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# Pat bought a new car for P dollars and sold it later for M dollars. Th

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Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 01:09
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35% (medium)

Question Stats:

74% (00:56) correct 26% (01:26) wrong based on 53 sessions

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Competition Mode Question

Pat bought a new car for P dollars and sold it later for M dollars. The difference between the two sale prices was what percent of the initial price?

(1) M - P = 10,000

(2) P/M = 2/3

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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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Updated on: 29 Aug 2019, 03:12
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ANSWER IS OPTION B. Here's how I solved.

Hope it helps
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Originally posted by EncounterGMAT on 29 Aug 2019, 01:32.
Last edited by EncounterGMAT on 29 Aug 2019, 03:12, edited 1 time in total.
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Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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Updated on: 06 Sep 2019, 10:00
1
The question is basically asking $$\frac{M-P}{P}$$

a. gives us the differences but we do not know what P is
insufficient

b. gives the ratio of P and M, we know what we are looking for
sufficient

therefore, B

Originally posted by joohwangie on 29 Aug 2019, 01:41.
Last edited by joohwangie on 06 Sep 2019, 10:00, edited 1 time in total.
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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 01:46
1
We are to basically find the value of (M-P)/P

Statement 1 - Not sufficient, for we do not know the value of P alone

Statement 2 -> the ratio of M:P is 3:2 . then we assume M is 3 and P is 2, then (3-2) / 2 = .5 or 50%

Since this is a ratio, 6:4 , 12:8 or whatever in line with this ratio should yield the same answer.

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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 02:18
1
Cost Price =P, Selling Price=M
We are to find percentage of the difference in the two prices as a percentage of Initial Price P.

1 is insufficient since It only tells us M-P=10,000
(M-P)/P= 10,000/P
Since we don’t know what P is, we are unable to find a unique percentage.

2 Is sufficient. It gives us a relation between M and P in terms of ratios. i.e. P/M=2/3
So we can say that M=3/2 * P
M-P=(3/2 - 1)P =1/2 P
(M-P)/P = 1/2 which is 50%.

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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 03:31
1
Pat bought a new car for P dollars and sold it later for M dollars. The difference between the two sale prices was what percent of the initial price?

(1) M - P = 10,000

(2) $$\frac{P}{M} = \frac{2}{3}$$

Cost Price(CP) = P and Selling Price(SP) = M.
Question requires $$(\frac{(M – P)}{P})*100$$ i.e. $$\frac{(M – P)}{P}$$

Basically what is $$\frac{M}{P}$$ ?

Statement 1) M - P = 10,000

M and P can be anything to result difference as 10,000. For example M = 10001 & P = 1 or M = 20001 and P = 10001. Both the cases result in different values of M/P.

INSUFFICIENT.

Statement 2) $$\frac{P}{M} = \frac{2}{3}$$
Thus, $$\frac{M}{P} = \frac{3}{2}$$

SUFFICIENT.

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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 04:32
Given: Pat bought a new car for P dollars and sold it later for M dollars.

Asked: The difference between the two sale prices was what percent of the initial price?

$$\frac{(M-P)}{P}\%$$ = ?

(1) M - P = 10,000
Since P is unknown
NOT SUFFICIENT

(2) P/M = 2/3
P/M = 2/3
\frac{M-P}{P} = \frac{1}{2} = 50%
SUFFICIENT

IMO B
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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 06:30
(1) M - P = 10,000 but we do not have an information allowing us to calculate P and get what percentage 10 000 represents.

If M = 30 000, then P = 20 000 and M-P is 50% of P.
If M = 50 000, then P = 40 000 and M-P is 25% of P.

Insufficient

(2) P/M = 2/3 so P = 2M/3

If M = 3000, then P = 2000 and M-P = 1000, which is 50% of P
If M = 6000, then P = 4000 and M-P = 2000, which is 50% of P
And so on...

Sufficient

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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 06:50
IMO B alone is sufficient.

Because we know P/M is 2/3 so M-P is 1 and we can get 1/3 is the required percentage.

A is not sufficient because we don't know what is M or P.
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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 07:14
Pat bought a new car for P dollars and sold it later for M dollars. The difference between the two sale prices was what percent of the initial price?

(1) M - P = 10,000

(2) P/M = 2/3

we need to determine ; M-P/P %
#1
M - P = 10,000
value of P is not know insufficient
#2
P/M = 2/3
we can solve ; P=2M/3 ; M-P/P % ; M/3 *3/2M ; 50%
IMO B sufficient
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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 08:58
Given :

P - Initial Price (also first sale price)
M - Selling Price (Second sale price)

Difference = |M-P|

Required : |M-P|/P

Statement 1:

M-P = 10000 =>|M-P|/P = 10000/(10000-M)

Not sufficient

Down to BCDE

Statement 2:

P/M=2/3 => M=3P/2 =>|M-P|/P = |(3P/2)-P|/P = 50%

Sufficient

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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 09:03
Quote:
Pat bought a new car for P dollars and sold it later for M dollars. The difference between the two sale prices was what percent of the initial price?

(1) M - P = 10,000
(2) P/M = 2/3

$$\frac{M-P}{P}?$$
(1) M - P = 10,000: we dont know $$P$$, insufic;
(2) P/M = 2/3: $$3P=2M…M=3P/2…substitute:\frac{M-P}{P}…\frac{3P/2-P}{P}=0.5*100=50$$ sufic.

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Re: Pat bought a new car for P dollars and sold it later for M dollars. Th  [#permalink]

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29 Aug 2019, 12:33
Pat bought a new car for P dollars and sold it later for M dollars. The difference between the two sale prices was what percent of the initial price?

Question is can we find this?
$$\frac{|P-M|}{P} * 100$$

(1) M - P = 10,000
Change in values is 10000, but we don't know the original value, so not sufficient

(2) $$\frac{P}{M}$$ = $$\frac{2}{3}$$
P = 2x
M = 3x
can we plug in this in above equation and find the difference? yes

Or Other way is plug the no's Let's say P = 10 and M = 15 $$\frac{P}{M}$$ = 2/3
can we plug in these values in above equation and find the percent? yes
sufficient

Re: Pat bought a new car for P dollars and sold it later for M dollars. Th   [#permalink] 29 Aug 2019, 12:33
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