A financial advisory firm manages a portfolio of 90 assets, each of which is classified as… — GMAT

A financial advisory firm manages a portfolio of $90$ assets, each of which is classified as a Tech asset, a Biotech asset, or both. Exactly $50$ of the assets are Tech assets, and exactly $60$ of the assets are Biotech assets. Is the average (arithmetic mean) value of the Tech-only assets greater than the average value of the Biotech-only assets?

(1) The average value of all $50$ Tech assets is $\$12$ million, and the average value of all $60$ Biotech assets is $\$12$ million.
(2) The average value of the $20$ assets classified as both Tech and Biotech assets is $\$15$ million.

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.

Combining both statements allows us to solve for the exact average value of the Tech-only assets (

10

million) and the Biotech-only assets (

10.5

million). Because we can answer the stem's question with a definitive 'No' (

10

is not greater than

10.5

), both statements together are sufficient.

Step-by-Step Solution

Determine the number of assets in each non-overlapping subgroup using set theory.

Total assets

N = 90

, Tech assets

|T| = 50

, Biotech assets

|B| = 60

. Using

|T \cup B| = |T| + |B| - |T \cap B|

, we get

90 = 50 + 60 - |T \cap B| \implies |T \cap B| = 20

. Therefore, Tech-only assets

= 50 - 20 = 30

, Biotech-only assets

= 60 - 20 = 40

, and Both

= 20

Rephrasing the question stem into distinct, non-overlapping subset counts simplifies the algebraic system.

Evaluate Statement (1) independently.

Let

M_{T}

M_{B}

, and

M_{both}

represent the mean values of Tech-only, Biotech-only, and Both subsets respectively. From Statement (1), total value of Tech

= 30 M_T + 20 M_{both} = 50 \times 12 = 600

, and total value of Biotech

= 40 M_B + 20 M_{both} = 60 \times 12 = 720

. Subtracting the equations yields

40 M_B - 30 M_T = 120 \implies 4 M_B - 3 M_T = 12

Since

M_T

could be

16

(making

M_B = 15

, so

M_T > M_B

is Yes) or

M_T

could be

8

(making

M_B = 9

, so

M_T > M_B

is No), Statement (1) alone is NOT sufficient.

Evaluate Statement (2) independently.

Statement (2) gives

M_{both} = 15

. Without knowing the total asset values or subgroup means, we cannot compare

M_T

and

M_B

Statement (2) alone is NOT sufficient.

Evaluate Statements (1) and (2) together.

Substituting

M_{both} = 15

into Statement (1) equations:

30 M_T + 20(15) = 600 \implies 30 M_T = 300 \implies M_T = 10

. Similarly,

40 M_B + 20(15) = 720 \implies 40 M_B = 420 \implies M_B = 10.5

. Since

10 > 10.5

is definitively FALSE, we get a clear 'No' response.

In Yes/No Data Sufficiency questions, a definitive 'No' means the combined statements are sufficient.

Key Concept

Data Sufficiency decision logic for overlapping sets combined with weighted averages

Estimated Time:2m 0s

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