Grouping and Selection

Solve the question of 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: 3

Which one of the following substitutions can the artist always make without violating restrictions affecting the combination of paintings given that the painting mentioned first was not, and the painting mentioned second was, originally going to be chosen?

T replaces V
U replaces Y
V replaces X
W replaces Y
Z replaces W

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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

Given: 2nd painting was originally chosen:

T replaces V ⇒ If V was chosen then X must be there which makes it invalid for T to be a replacement w/o violating any condition.
U replaces Y ⇒ U and Y have to be together ⇒ This violates 2nd condition.
V replaces X ⇒ V and X have to be together ⇒ This violates 3rd condition
W replaces Y ⇒ U and Y have to be together ⇒ This violates 2nd condition.
Z replaces W ⇒ There is no condition regarding painting Z and W. So, this doesn’t violate any condition.

Hence Z replaces W is the answer.

Grouping and Selection

Question: 3

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Correct Answer: E

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