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CAT Exam  >  CAT Tests  >  Level-wise Tests for CAT  >  Test Level 1: Data Sufficiency - 2 - CAT MCQ

Test Level 1: Data Sufficiency - 2 - CAT MCQ


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20 Questions MCQ Test Level-wise Tests for CAT - Test Level 1: Data Sufficiency - 2

Test Level 1: Data Sufficiency - 2 for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 1: Data Sufficiency - 2 questions and answers have been prepared according to the CAT exam syllabus.The Test Level 1: Data Sufficiency - 2 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 1: Data Sufficiency - 2 below.
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Test Level 1: Data Sufficiency - 2 - Question 1
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Directions: This problem consists of a question followed by two statements numbered I and II given below it. Read the statements carefully and decide which of them is/are sufficient/necessary to answer the question.
Mark your answer as
a. if the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
b. if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
c. if the data in either of the statements alone is sufficient to answer the question
d. if the data in both statements I and II together is not sufficient to answer the question
e. if the data in both statements I and II together is necessary to answer the question

Q. What is the code for 'eat' in the code language in which, 'he eat food everyday' is written as 'go pro rey kol'?

I. In that code language, 'everywhere food and eat' is written as 'pro wer nom kol'.
II. In that code language, 'he runs and walks daily' is written as 'gwt zat rey woc'.

Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 1

We can figure out the code by observing the common words and symbols.
From the statement I alone, we can see that the common words are 'food' and 'eat' and common codes are 'pro' and 'kol'.
Thus, code for 'eat' can be either 'pro' or 'kol'.
Thus, statement I alone is insufficient.
From the statement II, we see the common word is 'he'. So, 'eat' is not mentioned there.
Thus, statement II alone is not sufficient.
I and II together are insufficient because II has no mention of 'eat'.
Thus, neither I nor II is sufficient to answer the question.

Test Level 1: Data Sufficiency - 2 - Question 2
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Directions: This problem consists of a question followed by two statements numbered I and II given below it. Read the statements carefully and decide which of them is/are sufficient/necessary to answer the question.
Mark your answer as
a. if the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
b. if the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
c. if the data in either of the statements alone is sufficient to answer the question
d. if the data in both statements I and II together is not sufficient to answer the question
e. if the data in both statements I and II together is necessary to answer the question

Q. If 'qw tr yh pl' is the code for 'Let the game begin', then what is the code for 'begin'?

I. 'Begin working right now' is coded as 'pj tr se qa'.
II. 'Work begin tomorrow again' is coded as 'jh mn tr we'.

Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 2

From I alone, we can decode by matching the common codes and words between two statements.
Between question and statement I, common word is 'begin' and common code is 'tr'.
Thus, code for 'begin' is 'tr'.
Hence, statement I alone is sufficient.
Between question and statement II, common word is 'begin' and common code is 'tr'. Thus, code for 'begin' is 'tr'.
Hence, either statement alone is sufficient to answer the question.

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Test Level 1: Data Sufficiency - 2 - Question 3
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Directions: This problem consists of a question followed by two statements numbered I and II given below it. Read the statements carefully and decide which of them is/are sufficient/necessary to answer the question.

Q. Amit celebrates his birthday on 2nd October, 2018. How old will Amit be on that day?
I. Amit's 27th birthday was in 2007.
II. On his birthday in 2050, Amit would turn 70 years old.

Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 3

From I: If Amit celebrated his 27th birthday in 2007, then in 2018 on his birthday, he would turn 27 + 11 = 38 years old.
So, statement I alone is sufficient.
From II: Amit would celebrate his 70th birthday in 2050. The difference of years between 2050 and 2018 = 2050 - 2018 = 32.
This means that in 2018, he would celebrate his (70 - 32 = 38th birthday). 
So, statement II alone is sufficient.
Hence, either of the two statements alone is sufficient for finding the answer.

Test Level 1: Data Sufficiency - 2 - Question 4
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Directions: In this problem, a question is given followed by two statements numbered I and II. Read the question and the statements carefully and decide which of the two statements is/are required to answer the question.
Q. There are five friends Ajhar, Bablu, Champu, Dharmesh and Ekam. Among them, who is the tallest?
Statements:
I. Dharmesh is taller than both Ajhar and Champu.
II. Bablu is shorter than Ekam, but taller than Dharmesh.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 4

From I, we have: Dharmesh > Ajhar, Dharmesh > Champu
From II, we have: Ekam > Bablu > Dharmesh
Combining the above two, we get:
Ekam > Bablu > Dharmesh > Ajhar > Champu or Ekam > Bablu > Dharmesh > Champu > Ajhar.
Thus, Ekam is the tallest.

