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

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.

BrentGMATPrepNow · Accepted Answer

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

amanvermagmat · Answer

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

harikrish · 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.

ScottTargetTestPrep · Answer

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

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

KarishmaB · Answer

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)

GMATinsight · Answer

Answer: Option A

Video solution by  GMATinsight

https://www.youtube.com/watch?v=nnM8y6DOfKo

avigutman · Answer

Video solution from Quant Reasoning: Subscribe for more: https://www.youtube.com/QuantReasoning? ... irmation=1 https://www.youtube.com/watch?v=-qUYYiWHVjg

bumpbot · Answer

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

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