RRB NTPC Data Sufficiency Questions PDF

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RRB NTPC Data Sufficiency Questions PDF
RRB NTPC Data Sufficiency Questions PDF

RRB NTPC Data Sufficiency Questions PDF

Download RRB NTPC Data Sufficiency Questions and Answers PDF. Top 20 RRB NTPC Maths questions based on asked questions in previous exam papers very important for the Railway NTPC exam.

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Question 1: Rama was waiting for his turn at the reservation counter in a queue. What is Rama’s position from the front end of the queue?
Statement 1: There are a total of 90 people in the queue.
Statement 2: Rishabh is standing at the 75th position from the front end in the same queue. Also, there are exactly 19 people between Rishabh and Rama.

a) Statement I alone is sufficient, but statement II is not sufficient.

b) Statement II alone is sufficient, but statement I is not sufficient.

c) Both the statements together are sufficient.

d) Both the statements together are not sufficient.

Question 2: Ramesh was waiting for his turn at an ice-cream parlour in a queue. What is Ramesh’s position from the rear end of the queue?

Statement 1: Rajesh is standing at the 35th position form the front end in the same queue. Also, there are exactly 6 people between Rajesh and Ramesh.
Statement 2: There are a total of 85 people in the queue.

a) Statement I alone is sufficient, but statement II is not sufficient.

b) Statement II alone is sufficient, but statement I is not sufficient.

c) Both the statements together are sufficient.

d) Both the statements together are not sufficient.

Question 3: A question is followed by 2 statements. Using the information provided, check whether the given information is sufficient to solve the problem:
A bag contains a total of 20 balls. Some balls are white in color and the remaining balls are red in color. If a ball is randomly withdrawn from the bag, then what is the probability that this ball is red?
I) There were a total 12 white balls in the bag initially.
II) The number of red balls in the bag is greater than the number of white balls in the bag initially.

a) Statement I alone is sufficient, but statement II is not sufficient.

b) Statement II alone is sufficient, but statement I is not sufficient.

c) Both the statements together are sufficient.

d) Each statement individually is sufficient.

e) Both the statements together are not sufficient.

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Question 4: A question is followed by 2 statements. Using the information provided, check whether the given information is sufficient to solve the problem:
Find out the number of integral points that lie inside a quadrilateral.
I) The number of integral points on the boundary of the quadrilateral is 26.
II) The area of the quadrilateral is 160 cm$^2$.

a) Statement I alone is sufficient, but statement II is not sufficient.

b) Statement II alone is sufficient, but statement I is not sufficient.

c) Both the statements together are sufficient.

d) Each statement individually is sufficient.

e) Both the statements together are not sufficient.

Question 5: A question is followed by 2 statements. Using the information provided, check whether the given information is sufficient to solve the problem:
A triangle is drawn inside a circle and a square is drawn inside the triangle. All four vertices of the square lie on the sides of the triangle. The base of the square lies on the base of the triangle. What is the area of the square?
I) The perimeter of the circle is 44 $cm$.
II) The area of the circle is 154 $cm^2$.

a) Statement I alone is sufficient, but statement II is not sufficient.

b) Statement II alone is sufficient, but statement I is not sufficient.

c) Both the statements together are sufficient.

d) Each statement individually is sufficient.

e) Both the statements together are not sufficient.

Question 6: A question is followed by 2 statements. Using the information provided, check whether the given information is sufficient to solve the problem:
There are 5 distinct odd integers. What is the largest integer among the 5 integers?
I) The average of the 5 integers is less than the largest integer by 4.
II) The smallest integer among the given 5 integers is 123.

a) Statement I alone is sufficient, but statement II is not sufficient.

b) Statement II alone is sufficient, but statement I is not sufficient.

c) Both the statements together are sufficient.

d) Each statement individually is sufficient.

e) Both the statements together are not sufficient.

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Question 7: These statements provide data that may help answer the respective questions. Read the questions and the statements and determine if the data provided by the statements is sufficient or insufficient, on their own or together, to answer the questions. Accordingly, choose the appropriate option given below the questions.
Harry and Sunny have randomly picked 5 cards each from a pack of 10 cards, numbered from 1 to 10. Who has randomly picked the card with number 2 written on it?
Statement I: Sum of the numbers on the cards picked by Harry is 5 more than that of Sunny.
Statement II: One has exactly four even numbered cards while the other has exactly four odd numbered cards.

a) Statement I alone is sufficient to answer.

b) Statement II alone is sufficient to answer.

c) Either of the statement is sufficient to answer.

d) Both statements are required to answer.

e) Additional information is required.

