Data Sufficiency - MCQ Test(1)

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QUESTION: 1

Directions to SolveIn each of the following problems, there is one question and three statements I, II and III given below the question. You have to decide whether the data given in the statements is sufficient to answer the question. Read all the statements carefully and find which of the statements is/are sufficient to answer the given question. Choose the correct alternative in each question. Question: What is Suman's rank from the top in a class of forty students? Statements: I. Suman is 3 ranks below Deepak from the top. II. Deepak's rank from the bottom is 23. III. Suman is 3 ranks above Deepak from the bottom.

Solution:

Explanation:

From II, we conclude that in a class of 40, Deepak ranks 23rd from the bottom i.e. 18th from the top.

From I and II, we find that Suman is 3 ranks below 18th rank from the top i.e. she ranks 21st from the top.

From II and III, we find that Suman is 3 ranks above 23rd rank from the bottom

i.e. she ranks 20th from the bottom or 21st from the top.

QUESTION: 2

Question: Five persons - A, B, C, D and E are sitting in a row. Who is sitting in the middle? Statements: I. B is between E and C. II. B is to the right of E. III. D is between A and E.

Solution:

Explanation:

From I, the order is : E, B, C or C, B, E.

From II, the order is : E, B.

From III, the order is : A, D, E.

Combining the above three, we get the order as : A, D, E, B, C. Clearly, E is sitting in the middle.

QUESTION: 3

Question: How is 'DATE' written in the code language? Statements: I. DEAR is written as \$#@? in that code. II. TREAT is written as %?#@% in that code. III. TEAR is written as %#@? in that code.

Solution:

Explanation:

Observing I, II and III, we find that similar letters have similar code symbols at the corresponding places in the code. So, this is direct-coding.

Thus, to find the code for DATE, we need the code for D which can be obtained from I only (i.e. \$.) and the codes for A, T and E which can be obtained either from II or III (@, # and % respectively).

QUESTION: 4

Question:

In which year was Sanjay born?

Statements:

I. Sanjay is six years older than Gopal.

II. Gopal's brother was born in 1982.

III. Sanjay's brother is two years younger than Gopal's brother who was eight years younger than Gopal.

Solution:

Explanation:

From II, we know that Copal's brother was born in 1982.

From III, we find that Gopal's brother was 8 years younger to him i.e. Gopal was born in 1974.

From I, we find that Sanjay is 6 years older than Gopal. Thus, Sanjay was born in 1968.

QUESTION: 5

Question:

Who among Siddhartha, Nikunj, Vipul and Mukul is the youngest?

Statements:

I. Vipul is younger than Mukul but older than Siddhartha and Nikunj.

II. Mukul is the oldest.

III. Siddhartha is older than Nikunj.

Solution:

Explanation:

From I, we have: M > V, V > S, V > N ...(i)

From II, we have: Mukul is the oldest ...(ii)

From III, we have: S > N ...(iii)

Combining (i) and (iii), we get :M > V, V >S > N or M>V > S > N. Clearly, Nikunj is the youngest.

QUESTION: 6

Question:

In a certain code, 'XYZ' means 'We are friends'. Which letter stands for 'We'?

Statements:

I. 'PYN' means 'They are classmates'.

II. 'ZMS' means 'We love them'.

III. 'PX' means 'Hello friends',

Solution:

Explanation:

To find the code for 'we', we need to have any of the following:

(i) 'We are friends' should have only 'We' common with another statement, as in II;

(ii) 'We are friends' should have only 'are' and 'friends' common with another single or two statements, as in I and III. Thus, we need Either II only or I and III only.

QUESTION: 7

Question:

Among P, Q, R, S and T, Q is the second tallest and S is immediate taller than the shortest. Who among them is in the middle when they stand in the order of their heights?

Statements:

I. T is not the shortest.

II. R is taller than S but shorter than Q.

III. P ranks third in height above S when all are arranged in the order of height.

Solution:

Explanation:

From the given statement, the descending order of heights is :__, Q,__, S,__.

From II, we have the order: _, Q, R, S,__. Thus, R is in the middle.

From III, we have the order : P, Q,__, S,__. But, according to I, T is not the shortest.

So, R is the shortest. Thus, we have the order : P, Q, T, S, R. So, T is in the middle.

QUESTION: 8

Question: Four subjects - Physics, Chemistry, Mathematics and Biology - were taught in four consecutive periods of one hour each starting from 8.00 a.m. At what time was the Chemistry period scheduled ?

Statements:
I. Mathematics period ended at 10.00 a.m., which was preceded by Biology.
II. Physics was scheduled in the last period.
III. Mathematics period was immediately followed by Chemistry.

Solution:

Explanation:

From I and II, we conclude that Mathematics period began at 9.00 a.m., Biology period began at 8.00 a.m. and Physics period began at 11 a.m. So, the Chemistry period began at 10.00 a.m.

From I and III, we conclude that Mathematics period ended and Chemistry period began at 10.00 a.m.

QUESTION: 9

Question:

What is the total monthly salary of Vasu?

Statements:

I. Vasu's basic salary is Rs 100 more than Rajan's salary who also serves in Vasu's company.

II. Other allowances drawn by Rajan besides his basic salary are Rs 2000 per month which is Rs 50 less than Vasu's salary.

III. Rajan's basic salary is Rs 1550 per month,

Solution:

Explanation:

From III, we have: Rajan's basic salary = Rs. 1550.

From I, we have: Vasu's basic salary = Rs. (1550 + 100) = Rs. 1650.

From II, we have: Rajan's other allowances = Rs. 2000 and Vasu's other allowances = Rs. 2050.

Therefore Vasu's monthly salary = Rs. (1650 + 2050) = Rs. 3700.

QUESTION: 10

Question:

Who is the tallest among six boys P, T, N, D, Q and R?

Statements:

I. P is taller than D and N but not-as tall as T.

II. R is taller than Q but not as tall as T.

III. Q is not taller than T and R.

Solution:

Explanation:

From I, we have: P > D, P > N, T > P i.e. T > P > D > N or T > P > N > D ...(i)

From II, we have: R > Q, T > R i.e. T > R > Q ...(ii)

From III, we have: T > Q, R > Q ...(iii)

Clearly, from (i) and (ii), we conclude that T is taller than each one of P, N, D, R and Q. So, T is the tallest.

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