Maya bought a framed print at an art gallery and paid a total of $96.

Question

Maya bought a framed print at an art gallery and paid a total of $96. If the $96 total consisted of the pre-tax price of the framed print plus sales tax on that pre-tax price, was the sales tax rate less than 20%?

(1) The pre-tax price of the framed print was less than $80.

(2) The sales tax Maya paid on the framed print was less than $19.20.

M47-202

Bunuel · Accepted Answer

GMAT Club Official Solution:

Maya bought a framed print at an art gallery and paid a total of $96. If the $96 total consisted of the pre-tax price of the framed print plus sales tax on that pre-tax price, was the sales tax rate less than 20%?

Let P be the pre-tax price of the framed print, and let T be the sales tax.

Since Maya paid $96 total:

P + T = 96

The question asks whether T/P < 0.20.

(1) The pre-tax price of the framed print was less than $80.

This gives P < 80. Since P + T = 96, we have T > 16. So:

T/P > 16/80 = 0.20

Therefore, the sales tax rate was not less than 20%.

Sufficient.

(2) The sales tax Maya paid on the framed print was less than $19.20.

This is not enough.

For example, if T = 1, then P = 95, and the tax rate is 1/95, which is less than 20%.

But if T = 18, then P = 78, and the tax rate is 18/78, which is greater than 20% because 20% of 78 is 15.6, and 18 > 15.6.

Not sufficient.

Answer: A.

vasu1104 · Answer

total paid = 96
pre tax + tax = 96

assume pre tax = p
tax rate = t%

find : t < 20%

S-1
here max p < 80.
now lets find the the min limit of t with the help of p.
if p =80

80+80t/100 = 96

80t/100 = 16
t = 20.
when p 80, t can be 20%

but the moment the value of p starts to decrease, the value of t goes up to compensate on that so that final amount will be 96.

so t will be greater than 20%. 
this is sufficient.

S-2

pt/100 < 19.20
from here we can find both pre tax price and tax rate.

lets consider max price of 19.20 as tax price.

p+19.20 = 96
p = 76.80 
p will be always greater than 76.80.

now we can find tax rate from this value of p.

19.20 is what percent of 76.80
19.20 = (t/100) 76.80

t = 25.
so t can be utmost 25%.

so as the price of p goes up, the tax value goes down and hence tax rate goes down.

but here our max tax rate is 25% so it can be or can not be less than 20%.
we get yes or no for this.

so not sufficient.

only A

GulfTube · Answer

Let P = pre-tax price of item and t = tax.
Given =>
P+t = 96
P=96-t
Is t/P*100<20?
t<0.2*P
t<0.2*(96-t)
t<16?

i) P<80,
96-t<80
t>16 sufficient.

ii) t<19.2, since t could also be anything between 16 and 19.2, it is not sufficient.

answer A

SS990 · Answer

GIven: Item post tax=96
to find: if tax rate t<20% for item with pretax price p

Deduction: if t=20% then 1.2p=96 so p=80..if p>=80 then t<=20%

1) p<80..so we know that t>20% hence sufficient

2) tax=19.2 but we dont know p or t hence insufficient

so answer is A

Maya bought a framed print at an art gallery and paid a total of $96.

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Maya bought a framed print at an art gallery and paid a total of $96.

Prep Toolkit

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