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

Question

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.

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

kraizada84 · Answer

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..!!

Bunuel · Answer

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 5051 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.

mvictor · Answer

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

junsung04 · Answer

Bunuel

Can we simply assume that all patients will have either health insurance or prescription drug coverage or both? Is neither not considered for this question?

mavelous · Answer

I also feel like this should have been explicitly stated, for those of us naive creatures ))

Bunuel · Answer

We are told that  "Of a physician's clients, 120 have health insurance or prescription drug coverage or both" , so there are no students which have none.

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