Question 8: Rohit Sharma and Virat Kohli are two of the highest run scorers for India in the year 2017. The average of any cricketer is defined as the number of runs scored by him divided by the number of times he has been dismissed. Similarly, the strike rate of a batsman is defined as $\frac{\textrm{No of runs scored}}{\textrm{No. of balls faced}}*100$.
At the start of the year, Virat Kohli averaged 53.55 and Rohit averaged 47.54. The strike rate of Kohli till last year was 91 and that of Rohit was 87. In the year 2017, both of them played the same number of matches. Who averaged more at the end of 2017?
Statement I: Till 2016, Virat had played 192 matches and Rohit had played 180 matches. In 2017, Virat scored 900 runs from 20 matches and Rohit scored 1700 runs.
Statement II: Rohit was dismissed only 10 times in 2017 while Virat was dismissed 14 times.

a) Statement I alone is sufficient

b) Statement II alone is sufficient

c) Either of the two statements alone are sufficient

d) Both the statements are needed to answer the question

e) The question cannot be answered even by using both the statements together.

Question 9: Four friends – A, B, C, D have 1, 2 , 3 and 4 marbles with them in no particular order. Who has the most number of marbles?
Statement 1: A has a marble more than B
Statement 2: Sum of number marbles with B and C is equal to the sum of number of marbles with the other two.

a) if the question can be answered by using statement I alone but not by using statement II alone.

b) if the question can be answered by using statement II alone but not by using statement I alone.

c) if the question can be answered by using both the statements together but not by either of the statements alone.

d) if the question can be answered by using either of the statements alone.

e) if the question cannot be answered on the basis of the two statements.

Question 10: What is the remainder when N is divided by 73?
I. When 2N is divided by 73 the remainder is 27.
II. When N is divided by 27, it leaves a remainder of 23.

a) if the question can be answered by using statement I alone but not by using statement II alone.

b) if the question can be answered by using statement II alone but not by using statement I alone.

c) if the question can be answered by using both the statements together but not by either of the statements alone.

d) if the question can be answered by using either of the statements alone.

e) if the question cannot be answered on the basis of the two statements.

Question 11: These questions are based on data sufficiency. Each problem consists of a question and two statements labeled I and II. Decide whether the data given in the statements is sufficient or not to answer the question. Make an appropriate choice from (A) to (E) as follows.
a, b, c, d and e are 5 consecutive natural numbers. Is ‘b’ even?
Statement I: The product all the five terms is even.
Statement II: The sum of all the five terms is even.

a) if the question can be answered by using statement I alone but not by using statement II alone.

b) if the question can be answered by using statement II alone but not by using statement I alone.

c) if the question can be answered by using both the statements together but not by either of the statements alone.

d) if the question can be answered by using either of the statements alone.

e) if the question cannot be answered on the basis of the two statements.

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Question 12: These questions are based on data sufficiency. Each problem consists of a question and two statements labelled I and II. Decide whether the data given in the statements is sufficient or not to answer the question. Make an appropriate choice from (A) to (E) as follows.
How many terms are there in the geometric progression 3, 12, 48, …
I) The ratio of the last term to the fifth last term is 256.
II) The middle term of the series is 3072.

a) if the question can be answered by using statement I alone but not by using statement II alone.

b) if the question can be answered by using statement II alone but not by using statement I alone.

c) if the question can be answered by using both the statements together but not by either of the statements alone.

d) if the question can be answered by using either of the statements alone.

e) if the question cannot be answered on the basis of the two statements.

Question 13: These questions are based on data sufficiency. Each problem consists of a question and two statements labelled I and II. Decide whether the data given in the statements is sufficient or not to answer the question. Make an appropriate choice from (A) to (E) as follows. A, B, C are three friends. They all appeared for their final exams. The average marks secured by A and B were 68. The average marks secured by B and C were 78. What was the average of the marks secured by A and C?Statement I: The average marks secured by all three of them were 70.
Statement II: C secured 10 marks more than B.

a) if the question can be answered by using statement I alone but not by using statement II alone.

b) if the question can be answered by using statement II alone but not by using statement I alone.

c) if the question can be answered by using both the statements together but not by either of the statements alone.

d) if the question can be answered by using either of the statements alone.

e) if the question cannot be answered on the basis of the two statements.

