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# If the cost of House L increased by 20% over the same time that the

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Joined: 23 Sep 2015
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If the cost of House L increased by 20% over the same time that the  [#permalink]

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28 Mar 2019, 07:29
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Difficulty:

95% (hard)

Question Stats:

33% (01:52) correct 67% (01:45) wrong based on 55 sessions

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If the cost of House L increased by 20% over the same time that the cost of House M decreased by 20%, then the ratio of the new price of House M to the new price of House L is what percent of the original cost of House M ?

(1) If House L had increased by 30%, then the increased price of House L would have been equal to the original price of House M.

(2) The price of House L is $300,000. _________________ Thanks! Do give some kudos. Simple strategy: “Once you’ve eliminated the impossible, whatever remains, however improbable, must be the truth.” Want to improve your Score: GMAT Ninja YouTube! Series 1| GMAT Ninja YouTube! Series 2 | How to Improve GMAT Quant from Q49 to a Perfect Q51 | Time management My Notes: Reading comprehension | Critical Reasoning | Absolute Phrases | Subjunctive Mood Intern Joined: 24 Jul 2018 Posts: 40 Location: India Re: If the cost of House L increased by 20% over the same time that the [#permalink] ### Show Tags 06 Apr 2019, 00:26 2 aragonn wrote: If the cost of House L increased by 20% over the same time that the cost of House M decreased by 20%, then the ratio of the new price of House M to the new price of House L is what percent of the original cost of House M ? (1) If House L had increased by 30%, then the increased price of House L would have been equal to the original price of House M. (2) The price of House L is$300,000.

The only explanation that I can come up with this:

Question: Ratio/Original Price * 100 %
Lets consider
L(O)=Original price of house L
L(N)=New price of house L
M(O)=Original price of house M
M(N)=New price of house M

Given in the Q-stem,
$$L(N)=1.2*L(O)$$
$$M(N) = 0.8* M(O)$$

Now we have to find, $$((\frac{M(N)}{L(N)})/M(O))*100$$.......................(i)

Now let's consider the given statements,

St.1 : If House L had increased by 30%, then the increased price of House L would have been equal to the original price of House M.
=> $$1.3* L(O) = M(O)$$
=> $$L(O)= \frac{M(O)}{1.3}$$.............(ii)

Now from the Q-stem,
$$L(N)=1.2*L(O)$$
=> $$L(N)= 1.2 * \frac{M(O)}{1.3}$$ .............from (ii)

Also from the Q-stem, we have $$M(N) = 0.8* M(O)$$

So putting these values in (i),
$$\frac{(0.8* M(O))}{(1.2 *M(O)/1.3)}/M(O))*100$$
=> $$(\frac{0.8*1.3}{1.2}/M(O))*100$$

Now as M(O) is unknown to us, this statement is insufficient.

St.2: The price of House L is \$300,000
=> $$L(O)=300,000$$

From Q-stem, we have
$$L(N)=1.2*L(O)$$
=>$$L(N)=360,000$$

and
$$M(N) = 0.8* M(O)$$

So putting these values in (i),
$$((\frac{M(N)}{L(N)})/M(O))*100$$
=> $$(\frac{(0.8*M(O)}{360,000})/M(O))*100$$
=> $$\frac{(0.8*100)}{360,000}$$

Hence we do have a value for the required question and thus statement 2 is sufficient.
Re: If the cost of House L increased by 20% over the same time that the   [#permalink] 06 Apr 2019, 00:26
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