## Saturday, 20 May 2017

1 . Directions (Q. 1-5): Each of the questions below consists of a question and two statements (I) and (II). You have to decide whether the data provided in the statements are sufficient to answer the question and based o n this give answer

What is the difference between the present ages of A and B if the sum of their present ages is 70 years?
I.Five years ago the age of B was twice the age of A.
II.After five years the age of A will be 60% of the age of B

 A.   If the data in statement (I) alone are sufficient to answer the question, while the data in statement (II) alone are not sufficient. B.   If the data in statement (II) alone are sufficient to answer the question, while the data in statement (I) alone are not sufficient. C.   If the data either in statement (I) alone or in statement (II) alone are sufficient to answer the question D.   If the data given in both the statements (I) and (II) together are not sufficient to answer the question.
2 . What is a two-digit number?
I.The difference between the digits of the two-digit number is 3.
II.The digit in the unit’s place is greater than the digit in the ten’s place.

 A.   If the data in statement (I) alone are sufficient to answer the question, while the data in statement (II) alone are not sufficient. B.   If the data in statement (II) alone are sufficient to answer the question, while the data in statement (I) alone are not sufficient C.   he data either in statement (I) alone or in statement (II) alone are sufficient to answer the question D.   If the data given in both the statements (I) and (II) together are not sufficient to answer the question.
3 . Among three integers X, Y and Z, which is the greatest?
I.X is 62.5% of Z
II.The difference between X and Y is 30.

 A.   If the data in statement (II) alone are sufficient to answer the question, while the data in statement (I) alone are not sufficient B.   If the data either in statement (I) alone or in statement (II) alone are sufficient to answer the question C.   If the data given in both the statements (I) and (II) together are not sufficient to answer the question. D.   If the data in both the statements (I) and (II) together are necessary to answer the question
4 . If X and Y are integers, then is X + Y an even number?
I.X > Y
II.12 < X < 14 and 10 < Y < 14

 A.   If the data in statement (I) alone are sufficient to answer the question, while the data in statement (II) alone are not sufficient. B.   If the data in statement (II) alone are sufficient to answer the question, while the data in statement (I) alone are not sufficient C.   If the data either in statement (I) alone or in statement (II) alone are sufficient to answer the question D.   If the data given in both the statements (I) and (II) together are not sufficient to answer the question
5 . What is the ratio of the speed of a boat in still water to the speed of the stream?
I.It takes 3 hours to cover a distance downstream.
II.It takes 5 hours to cover the same distance upstream.

 A.   If the data in statement (II) alone are sufficient to answer the question, while the data in statement (I) alone are not sufficient B.   If the data either in statement (I) alone or in statement (II) alone are sufficient to answer the question. C.   If the data given in both the statements (I) and (II) together are not sufficient to answer the question D.   If the data in both the statements (I) and (II) together are necessary to answer the question.
6 . Directions (Q. 6-10): Study the following information carefully answer the questions given below:

In an examination (consisting of two papers Physics and Chemistry) total 300 students appeared. Out of that the ratio of boys to girls is 3 : 2. The number of boys who passed only in Physics is 25% of the total number of boys and this number is$3\over2$ of the number of girls who passed only in Chemistry. The number of girls who passed in both the papers is 13$1\over3$% of the total number of students and the number of boys who passed in both the papers is 180% of the number of girls who passed in both the papers. None of the candidate failed in both the papers.

How many girls are there who passed only in Physics paper?

 A.   35 B.   40 C.   45 D.   50
7 . The number of boys who passed only in Chemistry is what percentage of the total number of students who appeared in the examination?

 A.   21% B.   36% C.   48% D.   72%
8 . How many students passed in Physics?

 A.   192 B.   197 C.   201 D.   207
9 . What is the ratio of the number of boys who passed in Chemistry to the number of girls who passed only in Physics?

 A.   23 : 8 B.   25 : 11 C.   27 : 10 D.   29 : 15
10 . How many students are there who passed at most in one subject?

 A.   172 B.   178 C.   181 D.   188
Answers & Solutions
1 .
 Answer : Option C Explanation : Let the present age of A and B be ‘x’ and ‘y’ respectively.x + y = 70... (i)From (I), (y – 5) = 2(x –5) or 2x – y = 5 ... (ii)From eqn (i) and (ii), x = 25 and y = 45From (ii), (x + 5) =$60\over100$(y+5)or, 5x – 3y = – 10 ... (iii)From eqn (i) and (iii),x = 25, y = 45
2 .
 Answer : Option D Explanation : Let the number be 10x + y.From (II), y > x and from (I), y – x = 3 but to find the value of ‘x’ and ‘y’ we need one more equation
3 .
 Answer : Option D Explanation : From (I), X = $62.5\over100$x Zor X < Z ... (1)From (II), X – Y = 30or X > Y ... (2)From (1) and (2), Z > X > Y‘Z’ is the greatest.
4 .
 Answer : Option D Explanation : From (II), 12 < X < 14‘X’ can be 13And 10 < Y < 14, so ‘Y’ can be 11, 12, 13From (I) X > YY = 11 or 12when Y = 11 then X + Y = 13 + 11 = 24 (even number).But when Y = 12 then X + Y = 13 + 12 = 25, which is an odd number.So, data given is not sufficient.
5 .
 Answer : Option D Explanation : Let the speed of the boat in still water be ‘x’ and the speed of the stream be ‘y’.Speed downstream = x + yAnd speed upstream = x – yFrom (I), distance = 3x(x + y)And from (II), distance = 5(x – y)3(x + y) = 5(x – y)3x + 3y = 5x – 5y2x = 8y$x\over y$=$4\over1$x : y = 4 : 1
6 .
 Answer : Option D Explanation : 7 .
 Answer : Option A Explanation : Reqd%=$63\over300$x100=21%
8 .
 Answer : Option D Explanation : Total students who passed in Physics = 45 + 50 + 40 + 72 = 207
9 .
 Answer : Option C Explanation : Ratio =$72+63\over50$=$135\over50$=$27\over10$=27:10
10 .
 Answer : Option D Explanation : Students who passed at most in one subject = 45 + 50 + 30 + 63 = 188

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