Instructions

are followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:

A. Statement I alone is sufficient to answer the question.
B. Statement II alone is sufficient to answer the question.
C. Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.
D. Either Statement I or Statement II alone is sufficient to answer the question.
E. Neither Statement I nor Statement II is necessary to answer the question.

Question 14: Given below is an equation where the letters represent digits.
(PQ). (RQ) = XXX. Determine the sum of P + Q + R+ X.
I. X = 9.
II. The digits are unique.

a) Statement I alone is sufficient to answer the question.

b) Statement II alone is sufficient to answer the question.

c) . Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

d) Either Statement I or Statement II alone is sufficient to answer the question.

e) Neither Statement I nor Statement II is necessary to answer the question.

Question 15: Let PQRS be a quadrilateral. Two circles O1 and O2 are inscribed in triangles PQR and PSR respectively. Circle O1 touches PR at M and circle O2 touches PR at N. Find the length of MN.
I. A circle is inscribed in the quadrilateral PQRS.
II. The radii of the circles O1 and O2 are 5 and 6 units respectively.

a) Statement I alone is sufficient to answer the question.

b) Statement II alone is sufficient to answer the question.

c) . Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

d) Either Statement I or Statement II alone is sufficient to answer the question.

e) Neither Statement I nor Statement II is necessary to answer the question.

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Question 16: Lionel and Ronaldo had a discussion on the ages of Jose’s sons. Ronaldo made following statements about Jose’s sons:
i. Jose has three sons.
ii. The sum of the ages of Jose’s sons is 13.
iii. The product of the ages of the sons is the same as the age of Lionel.
iv. Jose’s eldest son, Zizou weighs 32 kilos.
v. The sum of the ages of the younger sons of Jose is 4.
vi. Jose has fathered a twin.
vii. Jose is not the father of a triplet.
viii. The LCM of the ages of Jose’s sons is more than the sum of their ages.
Which of the following combination gives information sufficient to determine the ages of Jose’s sons?

a) i, ii, iii and iv

b) i, ii, iv and vi

c) i, ii, iii and v

d) i, ii, v and vii

e) i, ii, v and vi

Question 17: The median of 11 different positive integers is 15 and seven of those 11 integers are 8, 12, 20, 6, 14, 22, and 13.

Statement I: The difference between the averages of four largest integers and four smallest integers is 13.25.
Statement II: The average of all the 11 integers is 16.

Which of the following statements would be sufficient to find the largest possible integer of these numbers?

a) Statement I only.

b) Statement II only.

c) Both Statement I and Statement II are required.

d) Neither Statement I nor Statement II is sufficient.

e) Either Statement I or Statement II is sufficient.

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Question 18: Anita, Biplove, Cheryl, Danish, Emily and Feroze compared their marks among themselves. Anita scored the highest marks, Biplove scored more than Danish. Cheryl scored more than at least two others and Emily had not scored the lowest.
Statement I: Exactly two members scored less than Cheryl.
Statement II: Emily and Feroze scored the same marks.

Which of the following statements would be sufficient to identify the one with the lowest marks?

a) Statement I only.

b) Statement II only.

c) Both Statement I and Statement II are required together.

d) Neither Statement I nor Statement II is sufficient.

e) Either Statement I or Statement II is sufficient.

Instructions

Questions are followed by two statements labelled as I and II. Decide if these statements are sufficient to conclusively answer the question. Choose the appropriate answer from the options given below:
A. Statement I alone is sufficient to answer the question.
B. Statement II alone is sufficient to answer the question.
C. Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.
D. Either Statement I or Statement II alone is sufficient to answer the question.
E. Both Statement I and Statement II are insufficient to answer the question

Question 19: A sequence of positive integer is defined as $A_{n+1}=A_{n}^{2}+1$ for each n ≥ 0. What is the value of Greatest Common Divisor of $A_{900}$ and $A_{1000}$ ?
I. $A_{0} = 1$
II. $A_{1} = 2$

a) Statement I alone is sufficient to answer the question.

b) Statement II alone is sufficient to answer the question.

c) Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

d) Either Statement I or Statement II alone is sufficient to answer the question.

e) Both Statement I and Statement II are insufficient to answer the question

Question 20: In the trapezoid PQRS, PS is parallel to QR. PQ and SR are extended to meet at A. What is the value of $\angle$PAS ?
I. PQ = 3, RS = 4 and $\angle$ QPS = 60°.
II. PS = 10, QR = 5.

