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


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)
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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
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


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)
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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
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
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


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)
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KarishmaB Understood this part Maam, thanks a lot! :)
KarishmaB
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


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)
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