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The original price of a camera was displayed as a whole

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The original price of a camera was displayed as a whole

by Gmat_mission » Sun May 06, 2018 11:02 am

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The original price of a camera was displayed as a whole dollar amount. After adding sales tax of 10 percent, the final price was also a whole dollar amount. Which of the following could be the final price of the camera?

A. $207
B. $209
C. $211
D. $213
E. $215

[spoiler]OA=B[/spoiler].

What is the equation that helps me to solve this PS question? I'd appreciate any help. Thanks. <i class="em em-disappointed"></i>
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by deloitte247 » Sat May 12, 2018 2:02 pm
Let the original price of the camera be 'x', and 'y' be the final price after 10% tax increment.
=> y = x + 10% of x
or y = x + 0.1x = 1.1x =>
$$x\ =\ \frac{y}{1.1}$$
We can get the value of y that will give x as a whole dollar amount by trying out all options given.
Trying y = $207,
$$x\ =\ \frac{207}{1.1}=188.1818...$$

Nah, that's not a whole number.
let's try y = $209,
$$x\ =\ \frac{209}{1.1}=190$$
That is a whole number.
Similarly trying the remaining options, we'll find out that they don't give whole number values of x.
So only y = $209 gives whole value of $190.
Option B is the correct answer.
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by [email protected] » Sun May 13, 2018 11:51 am
Hi Gmat_mission,

We're told that the original price of a camera was displayed as a whole dollar amount and after adding sales tax of 10 percent, the final price was ALSO a whole dollar amount. We're asked which of the following COULD be the final price of the camera. This question is based on a Number Property rule and can be solved with a bit of 'brute force.'

To start, the only way to increase an integer by 10% and END with an integer is if the starting integer is a multiple of 10:
0 + (10% of 0) = 0
10 + (10% of 10) = 11
20 + (10% of 20) = 22
30 + (10% of 30) = 33
Etc.

If you perform that calculation with a number that is NOT a multiple of 10, then you WON'T end up with an integer:
5 + (10% of 5) = 5.5

Thus, the original price of the camera MUST be some multiple of $10. Since the Answer Choices are relatively 'close' together - and a little greater than $200 - the original price of the camera must be a little LESS than $200 (since $200 + 10% of $200 = $220, which is a little bigger than all 5 answer choices). Let's TEST the closest multiple of 10 that's LESS than 200....

IF... original price = $190, then...
the tax = 10% of $190 = $19...
and the total price = $190 + $19 = $209

Final Answer: B

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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