Grouping and Selection

Solve the question of Grouping and Selection and select the option from the choices A through D/E. Check your Answer and view the explanation.

An artist has exactly seven paintings T, U, V, W, X, Y and Z from which she must choose exactly five to be in an exhibit. Any combination is acceptable provided it meets the following conditions:

If T is chosen, X cannot be chosen
If U is chosen, Y must also be chosen
If V is chosen, X must also be chosen

Question: 1

Which one of the following is an acceptable combination of paintings for inclusion in the exhibit?

T, U, V, X, Y
T, U, V, Y, Z
T, W, X, Y, Z
U, V, W, Y, Z
U, V, X, Z, Y

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Correct Answer: E

Paintings: T, U, V, W, X, Y, and Z

To be chosen: 5

Condition:

If T is chosen, X cannot be chosen ⇒ T – X not together
If U is chosen, Y must also be chosen ⇒ U – Y together
If V is chosen, X must also be chosen ⇒ V – X together

Let’s explore all individual options:

T, U, V, X, Y ⇒ This is not valid as it violates 1st condition.
T, U, V, Y, Z ⇒ This is not valid as V requires X, which can’t be together with T.
T, W, X, Y, Z ⇒ This is not valid as it violates 1st condition.
U, V, W, Y, Z ⇒ This is not valid as it violates 3rd condition.
U, V, X, Z, Y ⇒ This is valid as it doesn’t violates any condition.

Hence answer is U, V, X, Z, Y.

Grouping and Selection

Question: 1

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Correct Answer: E

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