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.
Official Guide question
Answer: A
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Max purchased a guitar for a total of $624,
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jjjinapinch
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Given: Total price of the guitar, incl. sales tax = $624.jjjinapinch 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.
Official Guide question
Answer: A
We have to determine whether the rate of sales tax < 3%.
Statement 1: The price of the guitar that Max purchased was less than $602.
Let's test two extreme cases.
Case 1: Say the price, excl. tax = $100 (< $602), then S. T> = 624 - 100 = $524, thus rate of tax = (524/100)*100% = 524% > 3%. The answer is NO.
Case 2: Say the price, excl. tax = $600 (< $602), then S. T> = 624 - 600 = $24, thus rate of tax = (24/600)*100% = 4% > 3%. The answer is NO.
Sufficient!
Statement 2: The sales tax for the guitar that Max purchased was less than $30.
Let's test two extreme cases.
Case 1: Say tax = $1, then price, excl. tax = 624 - 1 = $623, thus rate of tax = (1/623)*100% = TOO less < 3%. The answer is Yes.
Case 2: Say tax = $24, then price, excl. tax = 624 - 24 = $600, thus rate of tax = (24/600)*100% = 4% > 3%. The answer is No.
Insufficient.
The correct answer: A
Hope this helps!
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Target question: Was the sales tax rate greater than 3 percent?jjjinapinch 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.
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 $29, 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
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Matt@VeritasPrep
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Let's rephrase the question. We know that
Guitar + Tax = 624
If we say the tax is p% of the guitar, we've got
Guitar * (1 + p%) = 624
or (1 + p%) = 624/Guitar
p% = (624/Guitar) - 1
From here, we can write the question as:
"Is 624/Guitar - 1 > .03"?
S1 tells us the guitar cost less than $602. That means that our sales tax must be greater than whatever it would have been if we paid exactly $602. Plugging in $602, we get
$624/$602 - 1 > 3.5%
So we MUST have paid more than 3.5%, and S1 is SUFFICIENT!
As for S2, try numbers. If the tax = $1, then it's less than 3%. If the tax = $29, then it's more. That's a contradiction, so S2 is NOT SUFFICIENT.
Guitar + Tax = 624
If we say the tax is p% of the guitar, we've got
Guitar * (1 + p%) = 624
or (1 + p%) = 624/Guitar
p% = (624/Guitar) - 1
From here, we can write the question as:
"Is 624/Guitar - 1 > .03"?
S1 tells us the guitar cost less than $602. That means that our sales tax must be greater than whatever it would have been if we paid exactly $602. Plugging in $602, we get
$624/$602 - 1 > 3.5%
So we MUST have paid more than 3.5%, and S1 is SUFFICIENT!
As for S2, try numbers. If the tax = $1, then it's less than 3%. If the tax = $29, then it's more. That's a contradiction, so S2 is NOT SUFFICIENT.
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We are given that Max purchased a guitar for a total of $624, which was the price of the guitar and the sales tax. If we let the price of the guitar = p and n = the tax rate, then we have:jjjinapinch 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.
624 = p + (n/100)p
624 = p(1 + n/100)
624 = p[(100 + n)/100]
62,400 = p[(100 + n)
62,400/(100 + n) = p
We need to determine whether n > 3.
Statement One Alone:
The price of the guitar that Max purchased was less than $602.
Since p < 602 and 62,400/(100 + n) = p, we have:
62,400/(100 + n) < 602
62,400 < 60,200 + 602n
2,200 < 602n
2,200/602 ≈ 3.65 < n
Since n is greater than 3.65, the sales tax is greater than 3%.
Statement Two Alone:
The sales tax for the guitar that Max purchased was less than $30.
Statement two alone is not sufficient to answer the question. For instance, if the tax was $0, then the tax rate was less than 3%; however, if the tax was $24, the price of the guitar would be $600, and the tax rate would be 24/600 = 4/100 = 4%, which is greater than 3%.
Answer: A
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Target question: Was the sales tax rate greater than 3 percent?jjjinapinch 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.
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 $29, 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
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Brent
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