Ken bought a shirt at a price of D dollars, to which a sales tax of p

Question

Ken bought a shirt at a price of D dollars, to which a sales tax of p percent was added. He paid with a 20-dollar bill and received less than C dollars in change. Was the price of the shirt, without taxes, more than 15 dollars?

(1) p = 6
(2) c = 5

(1) p = 6
(2) c = 5

stne · Accepted Answer

Ken's total amt can be represented by =  (\frac{100+P}{100})*d

We need to know whether  d > 15

1. p=6

Thus we know total amt  = 1.06*d

However we still cannot find d

INSUFF.

2. c=5

Now we know

(\frac{100+P}{100})*d > 15

However we still cannot find d

INSUFF.

1+2

1.06*d> 15

d > 14.15

Hence we still cannot answer the stem.

INSUFF.

Ans E

Hope it helps.

gmatophobia · Answer

Given Price of shirt without tax = $ D Sales Tax = p % Change < $ C Let's visualize this information on a number line. As Ken received a change, we can conclude that the price of the shirt (including taxes) is less than 20. Hence the price lies to the left of 20 on a number line as shown below- Screenshot 2023-10-26 010727.png Question : Is D > $15 Inference : The question wants us to find if D lies to the right of 15 Screenshot 2023-10-26 011134.png Statement 1 1. p=6 Without knowing the change received, we can have multiple possibilities as shown below. In one case, the cost price of the shirt is less than $15, and in the other case, the cost price of the shirt is greater than $15. Hence, the statement alone is not sufficient. Screenshot 2023-10-26 011543.png Eliminate A and D. Statement 2 2. c=5 This statement tells us that, the price of the shirt including taxes is greater than $15. However, we can have multiple possible values depending on the percentage of the tax applied. Hence, the statement alone is not sufficient. Screenshot 2023-10-26 012222.png Combined The statements combined give us the following information p = 6 c = 5 Assume, D = $15 → 1.06 * D = $15.90 ⇒ In this case, The response to the question "Was the price of the shirt, without taxes, more than 15 dollars?" is No D = $15.01 → 1.06 * D \approx $15.90 ⇒ In this case, The response to the question "Was the price of the shirt, without taxes, more than 15 dollars?" is Yes As we are getting contradicting answers, we can conclude that the statements combined do not help either. Option E

tuyaras · Answer

For (2) c = 5, doesn't that mean price of the shirt = $15+?

Let's say you pay $20 and get the change back = $5 so the price of the shirt even without tax = 15?
Or is it because "less than" which is not "not more than" so you will never get the change back = $5 ?

vaishmahe · Answer

KarishmaB   chetan2u  Can you please post an explanation to this question?

KarishmaB · Answer

Given: D + p% of D > 20 - C

Is D > $15?

(1) p = 6

1.06D > 20 - C
If C = 1, D > 15
If C = 10, D could be 15
Not sufficient alone.

(2) c = 5

D + p% of D > 15
But is D > 15? We cannot say. 
D could be 10 and p could be 100% so D < 15
D could itself be greater than 15.

Using both , we know,

D + 6% of D > 15
1.06D > 15

Still, D could be 14.9 and this inequality will hold. 
D could be 16 and this inequality will hold. 
So D could be less than or greater than 15.

Answer (E)

ragnarok13 · Answer

KarishmaB  Ma'am, for statement 2 :

"(2) c = 5

D + p% of D > 15 "

D > 15 / (1 + p/100) and due to this D will always be less than 15. So statement 2 is sufficient in saying that d will not be greater than 15. (Unless p = 0 %)

Am I missing something in my understanding. Please help. Thanks.

KarishmaB · Answer

You got:  
 D > 15 / (1 + p/100)

Say we put p = 100 and get

D > 15/2 i.e. D > 7.5

How can we say that D is less than 15? All this tells me is that D is certainly greater than 7.5. It could be 8 or 10 or 20 or 500 etc.

ragnarok13 · Answer

KarishmaB Understood this part Maam, thanks a lot!

ManishaPrepMinds · Answer

Total price paid = d + (p/100)·d = d(1 + p/100)
Change received = 20 – total price = 20 – d(1 + p/100)
We are told: 20 – d(1 + p/100) < c → d(1 + p/100) > 20 – c
Is d > 15?

Statement (1): p = 6
We now have:
d(1 + 6/100) > 20 – c
⇒ 1.06d > 20 – c
But we don’t know c
Not sufficient

Statement (2): c = 5
We now have:
d(1 + p/100) > 15
But we don’t know p
Not sufficient

Statements (1) and (2) Together:
We now know:
p = 6, c = 5
d(1.06) > 15
⇒ d > 15 / 1.06
Since denominator > 1 → the fraction is < 15
→ So d could be just below or above 15

Insufficient together
ANSWER: E

nick13

Ken bought a shirt at a price of D dollars, to which a sales tax of p percent was added. He paid with a 20-dollar bill and received less than C dollars in change. Was the price of the shirt, without taxes, more than 15 dollars?

(1) p = 6
(2) c = 5

bumpbot · Answer

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Ken bought a shirt at a price of D dollars, to which a sales tax of p

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