AbdurRakib wrote:
Max purchased a guitar for a total of $624,which consisted of the price of the guitar and the sales tax.Was the sales tax rate greater than 3 percent ?
(1) The price of the guitar that Max purchased was less than $602.
(2) The sales tax for the guitar that Max purchased was less than $30.
Target question: Was the sales tax rate greater than 3 percent? Given: Max purchased a guitar for a total of $624, which consisted of the price of the guitar and the sales tax. Statement 1: The price of the guitar that Max purchased was less than $602. Let's see what would happen if the sales tax were EXACTLY 3%
1% of $602 = $6.02
So, 3% of $602 ≈ $18
So with a sales tax of EXACTLY 3%, the tax would be $18
This means the TOTAL price would equal $602 + $18 =
$620 However, we're told that Max paid $624. Therefore,
the tax rate must be GREATER than 3% NOTE: we're actually told that the price of the guitar was less than $602. This doesn't matter. If the price of the guitar is less than $602, then getting the TOTAL cost to $624, would require an even greater sales tax.
So, we can be certain that
the tax rate is GREATER than 3% Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The sales tax for the guitar that Max purchased was less than $30. Let's test some possible cases.
Case a: the sales tax is $24. This means the pre-tax price = $624 - $24 = $600. We know that 1% of $600 is $6, which means 3% of $600 is $18. Since the actual sales tax (in this scenario) is $24, we can conclude that
the tax rate is GREATER than 3% Case b: the sales tax is $4. This means the pre-tax price = $624 - $4 = $620. We know that 1% of $620 is $6.20, which means 3% of $620 is $18.60. Since the actual sales tax (in this scenario) is $4, we can conclude that
the tax rate is LESS than 3% Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
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