Test Level 1: Data Sufficiency - 2 - Question 5
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Directions: In this problem, a question is given followed by three statements numbered I, II and III. Read the statements carefully and decide which of them is/are sufficient/required to answer the question.
Q. What is the monthly salary of Ram?
I. Ram's basic salary is Rs. 500 more than Sita's basic salary.
II. Other allowances drawn by Sita, besides her basic salary, amount to Rs. 5000 per month, which is Rs. 1000 less than Ram's allowances.
III. Sita's basic salary is Rs. 15,000 per month.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 5

From III, Sita's basic salary is Rs. 15,000.
From I, Ram's basic salary is Rs. (15,000 + 500) = Rs. 15,500
From II, Sita's other allowances = Rs. 5000, and Ram's other allowances = Rs. 6000
Therefore, Ram's monthly salary = (15,500 + 6000) = Rs. 21,500

Test Level 1: Data Sufficiency - 2 - Question 6
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Directions: The following problem contains a question and statements numbered I, II and III. Read the statements carefully and determine which of them is/are sufficient/required to answer the question.
Q. Persons X, Y and Z are sitting in a row facing the same direction. What is the position of X with respect to Y?
I. X is sitting at an extreme end of the row.
II. Z is sitting to the left of X.
III. Y is sitting in the middle of the row.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 6

(I) says that X sits at the extreme left or the extreme right end of the row.
(II) alone tells us that Z is sitting to the left of X.
(III) alone tells us that Y is sitting in the middle of the row.
(I) and (II) together show that X is sitting at the extreme right end, which means X is to the right of Y, but it is not clear if its immediate to the right of Y or second to the right of Y.
From (II) and (III), we get that X is sitting at the extreme right end and Y sits in the middle of the row. Thus, X is to the immediate right of Y.
Hence, option (4) is correct.

Test Level 1: Data Sufficiency - 2 - Question 7
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Directions: The following problem consists of a question followed by statements I, II and III. Read all the statements carefully and find out which of them is/are sufficient to answer the given question.
Q. What was the standing of team A in the tournament consisting of 5 teams, where each team had a different standing?

I. Team A finished above team B, but below team C.
II. Team A did not finish either at the extreme or in the exact middle.
III. There were exactly two teams between team A and team B.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 7

From I and III, the arrangement will be as follows.
Team C
Team A
-
-
Team B
Team A's standing was second from the top.

Test Level 1: Data Sufficiency - 2 - Question 8
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Directions: The following problem has a question and three statements labelled I, II and III. You have to decide which of the following statements is/are sufficient to answer the question.

Q. In which direction is A with respect to the initial point?

I. A first walked 100 m in a straight line and then 50 m after taking a left turn.
II. A first walked in the East direction and then in the West direction.
III. A started moving towards North and travelled 100 m before taking right, and then travelled 50 m.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 8

I does not provide any information about direction.
II is not conclusive as we do not know the magnitude of the distance travelled.
Only III is sufficient to answer the question.

Test Level 1: Data Sufficiency - 2 - Question 9
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Directions: In this problem, a question is followed by two statements numbered I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Mark answer as

(a) if the question can be answered by using statement I alone, but cannot be answered by using statement II alone
(b) if the question can be answered by using statement II alone, but cannot be answered by using statement I alone
(c) if both statements I and II together are required to answer the question
(d) if the question can be answered by using either of the two statements alone
(e) if both the statements together are not sufficient to answer the question

Q. Find the largest possible two-digit number.

I. Sum of the digits of the number is a multiple of 15.
II. The difference between the original number and the number obtained on reversing the digits of the number is 9.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 9

Let the possible two-digit number be xy.
I. x + y = 15 → Not sufficient
II. 10x + y - (10y + x) = 9
9x - 9y = 9
x - y = 1 → Not sufficient
Using both I and II together:
Now, taking x + y = 15 and x - y = 1
Solving both equations, x = 8 and y = 7
So, the number is 87.
So, the largest possible two-digit number is 87.

Test Level 1: Data Sufficiency - 2 - Question 10
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Directions: The question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer

(a) if the question can be answered by using statement I alone but cannot be answered by statement II alone
(b) if the question can be answered by using statement II alone but cannot be answered by statement I alone
(c) if both statements I and II together are required to answer the question
(d) if the answer can be found by using any of the two statements alone
(e) if both the statements together are not sufficient to answer the question

Q. Find the numbers, if
I.   average of the 3 numbers is 29.
II.  two of the three numbers are in the ratio 5 : 7 and the other number, when divided by 5, leaves remainder 2.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 10

