Bunuel
The sale price of an article is 25% more than its cost price. If the sale price is an integer, which of the following cannot be the cost price?
A. $60
B. $80
C. $100
D. $150
E. $200
Solution
Step 1: Understand Question Statement
• The sale price of an article is 25% more than its cost price.
• The sale price is an integer.
We need to find that out of the given options which one cannot be the cost price.
Step 2: Define Methodology
• Let us assume the sale price and cost price of the article (in dollars) as SP and CP, respectively.
o \(SP = CP + CP*\frac{25}{100}\)\( = CP*(1+\frac{25}{100}) =CP*\frac{125}{100} =CP*\frac{5}{4}\)
• Since, SP is an integer, so \(CP*\frac{5}{4}\) must be an integer.
o This means, CP must be a multiple of 4.
Now, we will check the options to see which one is not a multiple of 4.
Step 3: Calculate the final answer
• Option A: $60
o \(\frac{60}{4} =15\); So, it is a multiple of 4.
• Option B: $80
o \(\frac{80}{4} =20\); So, it is a multiple of 4.
• Option C: $100
o \(\frac{100}{4} =25\); So, it is a multiple of 4.
• Option D: $150
o \(\frac{150}{4} =\frac{75}{2 }\)which is not an integer. So, clearly 150 is not a multiple of 4.
• Option E: $200
o \(\frac{200}{4} =50\); So, it is a multiple of 4.
Therefore, out of the given options only 150 is not a multiple of 4.
Thus, the correct answer is
Option D.