a) Statement I alone is sufficient to answer the question.

b) Statement II alone is sufficient to answer the question.

c) Statement I and Statement II together are sufficient, but neither of the two alone is sufficient to answer the question.

d) Either Statement I or Statement II alone is sufficient to answer the question.

e) Both Statement I and Statement II are insufficient to answer the question

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Answers & Solutions:

1) Answer (C)

In statement (2), it is given that Rishabh is standing at the 75th position from the front end in the same queue. Also, there are exactly 19 people between Rishabh and Rama. Hence, we can say that Rama can be either at 55th or 95th position from the front end of the queue.
From statement (2), we can’t find any relevent information.
If we combine statement (1) and statement (2),  we know that only 90 people are standing in the queue. Therefore, we can say that Rama is standing at 55th position from the front end of the queue. Hence, option C is the correct answer.

2) Answer (D)

In statement (1), it is given that Rajesh is standing at the 35th position form the front end of the same row. Also, there are exactly 6 people between Rajesh and Ramesh. Hence, we can say that Ramesh can be either at 28th or 42th position from the front end of the queue.
From statement (2), we can’t find any relevent information.
If we combine statement (1) and statement (2),  then we can say that Ramesh is standing either at 44th or 58th position from rear end. We can’t find the absolute position of Ramesh from rear end. Hence, option D is the correct answer.

3) Answer (A)

From the statement 1, we can see that there are 12 white balls in the bag. So the remaining balls should be of red colored balls. Hence, the number of red balls in the bag initially = 8. Hence, the required probability = $\dfrac{8}{20}$ = 2/5.
From the statement 2, we can say that the probability, that this withdrawn ball is red, is greater than 0.5. But we can’t determine exact probability. Hence, this statement alone is not sufficient to answer the given problem. Thus, option A is the correct answer.

4) Answer (C)

Using Pick’s Theorem:
A = I + (B/2) -1

A = Area of the polygon.
B = Number of integral points on edges of the polygon.
I = Number of integral points inside the polygon.

Using the above formula, we can deduce,
I = (2A – B + 2) / 2
Here, A = 160 B = 26. Therefore, I = $\dfrac{320-26+2}{2}$ = 148.
We can find out the number of integral points within the quadrilateral using both the statements together. Thus, option C is the correct answer.

5) Answer (E)

Using the information provided by either of the statements, we can find out the radius of the circle. However, we do not have any information regarding the triangle. The triangle can be equilateral, isosceles, or scalene. Therefore, we cannot determine the area of the square using the given information and hence, option E is the right answer.

6) Answer (C)

We know that all the 5 values are distinct odd integers.
Just by using statement 1, we can infer that the numbers should be 5 consecutive odd integers. Because the average will be less than the highest by 4 only if the numbers are a-4, a-2, a, a+2, a+4.
However, we cannot obtain any absolute value. Therefore, statement 1 is insufficient to answer the question.

Using statement 2, we can obtain the lowest among the 5 values. However, we cannot obtain any relation between the smallest number and the highest number.

Using both the statements together, we can infer that 123 is the smallest integer and the 5 odd integers must be consecutive. Therefore, the largest integer among the five must be 123+8 = 131. We can determine the answer using both the statements together. Therefore, option C is the right answer.

7) Answer (D)

Harry and Sunny have cards numbered from 1 to 10.
Sum of the number of cards picked by them = 1+2+3+…+10 = 55.

Sum of the numbers on the cards picked by Harry is 5 more than that of Sunny.
Let x be the sum of the numbers picked by Sunny.
x+x+5 = 55
x = 25
25 can be written as 10+9+1+2+3 or 9+7+5+1+3 etc. (There are many such combinations). We cannot determine the person who has card number 2.
Statement I alone is insufficient.

Statement II states that one of the 2 persons has exactly 4 even-numbered cards.
The person with 4 even-numbered cards might or might not contain card number 2. Therefore, statement II alone is insufficient.

Combining both the statements, we know that the sum of the numbers on the cards with Harry is 5 more than the sum of the number on the cards with Sunny. Therefore, the sum of the number of cards with Sunny should be 25 and Harry should be 30.

