Max Purchased a Guitar for a Total of $624, Which Consisted of the Price of the Guitar and the Sales Tax.

Question: 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.

(A) Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
(B) Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
(C) BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
(D) EACH statement ALONE is sufficient.
(E) Statements (1) and (2) TOGETHER are not sufficient.

“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 ?” – is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book "GMAT Quantitative Review". GMAT Quant section consists of a total of 31 questions. GMAT Data Sufficiency questions consist of a problem statement followed by two factual statements. GMAT data sufficiency comprises 15 questions which are two-fifths of the total 31 GMAT quant questions.

Approach Solution 1

Given: Max purchased a guitar for a total of $624, which consisted of the price of the guitar and the sales tax.

We need to find out:
Was the sales tax rate greater than 3 percent?

We will check each statement one by one to find out if they are sufficient.

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 exactly 3% sales tax, 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 us 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 which means the pre-tax price = $624 - $4 = $620.
So, 1% of $620 is $6.20 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 isnot sufficient.

Hence, the correct option is A.

Approach 2

Let us consider the price of guitar is P, and sales tax on it is S.
Hence, total price including sales tax = P + S = $624.
However, we need to know whether S > 3% of P or whether S > 0.03P

Let us check both the statements:

Statement 1.
Lets say if P = $602,
In that case, with 3% sales tax, total price = 602 + 0.03*602 = 618.06
This is < 624
This means that even at price of 602, sales tax of greater than 3% has to be applied, so as to reach the required amount of 624.
So when the price is less than 602, sales tax would need to be higher than 3% to reach the required amount of 624. Thus the statement is sufficient.

Statement 2. Sales tax is < $30. Sales tax could be $4, thus P = $620, here tax is < 3%
But sales tax could be $24, thus P = $600, here tax is > 3%
Hence, the statement is not sufficient.

So A is the correct answer.

Approach 3

Statement 1) The price of the guitar that Max purchased was less than $602.

Maximum price of guitar can be 601. therefore sales tax price would be
624−601=23

Minimum sales tax percent = 23/624 *100 = 3.6%
Any reduction in the price of guitar will increase the sales tax price, ie; numerator will increase and hence the sales tax percent will also increase.

Therefore sales tax rate is greater than 3%. ------ Statement 1 is Sufficient.

Statement 2) The sales tax for the guitar that Max purchased was less than $30.

Maximum sales price would be $29 (less than $30). Therefore Sales price rate
= 29/624 *100 = 4.6%--------- Statement 2 is not sufficient

Hence, A is the correct answer.

Correct Answer: A

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