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# Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at

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Joined: 25 Dec 2018
Posts: 145
Location: India
GMAT 1: 490 Q47 V13
GPA: 2.86
Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at  [#permalink]

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23 Jan 2019, 09:38
4
00:00

Difficulty:

55% (hard)

Question Stats:

57% (01:48) correct 43% (02:20) wrong based on 76 sessions

Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for $12000, what was its cost price for Mr. C? I. m+n+mn/100=44 II. n+m=0.40 Director Status: Manager Joined: 27 Oct 2018 Posts: 685 Location: Egypt Concentration: Strategy, International Business GPA: 3.67 WE: Pharmaceuticals (Health Care) Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at [#permalink] ### Show Tags 23 Jan 2019, 10:17 4 akurathi12 wrote: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for$ 12000, what was its cost price for Mr. C?

I. m+n+mn/100=44
II. n+m=0.40

from the given:
$$B - A$$ = $$\frac{n}{100} A$$,
$$B$$ = $$A(\frac{n}{100} + 1)$$

$$C - B$$ = $$\frac{m}{100} B$$,
$$C$$ = $$B(\frac{m}{100} + 1)$$ = $$A(\frac{n}{100} + 1)(\frac{m}{100} + 1)$$

if A = 12000,
$$C$$ = $$12000*(\frac{n}{100} + 1)(\frac{m}{100} + 1)$$
$$C$$ = $$12000*(\frac{n}{100} + \frac{m}{100} + \frac{nm}{10000} + 1)$$

statement I: $$m+n+\frac{mn}{100}=44$$

$$\frac{n}{100} + \frac{m}{100} + \frac{nm}{10000} = \frac{44}{100}$$
$$C$$ = $$12000*(\frac{44}{100}+ 1)$$ = $$120*144$$(#sufficient)

statement II: $$n+m=0.40$$
2 variables with one equation , (#insufficient)

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Joined: 09 Mar 2018
Posts: 994
Location: India
Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at  [#permalink]

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23 Jan 2019, 10:18
akurathi12 wrote:
Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for $12000, what was its cost price for Mr. C? I. m+n+mn/100=44 II. n+m=0.40 Statement 1) So what m+n+mn/100=44 denotes = successive percentage change Cost of C will be 44% of 12000 + 12000 Sufficient Statement 2) This is not all sufficient, as the addition of profit percentages, can be in any order. Answer A _________________ If you notice any discrepancy in my reasoning, please let me know. Lets improve together. Quote which i can relate to. Many of life's failures happen with people who do not realize how close they were to success when they gave up. Read Only User Joined: 25 Dec 2018 Posts: 145 Location: India GMAT 1: 490 Q47 V13 GPA: 2.86 Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at [#permalink] ### Show Tags 23 Jan 2019, 19:09 KanishkM wrote: akurathi12 wrote: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for$ 12000, what was its cost price for Mr. C?

I. m+n+mn/100=44
II. n+m=0.40

Statement 1)
So what m+n+mn/100=44 denotes = successive percentage change

Cost of C will be 44% of 12000 + 12000

Sufficient

Statement 2)
This is not all sufficient, as the addition of profit percentages, can be in any order.

Hi, I didn't understand the statement 1. can you please explain elaborately.
Director
Joined: 09 Mar 2018
Posts: 994
Location: India
Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at  [#permalink]

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23 Jan 2019, 19:48
2
akurathi12 wrote:

Hi, I didn't understand the statement 1. can you please explain elaborately.

Sure.

Whenever there is a successive change, this means that for a single commodity when in a succession(like in the below example) percentage is increased/decreased we can use the inline formula( learning how its derived i think will not be that fruitful)

a + b + (ab)/100

here a, b based on the question can be the profit % or the loss %.

Since they both are +ive in the question, we can use them as it is,but if one % was a loss then we will take the sign as negative

a = 10 % profit
b = 10 % loss

Successive percentage = 10 -10 -100/100 = -1%

Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at m% profit. If Mr. A bought it for \$ 12000, what was its cost price for Mr. C?

So what m+n+mn/100=44 denotes = successive percentage change

Cost of C will be 44% of 12000 + 12000 or 144 % of 12000)

Sufficient.

Let me know if this helps you.
_________________
If you notice any discrepancy in my reasoning, please let me know. Lets improve together.

Quote which i can relate to.
Many of life's failures happen with people who do not realize how close they were to success when they gave up.
Re: Mr. A sold a house to Mr. B at n% profit and Mr. B sold it to Mr. C at   [#permalink] 23 Jan 2019, 19:48
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