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Max purchased a guitar for a total of $624,which consisted of the pric

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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.
[Reveal] Spoiler: OA

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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 624-602=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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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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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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New post 17 Nov 2017, 11:40
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] 17 Nov 2017, 11:40
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