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Gadget Review Matrix Missing Values

XAT 2025 · Quantitative Ability & Data Interpretation · Hard · Data Interpretation

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Passage / data set

GadRev firm reviews four tech gadgets (A, B, C, D) using four reviewers (R1, R2, R3, R4) on an integer scale of 1 to 5. Some ratings were deleted, but the row and column averages were preserved:

ABCDAverageSum
R143416
R234416
R35416
R4454.2517
Average4444.25
Sum16161617

Question 1 of 3

What rating provided by Reviewer R1 to Gadget A can help determining the remaining ratings uniquely?

  1. A.

    1

  2. B.

    4

  3. C.

    2

  4. D.

    5

  5. E.

    3

Answer

B

Explanation

R1's total sum is 16. Ratings for B=4, D=3   ⟹  \implies rating(A) + rating(C) = 9. Possibilities for R1: (A=5, C=4) or (A=4, C=5). If R1 gives 4 to A, the grid fills uniquely without requiring any reviewer to give > 5.

Question 2 of 3

In how many different ways could Reviewer R2 have rated Gadget B so that the ratings lead to the same averages for the gadgets and the reviewers as shown in the table?

  1. A.

    1

  2. B.

    5

  3. C.

    2

  4. D.

    4

  5. E.

    3

Answer

C

Explanation

Analyzing valid grid configurations shows R2 could rate B as either 4 or 5. Thus, there are 2 different ways.

Question 3 of 3

How many different valid combinations of the missing ratings are possible?

  1. A.

    4

  2. B.

    1

  3. C.

    5

  4. D.

    2

  5. E.

    3

Answer

E

Explanation

Constructing all valid grids with ratings in {1,2,3,4,5}\{1,2,3,4,5\} yielding the required sums gives exactly 3 valid combinations.

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