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# If toaster X costs 10 percent more than toaster Y costs, which of the

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Math Expert
Joined: 02 Sep 2009
Posts: 58427
If toaster X costs 10 percent more than toaster Y costs, which of the  [#permalink]

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09 Oct 2015, 02:23
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35% (medium)

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69% (01:22) correct 31% (01:34) wrong based on 131 sessions

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If toaster X costs 10 percent more than toaster Y costs, which of the following COULD be true?

I. Toaster Y costs \$10 less than toaster X costs
II. Toaster X costs \$20 more than toaster Y costs
III. Toaster Y costs 10 percent less than toaster X costs

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III

Source: GMATPrepNow.

Kudos for a correct solution.

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Re: If toaster X costs 10 percent more than toaster Y costs, which of the  [#permalink]

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09 Oct 2015, 02:43
1. In case p=100 , Toaster X = 110
Toaster Y = 100

1 could be true .

2. In case p=200 ,
Toaster X = 220
Toaster Y = 200

2 could be true .

3. Never true .
Toaster Y will be (1/11)x100 percent lesser i.e 9.09 percent

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Re: If toaster X costs 10 percent more than toaster Y costs, which of the  [#permalink]

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09 Oct 2015, 02:52
x=y+10%y,

So 1 and 2 satisfies the condition and 3 does not.

Math Expert
Joined: 02 Sep 2009
Posts: 58427
Re: If toaster X costs 10 percent more than toaster Y costs, which of the  [#permalink]

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11 Oct 2015, 08:46
Bunuel wrote:
If toaster X costs 10 percent more than toaster Y costs, which of the following COULD be true?

I. Toaster Y costs \$10 less than toaster X costs
II. Toaster X costs \$20 more than toaster Y costs
III. Toaster Y costs 10 percent less than toaster X costs

(A) I only
(B) I and II only
(C) I and III only
(D) II and III only
(E) I, II and III

Source: GMATPrepNow.

Kudos for a correct solution.

GMAT Prep Now OFFICIAL SOLUTION:

Let’s check each statement.

Statement I: toaster Y costs \$10 less than toaster X costs.If toaster Y cost \$100, then toaster X would cost \$110, in which case statement I would be true.
Statement II: toaster X costs \$20 more than toaster Y costs.If toaster Y cost \$200, then toaster X would cost \$220, in which case statement II would be true.
Statement III: toaster Y costs 10 percent less than toaster X costs.This statement can never be true (we’ll see why shortly).

So, the correct answer is B.

If you thought the answer was E, then you probably have a common misconception that goes something like this: If A is k percent greater than B, then B must be k percent less than A. This, however, is not true. In fact, if we were to create a rule, it would go something like this:

If A is k percent greater than B, then B is NOT k percent less than A.

So, for example, if toaster X costs 10 percent more than toaster Y costs, then toaster Y does NOT cost 10 percent less than toaster X costs.

To demonstrate this, let’s plug in some nice prices for the two toasters. We already recognized that, if toaster Y cost \$100, then toaster X would cost \$110. Here, we can see that toaster X costs 10% more than toaster Y, but toaster Y does not cost 10 percent less than toaster X.

The price difference is \$10, and since 10/110 ≈ 9.09%, we can see that toaster Y actually costs about 9.09% less than toaster X.

Now, I’m not going to provide a global proof of the above statement (in blue); I’ll leave that to you. Rather, let’s examine a few examples that illustrate the main central concept here.

Example A: Lisa is 4 feet tall, and Bart is 5 feet tall

The height difference is 1 foot. So, Bart is 25% taller than Lisa (since 1/4 = 25%), but Lisa is NOT 25% shorter than Bart. Lisa is 20% shorter than Bart (since 1/5 = 20%)

Example B: Car X costs \$20,000, and car Y costs \$40,000

The price difference is \$20,000. So, car Y costs 100% more than car X (since 20,000/20,000 = 100%), but car X does NOT cost 100% less than car Y. Car X costs 50% less than car Y (since 20,000/40,000 = 50%).

So, when dealing with percents, be sure to remember the following:

If A is k percent greater than B, then B is NOT k percent less than A.
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Re: If toaster X costs 10 percent more than toaster Y costs, which of the  [#permalink]

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06 Oct 2018, 10:49
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Re: If toaster X costs 10 percent more than toaster Y costs, which of the   [#permalink] 06 Oct 2018, 10:49
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