Among a group of 50 healthcare professionals, each professional has certified training in … — GMAT

Among a group of $50$ healthcare professionals, each professional has certified training in either Telemedicine, Robotic Surgery, or both. Exactly $30$ professionals are certified in Telemedicine and exactly $35$ are certified in Robotic Surgery. What is the average (arithmetic mean) years of experience of the professionals who are certified in BOTH Telemedicine and Robotic Surgery?

(1) The average years of experience of all $30$ professionals certified in Telemedicine is $9$ years, and the average years of experience of all $35$ professionals certified in Robotic Surgery is $8$ years.
(2) The average years of experience of the $15$ professionals certified ONLY in Telemedicine is $10$ years, and the average years of experience of the $20$ professionals certified ONLY in Robotic Surgery is $8$ years.

A
Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.Answer
D
EACH statement ALONE is sufficient.
E
Statements (1) and (2) TOGETHER are NOT sufficient.

Answer

BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

The correct option is the one stating that BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. Rephrasing the stem shows there are

15

professionals in the 'Telemedicine Only' group,

20

in the 'Robotic Surgery Only' group, and

15

in 'Both'. Statement (1) gives total Telemedicine experience sum

S_T = 270

, but cannot separate

S_{T_{only}}

from

S_B

. Statement (2) gives

S_{T_{only}} = 150

, but gives no total experience bound. Together,

S_B = 270 - 150 = 120

, giving a unique mean of

\frac{120}{15} = 8

years.

Step-by-Step Solution

Rephrase the question stem using overlapping set formulas to find subgroup counts.

Let

N = 50

T = 30

, and

R = 35

. Using

N = T + R - B

, we get

50 = 30 + 35 - B \implies B = 15

(professionals in Both). Thus, 'Telemedicine Only' count is

30 - 15 = 15

, and 'Robotic Surgery Only' count is

35 - 15 = 20

. Target: Find the mean experience of the

15

professionals in Both,

\mu_B = \frac{S_B}{15}

Simplifying the stem establishes the exact numerical count of professionals in each of the three distinct subgroups: Telemedicine Only (

15

), Robotic Surgery Only (

20

), and Both (

15

Evaluate Statement (1) independently.

Statement (1) gives total experience

S_T = 30 \times 9 = 270

and

S_R = 35 \times 8 = 280

. Since

S_T = S_{T_{only}} + S_B = 270

S_B

depends on

S_{T_{only}}

, which is unknown. Multiple values of

S_B

are possible. NOT sufficient.

Knowing total group averages does not isolate how experience is divided between single-category members and dual-category members.

Evaluate Statement (2) independently.

Statement (2) gives

S_{T_{only}} = 15 \times 10 = 150

and

S_{R_{only}} = 20 \times 8 = 160

. Without knowledge of

S_T

S_R

, or total group experience,

S_B

can take any real value. NOT sufficient.

Knowing only the single-category subgroup totals provides no boundary or equation for the overlapping group.

Evaluate Statement (1) and Statement (2) together.

From Statement (1),

S_T = S_{T_{only}} + S_B = 270

. From Statement (2),

S_{T_{only}} = 150

. Substituting gives

150 + S_B = 270 \implies S_B = 120

. Thus,

\mu_B = \frac{120}{15} = 8

years. SUFFICIENT.

Combining both statements yields a unique value for the total experience sum of the overlapping group.

Key Concept

Data Sufficiency with Overlapping Sets and Weighted Averages

Estimated Time:2m 0s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic