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# Dr. Wright, a dermatologist, sees patients in his clinic from 8am to

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Dr. Wright, a dermatologist, sees patients in his clinic from 8am to [#permalink]

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12 Nov 2012, 17:31
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Difficulty:

65% (hard)

Question Stats:

54% (03:02) correct 46% (01:51) wrong based on 136 sessions

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Dr. Wright, a dermatologist, sees patients in his clinic from 8am to 12pm (noon), and from 2pm until the last patient leaves. During the first session he sees 7.5 patients an hour, while in the second session this rate is multiplied by X.

If the number of patients seen in the second session is Y more than in the first session, then which of the following expressions would describe the amount of time that elapses from 12:00, when Dr. Wright takes his noon break, until he leaves his office in the evening?

(A) (30 + y)/(7.5x)
(B) 2 + 4y/x
(C) 2 + (7.5x + y)/x
(D) (30 + 15x + y)/(7.5x)
(E) 2 + (30x + y) /(7.5x)
[Reveal] Spoiler: OA
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Re: Dr. Wright, a dermatologist, sees patients in his clinic from 8am to [#permalink]

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12 Nov 2012, 18:49
Oh gosh is ridiculous how a question like this is so tricky.

Maybe under time pressure even more 50 % of students take it wrong. I'm sure of this.

Anyway.

First part of visits by the doctor are RTW formula 7.5 * 4 = 30 and the rate is 7.5 per hour

After our W is 30 + y our R is 7.5x BUT as the statement says
Quote:
then which of the following expressions would describe the amount of time that elapses from 12:00, when Dr. Wright takes his noon break, until he leaves his office in the evening?

So we need to take in account patients at rate of 7.5 from 12 to 2 pm ---------> 7.5 * 2 = 15 x

T = 30 + y + 15x / 7.5x.

I do not see anything else
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Re: Dr. Wright, a dermatologist, sees patients in his clinic from 8am to [#permalink]

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13 Nov 2012, 03:49
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Expert's post
anon1 wrote:
Dr. Wright, a dermatologist, sees patients in his clinic from 8am to 12pm (noon), and from 2pm until the last patient leaves. During the first session he sees 7.5 patients an hour, while in the second session this rate is multiplied by X.

If the number of patients seen in the second session is Y more than in the first session, then which of the following expressions would describe the amount of time that elapses from 12:00, when Dr. Wright takes his noon break, until he leaves his office in the evening?

TOTAL PATIENTS --- AVERAGE PER HOUR
30 --------------------------------- 7.5 (from 8am to 12pm)
30+y ------------------------------ 7.5x (from 2pm to 12pm until the last patient leaves)

Thus the second session, from 2pm, lasted for $$\frac{30+y}{7.5x}$$ hours. Therefore the amount of time that elapses from 12:00 is 2 hours more than that: $$2+\frac{30+y}{7.5x}=\frac{15x+30+y}{7.5x}$$.

Hope it's clear.
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Re: Dr. Wright, a dermatologist, sees patients in his clinic from 8am to [#permalink]

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02 Dec 2012, 22:40
First Session:
$$7.5 (4) = 30 patients$$

Second Session:
$$W = 30 + y$$
$$R = 7.5X$$
$$t = ?$$

$$t = \frac{W}{R} = \frac{30 + y}{7.5X}$$

Time elapsed from noon (including break) to last patient = 2 hours + $$\frac{30+y}{7.5x}$$

Simplify further:
$$\frac{5x + 30 + y}{7.5X}$$

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Re: Dr. Wright, a dermatologist, sees patients in his clinic from 8am to [#permalink]

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12 Nov 2015, 09:22
If I plug in x=2 and y=30, option A works?!

30 + 60/15 = 6 (4 hours of work plus 2 hours break). Can you explain why A is wrong?
Re: Dr. Wright, a dermatologist, sees patients in his clinic from 8am to   [#permalink] 12 Nov 2015, 09:22
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