Kesha paid a sales tax of x percent on her purchase. If the sales tax

Question

Kesha paid a sales tax of x percent on her purchase. If the sales tax had only been 2 percent, she would have paid $27 less in sales tax on her purchase. What was the value of x if the total amount Kesha paid for her purchase, including sales tax, was $486?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 4

(A) 8
(B) 7
(C) 6
(D) 5
(E) 4

nisen20 · Accepted Answer

if the total amount, including tax, was just 486, price before tax must be less than 486.

price before tax = p
(A) 8    →   0.06p = 27   →   p = 450   you got it
(B) 7    →   0.05p = 27   →   P = 540   not a chance
(C) 6   not a chance
(D) 5   not a chance
(E) 4   not a chance

KarishmaB · Answer

Here is a  one minute video solution  without using any variables for this question.

MrWhite · Answer

Let A be the purchase price excluding sales tax.

Given,  A(1+x) = $486

Therefore,  A = \frac{$486}{(1+x)}  (Equation 1)

Given,  Ax - \frac{A*2}{100} = $27  (Equation 2)

Therefore substituting equation 1 in equation 2,  \frac{($486*x)}{(1+x)} - \frac{$486*2}{ } = $27

On Solving,  x = 0.08  
=> x = 8%

(A)

I was wondering if there are any other efficient ways of solving these types of percent problems which involve variables.

Anki111 · Answer

On such questions, back-solving can help. As formulating equation in a time crunch can lead to errors costing a question.
So, if you take each option and check, you will notice that the difference between 2% and the percentage options given, there is only one that can be an answer that is option A. 8%-2% i.e 6% of 486(it will be less than 486 excluding the sales tax), but still it will come 29.16. All other options, are way less than 27.

gmatophobia · Answer

Assume that the price of the item without sales tax =  p

if the total amount Kesha paid for her purchase, including sales tax, was  $486

p  = 486

If the sales tax had only been  2  percent, she would have paid  $27  less in sales tax on her purchase

p  - p  = 27

486 - p  = 27

486 - 27 = p

p = \frac{459*100}{102}

\frac{459*100}{102}  = 486

= \frac{486 * 102}{459 * 100}

\frac{x}{100} = \frac{486 * 102}{459 * 100}-1

x = \frac{3672}{459}

x = 8

Option A

tickledpink001 · Answer

hi, how were you able to get to 3672 as the numerator- did you multiply them out or is there a faster way?

Regor60 · Answer

There is a way that avoids significant multiplication.

The first two statements are equivalent to:

2P/100 + 27 = PX/100

Since we're solving for X, eliminate P:

P(X-2)/100 = 27, so:

P = 2700/(X-2)

The third statement says:

P(1+ X/100) = 486.

Substituting for P:

(2700/(X-2))*((100+X)/100) =486

This reduces to:

486 = (2700+27X)/(X-2)

Expanding this out:

486X-972 = 2700+27X, or

459X = 3672 and

X = 3672/459

Now, doing this division precisely isn't required.

Multiplying 7 by 460 is 32 hundred something , so 7 is too small.

Multiplying 8 by 460 is 36 hundred something, which is close to the numerator, so 8 is the correct answer.

Posted from my mobile device

sayan640 · Answer

Hey   gmatphobia  , did you multiply 486∗102  ?

sayan640 · Answer

Can you please elaborate this short method ?  gmatphobia   GMATNinja   Bunuel   KarishmaB

sayan640 · Answer

Lets say , the purchase amount = P
P*(1+x/100) = 486---------- eqn (1)

P*x/100 - p*2/100 = 27-----------------------eqn(2)
Add p on both sides of eqn 2 ,

p + p*x/100 -p*2/100 = 27 +p
486 - 27 = p + 2*p/100 ...... ( Replacing P*(1+x/100) = 486 )
102p/100 = 459
p=450

Use it on eqn (2),
(p/100) * (x-2)=27
450/100 * (x-2) = 27
x = 8

Yes2GMAT · Answer

nisen20  That was amazing.

hemanthPA · Answer

I got this in one of my mocks and here is how i approached it,

Given:
486 = C + (Ct/100)
486-27 = C+(2*C/100)
27 = C*(t-2)/100

459 = (100C+2C)/100
459 = 102C/100 = 51C/50
C = 459*50/51 = 9 * 50 = 450
C = 450

Now,
27 = C*(t-2)/100
27 = (450t – 900)/100
2700 = 450t – 900
450t = 3600
t = 360/45 = 40/5 = 8

t=tax, C=cost

C'est tout!

anirchat · Answer

This is not a question where you wanna solve tedious equations.

So, I tried option elimination.

Of the options, let us choose the mdidle one first 6 %. 
Now if x = 6%, x-2 = 4% and 4% of the sale price is equal to 27$. From this we can find the sale price = 675$, which is way greater thah 486. So we understand x=6 or any value <6 cannot be the answer.

We are now only left with 7 & 8.

Using the same logic with 7 , we find out that sale price is 540 $ , which is > than 486$. So the only option left is 8% which is the answer.

RheaChen · Answer

Purchase amount  including sale tax(x%)=486.
 Purchase amount including sale tax if tax rate is 2%=  *1.02 
 As we know that difference is 27 and the equation would be 486-  *1.02 =27 
 x would be 8.

juliansorre · Answer

A quick solution is as follows:

s*(2/100) = (x*s)/100 - 27 (1)

s + (x*s)/100=486 (2) => (x*s)/100 = 486-s (3)

Substituting (3) in (1):

0.02s = 486-s - 27
Solving for s:

1.02s = 459 => s = 450

Replacing s= 450 in (2)

450 + (450*x)/100 = 486 
(450*x)/100 = 36
450x = 3600
x = 360/45 = 8

Answer: 8

shubhim20 · Answer

For 27 less will the whole amount be 27 less or just sales tax calculated would be 27 less  Bunuel   KarishmaB

Krunaal · Answer

The sales tax calculated will be $27 less, and consequently the whole amount will be $27 less. Final Price = Item's price + Sales Tax, if Sales tax decreases by $27, so will the final price.

KarishmaB · Answer

We are given "$27 less in sales tax" which means she would have reduced her sales tax by $27. I have explained this question here: https://www.youtube.com/shorts/4fPAxkPzxhA

MartyMurray · Answer

Kesha paid a sales tax of x percent on her purchase. If the sales tax had only been 2 percent, she would have paid $27 less in sales tax on her purchase. What was the value of x if the total amount Kesha paid for her purchase, including sales tax, was $486?

(A) 8
(B) 7
(C) 6
(D) 5
(E) 4

Amount paid:  486

Amount  27  less:  486 - 27 = 459

Amount before  2  percent tax:  \frac{459}{1.02} = 450

Actual amount of tax:  486 - 450 = 36

Value of x:  \frac{36}{450} × 100 = 8   percent

(A) 8
(B) 7
(C) 6
(D) 5
(E) 4

Correct answer:   A

Kesha paid a sales tax of x percent on her purchase. If the sales tax

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Kesha paid a sales tax of x percent on her purchase. If the sales tax

Prep Toolkit

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