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.
Y - Z = .8X - .56X = .24X < .24*49 < 11.76 < $16
MUST BE TRUE

III. The Y-level price of the item is a percent greater than the Z-level price of the item, where \(0 < a < 30\).
Y/Z = .7X/.56X = 70/56 = 1.25; a = 25% ; 0<a=25<30
MUST BE TRUE

A. I only
B. III only
C. I and II only
D. II and III only
E. I, II and III

IMO D
­
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