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by Strongt » Mon May 23, 2011 1:05 pm
Dinner cost $230 including a 15% tip.
How much was dinner without the
tip?

My answer is 195.5

OA is
Answer: $200
If $230 includes the cost of the dinner plus an additional
15%, then it is 115% of the cost of the dinner, so 230 =
(115/100)x.
x 200 = x[/spoiler]
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by Ian Stewart » Mon May 23, 2011 1:17 pm
Strongt wrote:Dinner cost $230 including a 15% tip.
How much was dinner without the
tip?

My answer is 195.5

OA is
Answer: $200
If $230 includes the cost of the dinner plus an additional
15%, then it is 115% of the cost of the dinner, so 230 =
(115/100)x.
x 200 = x[/spoiler]
If you arrived at the answer 195.5, you've answered the wrong question - you've reduced $230 by 15%. The 15% in this question is not applied to the $230 at all; it's applied to the original cost of the dinner before the tip. We know that if we add 15% to the cost of the dinner, we get to $230, so if the dinner cost $d before the tip, the dinner cost $(1.15)d after the tip. That leads you to the equation

(1.15)d = 230
d = 200

It is crucially important, in many GMAT questions, to be certain you understand how this works. If, for example, someone sells a painting for $1100 and makes a 10% profit, we do not apply the 10% to the $1100 to find the amount of profit. If you make a 10% profit, your selling price is 10% greater than your purchase price. If your purchase price is p, then 1.1p = 1100, and p = 1000, so your profit is $100 (which is not equal to 10% of $1100). Similarly if the price of a share falls by 25% to $150, then this final price is 25% less than (or 75% of) the initial price; if you solve the equation 0.75x = 150 you'd find the original price was $200. We would not apply the 25% to $150.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by aftableo2006 » Thu May 26, 2011 8:08 am
115%of dinner cost =230$
so dinner cost=230*100/115=200$
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by irock » Fri May 27, 2011 12:36 am
let X be the cost of dinner without the tip.
so total cost= x+0.15x=230
ie, 1.15x=230 ==> x=200

Hence dinner is $200.
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by Strongt » Fri May 27, 2011 7:06 am
irock wrote:let X be the cost of dinner without the tip.
so total cost= x+0.15x=230
ie, 1.15x=230 ==> x=200

Hence dinner is $200.
that's exactly how i do it now. I think that's the best logic
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by GMATGuruNY » Fri May 27, 2011 7:22 am
Strongt wrote:
irock wrote:let X be the cost of dinner without the tip.
so total cost= x+0.15x=230
ie, 1.15x=230 ==> x=200

Hence dinner is $200.
that's exactly how i do it now. I think that's the best logic
An even safer approach would be to plug in the answers.
Just add 15% to the answer choices to see which yields a total of 230.

Answer choice C: 200
200 + .15(200) = 200+30 = 230.

If you plug in the answers, it's almost impossible to choose the wrong answer choice.
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