Let the numbers be 'x', 'y' and 'z'.
x + y + z = 29 $\times$ 3 = 87 → Not sufficient
II. Let the numbers be 5x, 7x and y.
y is the number when divided by 5, gives remainder 2, from which y cannot be calculated → Not sufficient
Both I and II together: 5x + 7x + y = 29 $\times$ 3 = 87, still no number can be found → Not sufficient

Test Level 1: Data Sufficiency - 2 - Question 11
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Directions: The question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer

(a) if the question can be answered by using statement I alone but cannot be answered by statement II alone
(b) if the question can be answered by using statement II alone but cannot be answered by statement I alone
(c) if both statements I and II together are required to answer the question
(d) if the answer can be found by using any of the two statements alone
(e) if both the statements together are not sufficient to answer the question

Q. How many times will the father be of his daughter's age after 5 years?

I.  The ratio of their ages after 4 years will be 2 : 1, respectively.
II. The average of their ages is 41.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 11

Let their present ages be 'f' and 'd' years, respectively.
I. (f + 4) : (d + 4) = 2 : 1
⇒ f - 2d = 4 → Not sufficient
II. f + d = 41 $\times$ 2
⇒ f + d = 82 → Not sufficient
Both I and II together:
4 + 2d + d = 82
⇒ d = 26 and f = 56 ⇒ Sufficient

Test Level 1: Data Sufficiency - 2 - Question 12
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Directions: The question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer

(a) if the question can be answered by using statement I alone but cannot be answered by statement II alone
(b) if the question can be answered by using statement II alone but cannot be answered by statement I alone
(c) if both statements I and II together are required to answer the question
(d) if the answer can be found by using any of the two statements alone
(e) if both the statements together are not sufficient to answer the question

Q. Sum of Rohit, Parul and Priya's present ages is 53 years. Find Priya's present age.

I.   Priya is 2 years elder than Parul.
II.  Ratio of Rohit and Parul's present ages is 5 : 6, respectively and that of Parul and Priya is 9 : 10, respectively.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 12

I. Let  Parul's present age = x years
 Priya's present age = x + 2 years
Rohit's present age = y years
Sum of present ages of all three = x + x + 2 + y = 53
2x + y = 51
But still, Priya's present age cannot be calculated → Not sufficient
II. Ratio of Rohit, Parul and Priya's present age = 15 : 18 : 20
15x + 18x + 20x = 53, x = 1
Priya's present age = 20 years → Data sufficient
So, (2) is the correct answer.

Test Level 1: Data Sufficiency - 2 - Question 13
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Directions: Each question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer
(a) if the question can be answered by using statement I alone but cannot be answered by statement II alone
(b) if the question can be answered by using statement II alone but cannot be answered by statement I alone
(c) if both statements I and II together are required to answer the question
(d) if the answer can be found by using any of the two statements alone
(e) if both the statements together are not sufficient to answer the question

Q. In a family of 2 grandparents, 2 parents and one child, find the age of the child, if

I.   average age of grandparents is 92.5 and that of parents is 69
II.  average age of all the family members is 68.6
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 13

Let ages of two 2 grandparents, 2 parents and one child are g1, g2, p1, p2, c respectively.
Statement I: g1 + g2 = 185, p1 + p2 =138 → not Sufficient
Statement II: g1 + g2 + p1 +  p2 +   c = 343 → not Sufficient
Both I and II together:
Present age of the child = 68.6 $\times$ 5 - (92.5 $\times$ 2 + 69 $\times$ 2) = 20 years → Sufficient

Test Level 1: Data Sufficiency - 2 - Question 14
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Directions: The question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer(a) if the question can be answered by using statement I alone but cannot be answered by statement II alone
(b) if the question can be answered by using statement II alone but cannot be answered by statement I alone
(c) if both statements I and II together are required to answer the question
(d) if the answer can be found by using any of the two statements alone
(e) if both the statements together are not sufficient to answer the question

Q. Find the length of a train which crosses a bridge in 10.2 seconds.

I.   Length of bridge is 75 m and train is moving at 25 m/s.
II.  Ratio of length of train and that of bridge is 12 : 5.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 14

I. Let length of train = 'x' m
Time taken to cross the bridge = 10.2 seconds
Distance covered by train to cross the bridge = (x + 75) = 10.2 × 25
x = 180
Length of train = 180 m → Data sufficient
II. Time taken to cross the bridge = 10.2 seconds
Length of train : Length of bridge = 12 : 5, length of train = 12y and length of bridge = 5y
Distance covered by train to cross the bridge = 17y = 10.2 × Speed of train
Length of train cannot be calculated because speed of train is unknown → Not sufficient

