nick13
Ken bought a shirt at a price of D dollars, to which a sales tax of p percent was added. He paid with a 20-dollar bill and received less than C dollars in change. Was the price of the shirt, without taxes, more than 15 dollars?
1. p=6
2. c=5
Given- Price of shirt without tax = $ \(D\)
- Sales Tax = \(p\) %
- Change < $\(C\)
Let's visualize this information on a number line. As Ken received a change, we can conclude that the price of the shirt (including taxes) is less than 20. Hence the price lies to the left of 20 on a number line as shown below-
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Screenshot 2023-10-26 010727.png [ 15.51 KiB | Viewed 14332 times ]
Question: Is \(D > $15\)
Inference: The question wants us to find if D lies to the right of 15
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Screenshot 2023-10-26 011134.png [ 14.72 KiB | Viewed 14245 times ]
Statement 11. p=6Without knowing the change received, we can have multiple possibilities as shown below. In one case, the cost price of the shirt is less than $15, and in the other case, the cost price of the shirt is greater than $15. Hence, the statement alone is not sufficient.
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Screenshot 2023-10-26 011543.png [ 20.03 KiB | Viewed 13999 times ]
Eliminate A and D.
Statement 22. c=5This statement tells us that, the price of the shirt including taxes is greater than $15. However, we can have multiple possible values depending on the percentage of the tax applied. Hence, the statement alone is not sufficient.
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Screenshot 2023-10-26 012222.png [ 25.42 KiB | Viewed 13861 times ]
CombinedThe statements combined give us the following information
p = 6
c = 5
Assume,
D = $15 → 1.06 * D = $15.90 ⇒ In this case, The response to the question "Was the price of the shirt, without taxes, more than 15 dollars?" is
NoD = $15.01 → 1.06 * D \(\approx\) $15.90 ⇒ In this case, The response to the question "Was the price of the shirt, without taxes, more than 15 dollars?" is
YesAs we are getting contradicting answers, we can conclude that the statements combined do not help either.
Option E