Data Sufficiency

Question: What time did the train leave today ?

Statements:

The train normally leaves on time.
The scheduled departure is at 14 : 30.

A:

I alone is sufficient while II alone is not sufficient

B:

II alone is sufficient while I alone is not sufficient

C:

Either I or II is sufficient

D:

Neither I nor II is sufficient

Answer: D

Clearly, even both I and II together do not reveal the exact time of departure of the train today.

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Question: Among five friends, who is the tallest ?

Statements:

D is taller than A and C.
B is shorter than E but taller than D.

A:

I alone is sufficient while II alone is not sufficient

B:

II alone is sufficient while I alone is not sufficient

C:

Either I or II is sufficient

D:

Neither I nor II is sufficient

Answer: E

From I, we have: D > A, D > C.

From II, we have: E > B > D.

Combining the above two, we get :E > B > D > A > C or E > B > D >C > A.

Thus, E is the tallest.

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Question: How many speeches were delivered in the two days' programme ?

Statements:

18 speakers were invited to give at least one speech (maximum of two speech), out of which one-sixth of the speakers could not come.
One-third of the speakers gave two speeches each.

A:

I alone is sufficient while II alone is not sufficient

B:

II alone is sufficient while I alone is not sufficient

C:

Either I or II is sufficient

D:

Neither I nor II is sufficient

Answer: E

From I, we find that number of speakers who attended programme =18-(1/6) of 18 = 15.

From II, we find that one-third of 15 i.e. 5 speakers gave 2 speeches each, while each of the remaining 10 speakers delivered only one speech.

So, total number of speeches delivered = (5 x 2 + 10 x 1) = 20.

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Question: In a row of five buildings - P, Q, R, S and T, which building is in the middle ?

Statements:

Buildings S and Q are at the two extreme ends of the row.
Building ,T is to the right of building R.

A:

I alone is sufficient while II alone is not sufficient

B:

II alone is sufficient while I alone is not sufficient

C:

Either I or II is sufficient

D:

Neither I nor II is sufficient

Answer: D

From I, we have the order : S, -, -, -, Q. From II, we have the order : R, T. Combining the above two, we get two possible orders : S, R, T, P, Q or S, P, R, T, Q. Thus, either T or R is in the middle.

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Question: What is the rank of P from the bottom in a class of 30 students ?

Statements:

M is third from the top and there are five students between M and P.
The rank of K is fourth from the bottom and there are 17 students between K and P.

A:

I alone is sufficient while II alone is not sufficient

B:

II alone is sufficient while I alone is not sufficient

C:

Either I or II is sufficient

D:

Neither I nor II is sufficient

Answer: C

From I, we conclude that P is 9th from the top. Thus, in a class of 30 students, P ranks 22nd from the bottom.

From II, we conclude that P is 22nd from the bottom.

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Questions for: Data Sufficiency