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# Of a physician's clients, 120 have health insurance or

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Of a physician's clients, 120 have health insurance or [#permalink]

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01 Apr 2012, 04:58
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Difficulty:

55% (hard)

Question Stats:

60% (02:54) correct 40% (01:41) wrong based on 85 sessions

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Of a physician's clients, 120 have health insurance or prescription drug coverage or both. If 40 of the clients do not have description drug coverage, how many of the clients have both health insurance and prescription drug coverage?

(1) A total of 92 of the clients have health insurance.
(2) Of the 120 clients, 28 do not have health insurance.
[Reveal] Spoiler: OA

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Re: People who have both [#permalink]

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01 Apr 2012, 08:07
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enigma123 wrote:
Of a physician's clients, 120 have health insurance or prescription drug coverage or both. If 40 of the clients do not
have prescription drug coverage, how many of the clients have both health insurance and prescription drug coverage?

(1) A total of 92 of the clients have health insurance.
(2) Of the 120 clients, 28 do not have health insurance.

health insurance =H;
prescription drug =P;
no. of clients with only H= a
no. of clients with only P=c
no. of clients with both H and P=b

hence we have
a+b+c=120
a=40
hence
b +c=80

we need to find b.

1) A total of 92 of the clients have health insurance.

i.e. a+b=92
=> c=28
hence b=80-28=52

SUFFICIENT

2) Of the 120 clients, 28 do not have health insurance.
i.e. c=28
hence as above b is calculable.

SUFFICIENT

Hence D.

hope this helps..!!
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Re: Of a physician's clients, 120 have health insurance or [#permalink]

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01 Apr 2012, 08:33
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Expert's post
Of a physician's clients, 120 have health insurance or prescription drug coverage or both. If 40 of the clients do not have description drug coverage, how many of the clients have both health insurance and prescription drug coverage?

Draw a diagram:
Attachment:

Insurance.png [ 5.38 KiB | Viewed 1568 times ]

(1) A total of 92 of the clients have health insurance --> we are told that 40+x=92 --> x=52. Sufficient.

(2) Of the 120 clients, 28 do not have health insurance --> we are told that blue area is 28, since there are total of 120 clients then 40+x+28=120 --> x=52. Sufficient.

Answer: D.
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Re: Of a physician's clients, 120 have health insurance or [#permalink]

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27 Oct 2015, 18:47
it's a very tricky one, especially if you try to solve these kind of problems with the matrix.
from the given information, we know that there are no such clients with neither HI nor PD.

let's assign some variables: with both - A, only PD - B, only HI - C
we know that A+B+C=120
and we know that C = 40
we can rewrite: A+B = 80
from this, we need to solve for A.

(1) A total of 92 of the clients have health insurance.
A+C = 92. knowing C, we can find A. - sufficient.
(2) Of the 120 clients, 28 do not have health insurance.
well, this one gives us value for B. again, we can find A. - sufficient.

D
Re: Of a physician's clients, 120 have health insurance or   [#permalink] 27 Oct 2015, 18:47
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# Of a physician's clients, 120 have health insurance or

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