Sum of the 5 even numbers = 2+4+6+8+10 = 30.
Sum of the 5 odd numbers = 1+3+5+7+9 = 25.
By replacing one of the odd numbers with even numbers, we have to make the sums 30 and 25. We cannot replace an odd number with an even number and still get the sum as 25. Therefore, the set with 4 odd numbers must add up to 30 and the set with 4 even numbers must add up to 25. We can interchange 1 with 6 or 3 with 8 or 5 with 10. The card with number 2 will always remain with the person with 4 even cards. The card with number 25 will always remain with Sunny. Therefore, we can determine the answer using both the statements together and hence, option D is the right answer.

8) Answer (E)

From the information given in the question, we only know that Virat Kohli averages 53.55 till the end of 2016 and Rohit averaged 47.54. Strike rate part is irrelevant to the question asked and is just unnecessary information. In order to calculate the number of runs scored by both these players till 2016, we need to know the number of times they have been dismissed till 2016. Since, we do not have any information in this regard, so we cannot say for sure who averages more at the end of 2017. Hence, even by using both the statements together, we cannot answer the given question. Thus, option E is the correct answer.

9) Answer (E)

Using statement 1, we can conclude that A can have 2,3 or 4 marbles and B can have 1,2 or 3 marbles.
Using statement 2, we can conclude that the B and C must contain (4,1) marbles or (2,3) marbles and A and D must be having the remaining set.

Using both the statements, we can conclude that A cannot have 1 marble. But, D can have 1 marble and A can have 4 marbles. The other possibility is B can have 1 marble and C can have 4 marbles. Hence, we cannot determine the person with the highest number of marbles even after using both the statements together. Hence, option E is the right answer.

10) Answer (A)

From I,
2N = 73k + 27

If N leaves a remainder p when divided by 73. 2N will leave a remainder of 2p.

Since 27/2 is 13.5, which is not possible. Let us consider 73 + 27 = 100. 100/2 = 50.

Thus, the remainder when 50 is divided by 73 is 50.

From II,
We cannot infer anything about what the remainder will be when N is divided by 73.

11) Answer (B)

Using statement I, we know that the product of the 5 terms is even.
Even if one of the 5 terms is even, the entire product will be even. Hence, we cannot determine whether b is odd or even.

Using statement 2, we know that the sum of the 5 terms is even.
Let us denote a as b-1, c as b+1, d as b+2 and e as b+3 (Since they are consecutive terms).
a + b + c + d + e = even.
b -1 + b + b + 1 + b + 2 + b +3 = even.
5b + 5 = even.
5 is an odd number. 2 odd numbers on addition yield an even number. Therefore, 5b must be odd.
Therefore, B is definitely an odd number. We can answer the question using statement II alone. Hence, option B is the right answer.

12) Answer (B)

Suppose there are n terms. Frist term is 3, and the common ratio is 4.
From 1st statement we know that $ \frac{3*4^{n-1}}{3*4^{n-5}} = 4^4 = 256 $. Thus we are not getting any information on ‘n’. Hence statement 1 alone is not enough to answer the question.
From statement 2 we know the middle term of series is 3072. So n is definitely odd.
Further $ 3072 = 3*4^5 = 3*4^{6-1}$
So the 6th term is the middle term. Hence the number of terms in the series is 5+ 1+ 5 = 11
Hence statement 2 alone is sufficient to answer the question.
Hence option B is the correct choice.

13) Answer (D)

Let the marks secured by A be a and the marks secured by B be b. Let the marks secured by C be ‘c’.
We know that
a + b = 136
b + c = 156
From statement I, we know that
a + b + c = 210
=> c = 74
Thus, we can find the values of a and b and hence the question can be answered using I alone.
From II
We know that
c = b + 10
Thus, from the given equations we can determine the values of a, b and c. Hence, the question can be answered using II alone as well. Hence, option D is the correct answer.

14) Answer (E)

Given relationship is $(PQ)(RQ) = XXX$

Since, X can take nine values from 1 to 9, thus we have 9 possibilities.

$111 = 3 \times 37$                    $666 = 18 \times 37$

$222 = 6 \times 37$                    $777 = 21 \times 37$

$333 = 9 \times 37$                    $888 = 24 \times 37$

$444 = 12 \times 37$                  $999 = 27 \times 37$

$555 = 15 \times 37$

But, out of these 9 cases, only in 999, we get the unit’s digit of the two numbers same. Since it is a unique value,

Thus, we need neither statement I nor II to answer the question.

15) Answer (A)

Using the property that, tangents from same point to a circle are equal in lengths.

