Analytical Reasoning MCQ Set 14

Correct Answer: E

Explanation:

• Three engineers from I, J, K and L must be chosen. The only combination are I J K - I K L - I J L - J K L - I J K L.
• Since I refuses to work with L, combinations I K L, I J L, and I J K L are ruled out. Thus the only combination with the engineer are I J K or J K L
• Since J refuses to work with M, and N refuses to work with O, the engineers I J K could only work with N and P or O and P.
• Thus possible combinations of the five-member groups are I J K N P or I J K O P
• Since J refuses to work with M, and L refuses to work with N, the engineers J K L could only work with O and P. Thus a possible combination of the group is J K L O P
• The only possible combinations are therefore
• I J K N P - I J K O P - J K L O P

It can be seen from the three combinations: I J K N P, I J K O P and J K L O P

That if O is rejected, the group must be I J K N P. Thus L is not in the group

Correct Answer: C

Explanation:

• Three engineers from I, J, K and L must be chosen. The only combination are I J K - I K L - I J L - J K L - I J K L.
• Since I refuses to work with L, combinations I K L, I J L, and I J K L are ruled out. Thus the only combination with the engineer are I J K or J K L
• Since J refuses to work with M, and N refuses to work with O, the engineers I J K could only work with N and P or O and P.
• Thus possible combinations of the five-member groups are I J K N P or I J K O P
• Since J refuses to work with M, and L refuses to work with N, the engineers J K L could only work with O and P. Thus a possible combination of the group is J K L O P
• The only possible combinations are therefore
• I J K N P - I J K O P - J K L O P

From the set of possible combinations : I J K N P, I J K O P, and J K L O P

It can be seen that only statement III is necessarily true

Correct Answer: B

Explanation:

• Three engineers from I, J, K and L must be chosen. The only combination are I J K - I K L - I J L - J K L - I J K L.
• Since I refuses to work with L, combinations I K L, I J L, and I J K L are ruled out. Thus the only combination with the engineer are I J K or J K L
• Since J refuses to work with M, and N refuses to work with O, the engineers I J K could only work with N and P or O and P.
• Thus possible combinations of the five-member groups are I J K N P or I J K O P
• Since J refuses to work with M, and L refuses to work with N, the engineers J K L could only work with O and P. Thus a possible combination of the group is J K L O P
• The only possible combinations are therefore
• I J K N P - I J K O P - J K L O P

(B) From the set of possible combinations: I J K N P, I J K O P, J K L O P

Only statement II must be true

Correct Answer: B

Explanation:

• Let us arrange the letters in two separate categories. The first category will be for age—older and younger. The second category will be for height—taller and shorter. We represent older with the mathematical “greater than” sign > . We represent taller with a double mathematical “greater than” sign > >. From the first statement (L is older than M and taller than N), we get this representation:
• L > M and L > > N
• The second statement (O is younger than P, older than N and shorter than Q) translates mathematically as
• P > O > N and Q > > O
• The third statement (R is older than S, younger than N, shorter than S, and taller than Q) gives us
• N > R > S and S > > R > > Q
• The fourth statement (S is older than L and shorter than N) gives us
• S > L and N > > S
• Thus consolidating, we have
• L > M ---------------------------- L > > N
• P > O > N------------------------- Q > > O
• N > R > S ------------------------ S > > R > > Q
• S > L ---------------------------- N > > S
• Again with the mathematical inequality sign we can further consolidate the above in two separate inequality statements:
• P > O > N > R > S > L > M
• and
• L > > N > > S > > R > > Q > > O
• Now we can proceed to answer questions 5-8 with reference to the mathematical representation above.

Since P > O > N > R > S > L > M, M must be the youngest of the groups because it is the least of all the given letters. Accordingly Choice B is correct.

Correct Answer: A

Explanation:

• Let us arrange the letters in two separate categories. The first category will be for age—older and younger. The second category will be for height—taller and shorter. We represent older with the mathematical “greater than” sign > . We represent taller with a double mathematical “greater than” sign > >. From the first statement (L is older than M and taller than N), we get this representation:
• L > M and L > > N
• The second statement (O is younger than P, older than N and shorter than Q) translates mathematically as
• P > O > N and Q > > O
• The third statement (R is older than S, younger than N, shorter than S, and taller than Q) gives us
• N > R > S and S > > R > > Q
• The fourth statement (S is older than L and shorter than N) gives us
• S > L and N > > S
• Thus consolidating, we have
• L > M ---------------------------- L > > N
• P > O > N------------------------- Q > > O
• N > R > S ------------------------ S > > R > > Q
• S > L ---------------------------- N > > S
• Again with the mathematical inequality sign we can further consolidate the above in two separate inequality statements:
• P > O > N > R > S > L > M
• and
• L > > N > > S > > R > > Q > > O
• Now we can proceed to answer questions 5-8 with reference to the mathematical representation above.

L > > N > > S > > R > > Q > > O
Therefore, L must be the tallest because it is the greatest of all the given letters. So Choice A is correct.

Correct Answer: B

Explanation:

• Let us arrange the letters in two separate categories. The first category will be for age—older and younger. The second category will be for height—taller and shorter. We represent older with the mathematical “greater than” sign > . We represent taller with a double mathematical “greater than” sign > >. From the first statement (L is older than M and taller than N), we get this representation:
• L > M and L > > N
• The second statement (O is younger than P, older than N and shorter than Q) translates mathematically as
• P > O > N and Q > > O
• The third statement (R is older than S, younger than N, shorter than S, and taller than Q) gives us
• N > R > S and S > > R > > Q
• The fourth statement (S is older than L and shorter than N) gives us
• S > L and N > > S
• Thus consolidating, we have
• L > M ---------------------------- L > > N
• P > O > N------------------------- Q > > O
• N > R > S ------------------------ S > > R > > Q
• S > L ---------------------------- N > > S
• Again with the mathematical inequality sign we can further consolidate the above in two separate inequality statements:
• P > O > N > R > S > L > M
• and
• L > > N > > S > > R > > Q > > O
• Now we can proceed to answer questions 5-8 with reference to the mathematical representation above.

From the final mathematical representation above, we can see that O>N and N > > S, thus indicating that N is younger than O and taller than S. Therefore, Choice B is correct. The other choices can be seen to be false