A store calls the original price of an item the X-level price.

Question

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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DiaPro · Answer

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.

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SaquibHGMATWhiz · Answer

Solution:

let the X level price be  p  
 So, Y level price  =0.7p  
 And Z level price  =0.8	imes 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}	imes 100=a 
 ⇒\frac{0.14}{0.7}	imes 100 
 ⇒20\%  which is in between 0 and 30 
 Thus this  must be true

Hence the right answer is    Option D

mcrea · Answer

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%?

Kinshook · Answer

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

A store calls the original price of an item the X-level price.

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A store calls the original price of an item the X-level price.

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