In above quadrilateral, PA = PM + MN, => $d = a + MN$ ———-Eqn(I)

RC = RN + NM

=> $PS = d + e$

$SR = e + c$

$QR = b + c + MN$

$PQ = a + b$

From statement I :

We can conclude that, $w + x + y + z = w + x + y + z$

=> $(w + z) + (x + y) = (w + x) + (y + z)$

=> $PQ + SR = PS + QR$

Substituting values from above equation, we get :

$\therefore a + b + e + c = d + e + b + c + MN$

Using eqn(I),

=> $a = a + MN + MN$

=> $MN = 0$

Thus, statement I alone is sufficient.

Statement II alone is not sufficient, for we can have more than one value of MN possible.

16) Answer (E)

Statement iii and iv are redundant. Thus, we can cancel out first three options.

From (i) , (ii) , (v), we have :

Let A,B,C be the ages of Jose’s sons in ascending order

and $A + B + C = 13$

and $A + B = 4$

=> $C = 13 – 4 = 9$

Now, from (vi) we get $A = B$

=> $A = B = \frac{4}{2} = 2$

$\therefore$ i, ii, v and vi are required to answer the question.

17) Answer (E)

Median of 11 integers is 15, => In ascending order 6th integer = 15

=> Numbers = 6,8,12,13,14,15,20,22

Statement I : Average of four smallest = 6 + 8 + 12 + 13

= $\frac{39}{4} = 9.75$

It is given that, avg of 4 largest – avg of 4 smallest = 13.25

=> Average of 4 largest = 13.25 + 9.75 = 23

=> Sum of 4 largest numbers = 23 * 4 = 92

So, we can easily allocate other three numbers different minimum values but more than 15 and maximize the remaining one value

Thus, statement I is sufficient.


Statement II : Sum of 11 integers = 11 * 16 = 176

Sum of given 8 integers = 6+8+12+13+14+15+20+22 = 110

Sum of remaining numbers = 176 – 110 = 66

So, we can easily allocate other three numbers different minimum values but more than 15 and maximize the remaining one value

Thus, statement II is sufficient.

$\therefore$ Either statement I or II is sufficient.

18) Answer (B)

Let A,B,C,D,E,F represents Anita, Biplove, Cheryl, Danish, Emily and Feroze respectively.

Statement I : It is not sufficient as nothing is mentioned about D and F.

Statement II : E = F, thus E and F cannot score the lowest.

Also, C scored higher than at least 2 and B scored more than D while A scored the highest.

The only person left with the lowest marks can be D.

Thus, statement II alone is sufficient.

19) Answer (D)

Expression : $A_{n+1}=A_{n}^{2}+1$ ———Eqn(I)

Statement I : $A_{0} = 1$

Putting n = 0 in Eqn (I), => $A_1 = A_0^2 + 1 = 1 + 1 = 2$

Similarly, $A_2 = A_1^2 + 1 = 4 + 1 = 5$ and so on

We can find the values of $A_{900}$ and $A_{1000}$ and also their greatest common divisor.

Thus, statement I alone is sufficient.


Statement II : We have $A_{1} = 2$

In the above manner, we can determine $A_{900}$ and $A_{1000}$ and also their greatest common divisor.

Thus, statement II alone is sufficient.

$\therefore$ Either statement alone is sufficient.

20) Answer (A)

In the figure, $\triangle AQR \sim \triangle APS$

=> $\frac{AQ}{AP} = \frac{QR}{PS} = \frac{AR}{AS} = k$ ——–Eqn(I)

Statement I : PQ = 3 cm , RS = 4 cm , $\angle$ QPS = 60°

In right $\triangle$ PQM

=> $sin 60^{\circ} = \frac{QM}{QP}$

=> $\frac{\sqrt{3}}{2} = \frac{QM}{3}$

=> $QM = \frac{3 \sqrt{3}}{2} = RN$

Similarly, $sin (\angle RSN) = \frac{3 \sqrt{3}}{8}$

=> $\angle RSN = sin^{-1} (\frac{3 \sqrt{3}}{8})$

$\therefore$ In $\triangle$ APS

=> $\angle PAS = 180^{\circ} – \angle APS – \angle PSA$

=> $\angle PAS = 120^{\circ} – sin^{-1} (\frac{3 \sqrt{3}}{8})$

Thus, statement I alone is sufficient.


Statement II : PS = 10, QR = 5

From eqn(I), $k = \frac{1}{2}$

But, we do not know anything regarding the measures of the remaining sides or any of the angles.

So, statement II is not sufficient.

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