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CAT Practice Test: September 8 - CAT MCQ


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30 Questions MCQ Test - CAT Practice Test: September 8

CAT Practice Test: September 8 for CAT 2024 is part of CAT preparation. The CAT Practice Test: September 8 questions and answers have been prepared according to the CAT exam syllabus.The CAT Practice Test: September 8 MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for CAT Practice Test: September 8 below.
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CAT Practice Test: September 8 - Question 1
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A monkey starts climbing a 15 feet tree. Each hour, he climbs 3 feet and rests for 30 minutes. During his rest, he slips back 2 feet. How many hours will the monkey take to reach the top?

Detailed Solution for CAT Practice Test: September 8 - Question 1

The monkey climbs 3 feet in 1 hour and drops by 2 feet in half an hour.
So, he climbs net 1 foot in (3/2) hours.
This way, he climbs 12 feet in 18 hours.
In the next hour, he will climb 3 more feet i.e. he will climb 15 feet in 19 hours and will reach the top of the tree.

CAT Practice Test: September 8 - Question 2
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A man covered a total distance of 1000 km in 16 hours, partly in a taxi at 36 km/hr and partly in a bus at 80 km/hr. The distance covered by the bus is

Detailed Solution for CAT Practice Test: September 8 - Question 2

Total distance = 1000 km
Total time = 16 hours
Let the time for bus travel be x hours.
Then, time for taxi travel be (16 – x) hours.
Then,
1000 = x × 80 + (16 – x)36
1000 = 80x + 576 – 36x
424 = 44x
x = 424/44 = 106/11 hours
Distance covered by bus = = 770.9 km

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CAT Practice Test: September 8 - Question 3
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x, y and z are the three contestants in a kilometre race. If x can give y a start of 50 metres and x can also give z a start of 69 metres, then how many metres start can y give to z, if the race is supposed to end in a dead heat?

Detailed Solution for CAT Practice Test: September 8 - Question 3

Given, race is to end in a dead heat i.e. they are all supposed to cross the finish line at the same time.
Position of x from finish line = 1000
Position of y from finish line = 1000 - 50 = 950
Position of z from finish line = 1000 - 69 = 931
So, y can give a 19 m start to z for the given scenario to be true.

CAT Practice Test: September 8 - Question 4
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A train passes a 60 metres long platform in 20 seconds and passes a man standing on the platform in 16 seconds. The speed of the train is
Detailed Solution for CAT Practice Test: September 8 - Question 4

Let L = Length of train
Speed = border=0 ........ (1)
Speed = L/16 ........ (2)
From (1) and (2),
L/16 = border=0
⇒ L = 240 m
Speed = L/16 =  240/16 = 15 m/s = border=0 = 54 kmph

CAT Practice Test: September 8 - Question 5
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In a flat race of L metres, A beats B by x1 metres and C by x3 metres. C will beat B, if 
Detailed Solution for CAT Practice Test: September 8 - Question 5

Distance covered by A is L metres to finish the race.
Then, distance covered by B = L - x1 metres
Distance covered by C = L - x3 metres
C beats B, if and only if the distance covered by C at that moment is greater than B.
So, (L - x3) > (L - x1)
Solving, x1 > x3.

CAT Practice Test: September 8 - Question 6
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Two trains starting from the same station and travelling in opposite directions are 227.5 km apart in 3 hours 15 min. Had they been travelling in the same direction, they would have been 32.5 km apart in the same time. Find their speeds (in kmph).
Detailed Solution for CAT Practice Test: September 8 - Question 6

When the trains are travelling in opposite direction, the sum of their speeds (relative speed) = (227.5/3.25) = 70 kmph
If they had been travelling in same directions, the difference of their speeds (relative speed) = (32.5/3.25) = 10 kmph
Hence, the speed of the faster train = (70 + 10)/2 = 40 kmph and the speed of the slower train = (70 - 10)/2 = 30 kmph

CAT Practice Test: September 8 - Question 7
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Javed wanted to reach the ground floor of the building. He went down at the rate of 1 stair in 1 minute. 16 minutes after he started, Salma started from the same point, from where Javed stared, to reach the ground floor of the building. She went down at the rate of 2 stairs in 1 minute. In how many minutes did Salma overtake Javed?
Detailed Solution for CAT Practice Test: September 8 - Question 7

