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

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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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

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.

(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)

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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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 ?

I have no idea why I didn't attempt the problem this way. Thank you and +1 kudos!

U are calculating the sales tax percent on 642. It has to be calculated on the PRICE BEFORE THE SALEX TAX was applied.
Example - In ur statement one.. It should be Minimum sales tax percent = 23/601 * 100

@amanvermaggmat Thank you so much! I loved the way you explained it!

Responding to a pm:

Total = 624 = Guitar Price + Sales Tax

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

Let's say the price of the guitar is actually 602 which means tax is $22.
1% of 602 is 6.02 so 3% is $18.06.
In this case, the tax is already more than 3%.

If the price of the guitar is lower than 602, the tax will always be more than 3%.
Sufficient.

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

Let's say the sales tax was exactly $30. In that case, the price of guitar is $594
1% of 594 is 5.94 so 3% is about $18.
But the tax is $30 which is much more than 3%.

The tax is lower than $30. Say, it is $10. In that case, cost of guitar is $614 and the tax is less than 3%.

So here, the tax may be more than 3% or less than 3%.
Not sufficient.

Answer (A)
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GMATPrepNow

Hi Brent,

The $29 seems like a typo in the highlighted part to me. Should it not be be $24? Let us know if that is the case.

Warm Regards,
Pritishd
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Good catch. That was, indeed, a typo.
I have corrected the error.
Thanks!

Kudos for you!!!

Cheers,
Brent
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1) let price 601 (less than 602), so tax will be = 23
Rate = [23/601]*100
(23/6.01)= 3x+5.01 Sufficient.

2) if tax is 24 then [(24/600)*100 = 4 yes, but if tax is 20 then (17/600)*100: No.

Ans. A.
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624=P+T
is T>3% ? -> is T > 624*3% ~ 18
-> is P< 624-18=606

(1) P< 602 < 606 -> sufficient
(2) T< 30 -> T = 19 (Sufficient) or T =17 (insufficient)

-> choose A

Would this be the right way of approaching it?

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.

Assume price = 600

624 = 600 + 6t
t = 4

In fact, the smaller the price of the guitar, the larger the tax rate is.

Sufficient.

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

tp/100 < 30
p = 299, t = 1 NO
p = 75, t = 4 YES

Insufficient.
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Answer: Option A

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