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

Question

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 .

Skywalker18 · Answer

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 
 
Answer B.

asethi · Answer

x=y+10%y,

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

So the answer is 'B'

Bunuel · Answer

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

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