Speed of Javed = 1 stair/min
After sixteen minutes, relative distance between Javed and Salma = 16 stairs
Speed of Salma = 2 stairs/min
Relative speed of Salma w.r.t. Javed = 2 - 1 = 1 stair/min
Time taken by Salma to cross Javed = 16/1 = 16 minutes

CAT Practice Test: September 8 - Question 8
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A man standing inside a tunnel notices that Train A is running inside the tunnel with a speed of 45 kmph. Another Train B, which is half the length of Train A and coming from opposite direction, is running at a speed of 81 kmph. Train A passes Train B in 4 seconds. Which of the following is the closest approximation of the length of the tunnel, if Train A passes completely through it in 4 minutes?
Detailed Solution for CAT Practice Test: September 8 - Question 8

Let the length of Train A be 2L and the length of Train B be L.
Speed of Train A = 45 kmph = 12.5 m/s and speed of Train B = 22.5 m/s
According to the given condition,
4 = $\frac{(L + 2L)}{35}$
L = $\frac{140}{3}$ m
Let length of tunnel be t.
So, 4 × 60 = $\frac{(t + 2L)}{12.5}$
Putting the value of L in the above equation and solving,
t = 2906.67 m = 2.9 km = 3 km (Approx.)

CAT Practice Test: September 8 - Question 9
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A train of length 500 m crosses a platform in 50 sec and another train of the same length, moving in the opposite direction with double the speed of the first train, crosses a pole in 20 sec. What is the length of the platform?
Detailed Solution for CAT Practice Test: September 8 - Question 9

Assume length of platform = L metres
Speed of first train = V m/sec
According to the given condition,
50V = L + 500
Speed of second train = 500/20 = 25 m/sec
Therefore, speed of first train = 12.5 m/sec
Hence, length of platform = 50 × 12.5 - 500 = 625 - 500 = 125 m

CAT Practice Test: September 8 - Question 10
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Varun went for a long ride last Sunday. Every hour, he maintained a constant speed of 60 kmph. But after every 1 hour ride, he took rest for 10 minutes. If he starts from a place A at 8 a.m. and reaches a place B at 2 p.m. on the same day, what is the distance between A and B?
Detailed Solution for CAT Practice Test: September 8 - Question 10

 Total time he travelled = 5 hours 10 minutes (∵ Varun rested for 50 minutes.)
So, d = 60 × 5border=0 = 60 × 31/6 = 310 km

CAT Practice Test: September 8 - Question 11
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Two poles of height 6 m and 11 m stand vertically upright on a plane ground. If the distance between their foot is 12 m, find the distance between their tops.
Detailed Solution for CAT Practice Test: September 8 - Question 11

BC = ED = 6 m
So AB = AC – BC = 11 – 6 = 5 m
CD = BE = 12 m
Then by Pythagoras theorem:
AE2 = AB2 + BE2 ⇒ AE = 13 m

CAT Practice Test: September 8 - Question 12
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Find the length of a chord that is at a distance of 12 cm from the centre of a circle of radius 13 cm.
Detailed Solution for CAT Practice Test: September 8 - Question 12

In the DOBC, OB = 12 cm, OC = radius = 13 cm.
Then using Pythagoras theorem;
BC2 = OC2 – OB2 = 25; BC = 5 cm
Length of the chord = 2 x BC = 2 x 5 = 10 cm

CAT Practice Test: September 8 - Question 13
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Find the value of ∠x in the given figure.
Detailed Solution for CAT Practice Test: September 8 - Question 13

∠AOM = 2∠ABM and
∠AON = 2∠ACN
because angle subtended by an arc at the centre of the circle is twice the angle subtended by it on the circumference on the same segment.
∠AON = 60° and ∠ AOM = 40°
∠X = ∠AON + ∠AOM
(∵ vertically opposite angles).
∠ X = 100°
Alternately, you could also solve this using the following process:

In the given figure, join the points BD and CD. Then, in the cyclic quadrilateral ABDC, the sum of angles x/2 and y would be 180o. Hence, y = 180 – x/2. Also, the sum of the angles OBD + OCD = 180 – 20 - 30
= 130°. Therefore, x + y = 230 (as the sum of the angles of the quadrilateral OBDC is 360). Solving, the two equations, we get x = 100.

