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Max purchased a guitar for a total of $624,which consisted of the pric [#permalink]
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24 Jun 2017, 03:09
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Question Stats:
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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.
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Re: Max purchased a guitar for a total of $624,which consisted of the pric [#permalink]
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24 Jun 2017, 03:22
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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.
Solution:
Tricky one. Be aware of the trap.
Statement 1: First calculate what's 3% of 624. It is 3x6.24=18.72. The difference between C.P of guitar and Cost paid is 624602=22. Therefore it is clear that the sales tax rate is greater than 3%.
Statement 2: We don't know the exact value of the sales tax. Though it is lesser than 30, it can be lesser,equal or greater than 3%(18.72). Insufficient.
Therefore, the answer is Option A.



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Re: Max purchased a guitar for a total of $624,which consisted of the pric [#permalink]
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24 Jun 2017, 03:24
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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. (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 \(= \frac{23}{624}*100 = 3.6\)%.
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%.  I is Sufficient.
(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 \(= \frac{29}{624} * 100 = 4.6\)%
or
If sales price is $1. Sales price rate \(= \frac{1}{624} * 100 = 0.16\)%
(2) gives multiple values of sales price rate. II is Not Sufficient.
Only I alone is Sufficient. Answer (A)



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Re: Max purchased a guitar for a total of $624,which consisted of the pric [#permalink]
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03 Jul 2017, 04:48
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If price of guitar is P, and sales tax on it is S. Total price including sales tax = P + S = $624. We have to answer whether S > 3% of P or whether S > 0.03P
Statement 1. Lets say if P = $602, then with 3% sales tax, total price = 602 + 0.03*602 = 618.06, which is < 624 So that means even at price of 602, we need to apply sales tax of greater than 3% so as to reach the required amount of 624. Thus when the price is less than 602, definitely for every such case sales tax would need to be higher than 3% to reach the required amount of 624. Thus 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% Clearly the statement is not sufficient.
Hence A answer



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Re: Max purchased a guitar for a total of $624,which consisted of the pric [#permalink]
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17 Nov 2017, 12:40
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. 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: 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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Re: Max purchased a guitar for a total of $624,which consisted of the pric [#permalink]
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07 Jan 2018, 08:17
sashiim20 wrote: 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. (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 \(= \frac{23}{624}*100 = 3.6\)%.
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%.  I is Sufficient.
(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 \(= \frac{29}{624} * 100 = 4.6\)%
or
If sales price is $1. Sales price rate \(= \frac{1}{624} * 100 = 0.16\)%
(2) gives multiple values of sales price rate. II is Not Sufficient.
Only I alone is Sufficient. Answer (A)Though Answer is A, the sale tax is calculated on the price of guitar ie. 601 or less. It cant be calculated in total. Total = Price + sale tax. Am I wrong ?



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Re: Max purchased a guitar for a total of $624,which consisted of the pric [#permalink]
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12 Jan 2018, 08:54
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 pretax 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 pretax 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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Re: Max purchased a guitar for a total of $624,which consisted of the pric [#permalink]
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12 Mar 2018, 20:54
amanvermagmat wrote: If price of guitar is P, and sales tax on it is S. Total price including sales tax = P + S = $624. We have to answer whether S > 3% of P or whether S > 0.03P
Statement 1. Lets say if P = $602, then with 3% sales tax, total price = 602 + 0.03*602 = 618.06, which is < 624 So that means even at price of 602, we need to apply sales tax of greater than 3% so as to reach the required amount of 624. Thus when the price is less than 602, definitely for every such case sales tax would need to be higher than 3% to reach the required amount of 624. Thus 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% Clearly the statement is not sufficient.
Hence A answer I have no idea why I didn't attempt the problem this way. Thank you and +1 kudos!




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