Test Level 1: Data Sufficiency - 2 - Question 15
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Directions: Each question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer(a) if the question can be answered by using statement I alone but cannot be answered by statement II alone
(b) if the question can be answered by using statement II alone but cannot be answered by statement I alone
(c) if both statements I and II together are required to answer the question
(d) if the answer can be found by using any of the two statements alone
(e) if both the statements together are not sufficient to answer the question

Q. Find the height of the platform formed after spreading the earth dug out from a well dug in the centre of the rectangular field of area 44 m by 28 m, if

I. area of the rest of the field is 1078 sq. m and the well is 20 m deep
II. 20 m deep well with diameter 14 m is dug in the centre of the rectangular field
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 15

Let the height of the platform formed be 'h' m.
I. (44 × 22 - 1078) × 20 = 1078 × h
h = 2.8 m → Data sufficient
II. 22/7 x 7 x 7 x 20 = (44 × 22 - 11 × 14) × h
h = 2.8 m → Data sufficient

Test Level 1: Data Sufficiency - 2 - Question 16
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Directions: Each question below is followed by statements I and II. You are to determine whether the data given in the statements is sufficient to answer the question. You should use the data and your knowledge of Mathematics to choose between the possible answers. Give answer(a) if the question can be answered by using statement I alone but cannot be answered by statement II alone
(b) if the question can be answered by using statement II alone but cannot be answered by statement I alone
(c) if both statements I and II together are required to answer the question
(d) if the answer can be found by using any of the two statements alone
(e) if both the statements together are not sufficient to answer the question

Q. Find the weight of iron ball, if density of iron is 10 gm/cc and

I. diametre of the ball is 4.2 cm
II. the iron ball is re-casted by melting 3 similar iron balls of radius 1.45 cm
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 16

I. Volume of iron ball = 4/3 x 22/7 x 2.1 x 2.1 x 2.1 = 38.808 cc
So, density of iron ball = 38.808 × 10 = 388.08 gm → Data sufficient
II. Volume of iron ball re-casted from 3 similar iron ball of radius 2 cm = 3 x 4/3 x 22/7 x 1.45 x 1.45 x 1.45 = 38.3 cc
o, density = 38.3 × 10 = 383 gm → Data sufficient

Test Level 1: Data Sufficiency - 2 - Question 17
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Directions: In the following problem, you have to find out which of the given statements is/are necessary for determining the answer of the question asked.

Q. How much time did A take to reach the destination?

I. The ratio of the speed of A to that of B is 3 : 4.
II. B takes 36 minutes to reach the same destination.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 17

From (I):
The ratio of the speed of A to that of B is 3 : 4.
We know, Time = Distance/Speed
Hence, ratio of time between A and B = 4 : 3
From II: If B takes time 36 minutes, then
Time taken by A = (4/3) × 36 = 48 minutes
Both the statements are necessary.

Test Level 1: Data Sufficiency - 2 - Question 18
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Directions: In the following problem, you have to find out which of the given statements is/are necessary for determining the answer of the question asked.

Q. In how many days can 20 women finish the work?

I. 20 men finish the work in 8 days.
II. 20 men and 20 women finish the work in 24/7 days.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 18

From I:
20 men's work for one day = 1/8
From I and II:
20 women's work for one day = (7/24 - 1/8) = 1/6
20 women can finish the work in 6 days.

Test Level 1: Data Sufficiency - 2 - Question 19
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Directions: In the following problem, you have to find out which of the given statements is/are necessary for determining the answer of the question asked.

Q. What will be the ratio between the ages of Bhavesh and Tarun after 6 years?
I. The ratio between their present ages is 9 : 8.
II. Four years ago the ratio between their ages was 7 : 6.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 19

From (I): Ratio of the age of Bhavesh to that of Tarun = 9z : 8z
From (II): (9z - 4)/(8z - 4) = 7/6
Solve statement (II).
(9z - 4) × 6 = (8z - 4) × 7
54z - 24 = 56z - 28
z = 2.
From (I): Present ages of Bhavesh and Tarun = 18 years and 16 years
After 6 years, ages of Bhavesh and Tarun = 24 years and 22 years
Hence, ratio of the age of Bhavesh to that of Tarun after 6 years = 24 : 22 = 12 : 11
Hence, both statements are required to solve the problem.

Test Level 1: Data Sufficiency - 2 - Question 20
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Directions: In the following problem, you have to find out which of the given statements is/are necessary for determining the answer of the question asked.

Q. How many people are there in the bus?

I.  25% passengers are women and 35% are children.
II. There are 24 men in the bus.
Detailed Solution for Test Level 1: Data Sufficiency - 2 - Question 20

From (I), we can conclude that there are 40% men in the bus; but we can't find the exact number of passengers.
From (II): Number of men passengers = 24
By combining both the statements, we get
Total number of passengers = 24/40 x 100 = 60

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