CAT Practice Test: September 8 - Question 14
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Find the value of x in the given figure.
Detailed Solution for CAT Practice Test: September 8 - Question 14

By the rule of tangents, we know:
62 = (5 + x)5 ⇒ 36 = 25 + 5x ⇒ 11 = 5x ⇒ x = 2.2 cm

CAT Practice Test: September 8 - Question 15
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Find the value of x in the given figure.
Detailed Solution for CAT Practice Test: September 8 - Question 15

By the rule of chords, cutting externally, we get
⇒ (9 + 6)6 = (5 + x)5 ⇒ 90 = 25 + 5x ⇒ 5x = 65

⇒ x = 13 cm

CAT Practice Test: September 8 - Question 16
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In the given figure AB is the diameter of the circle and ∠PAB = 25°. Find ∠TPA.
Detailed Solution for CAT Practice Test: September 8 - Question 16

∠APB = 90° (angle in a semicircle = 90°)
∠PBA = 180 – (90 + 25) = 65°
∠TPA = ∠PBA (the angle that a chord makes
with the tangent, is subtended by the chord on the circumference in the alternate segment).
= 65°

Note: This is also called as the Alternate Segment Theorem.

CAT Practice Test: September 8 - Question 17
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In the given figure, two straight lines PQ and RS intersect each other at O. If ∠SOT = 75°, find the value of a, b and c.
Detailed Solution for CAT Practice Test: September 8 - Question 17

From the given figure we have:
4b + 2c = 180    (1)
a + b = 105    (2)
4b = a    (3)
Solving these equations, we get that b = 21°; a = 84°; c = 48°.

CAT Practice Test: September 8 - Question 18
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In the following figure, it is given that o is the centre of the circle and ∠AOC = 140°. Find ∠ABC.
Detailed Solution for CAT Practice Test: September 8 - Question 18

(because the angle subtended
by an arc on the circumference is half of what it subtends at the centre). ABCD one cyclic quadrilateral
So ∠ABC = 180° – 70° = 110° (because opposite.angles of a cyclic quadrilateral are supplementary).

CAT Practice Test: September 8 - Question 19
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In the following figure, find the value of x
Detailed Solution for CAT Practice Test: September 8 - Question 19

∠BAC = 30° (∵ angles subtended by an arc anywhere on the circumference in the same segment are equal).

In DBAC; ∠x = 180° – (110° + 30°) = 40°
(∵ sum of angles of a triangle = 180°)

CAT Practice Test: September 8 - Question 20
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Find the perimeter of the given figure.
Detailed Solution for CAT Practice Test: September 8 - Question 20

Perimeter of the figure = 10 + 10 + 6 + 6π = 26 + 6π

CAT Practice Test: September 8 - Question 21
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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 CAT Practice Test: September 8 - Question 21

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.

CAT Practice Test: September 8 - Question 22
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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 CAT Practice Test: September 8 - Question 22

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.

CAT Practice Test: September 8 - Question 23
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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 CAT Practice Test: September 8 - Question 23

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.

CAT Practice Test: September 8 - Question 24
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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 CAT Practice Test: September 8 - Question 24

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.

CAT Practice Test: September 8 - Question 25
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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 CAT Practice Test: September 8 - Question 25

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

CAT Practice Test: September 8 - Question 26
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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 CAT Practice Test: September 8 - Question 26

(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.

CAT Practice Test: September 8 - Question 27
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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 CAT Practice Test: September 8 - Question 27

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.

CAT Practice Test: September 8 - Question 28
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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 CAT Practice Test: September 8 - Question 28

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.

CAT Practice Test: September 8 - Question 29
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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 CAT Practice Test: September 8 - Question 29

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.

CAT Practice Test: September 8 - Question 30
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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 CAT Practice Test: September 8 - Question 30

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

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