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IPMAT Mock Test - 6 (New Pattern) - Commerce MCQ


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30 Questions MCQ Test IPMAT Mock Test Series - IPMAT Mock Test - 6 (New Pattern)

IPMAT Mock Test - 6 (New Pattern) for Commerce 2024 is part of IPMAT Mock Test Series preparation. The IPMAT Mock Test - 6 (New Pattern) questions and answers have been prepared according to the Commerce exam syllabus.The IPMAT Mock Test - 6 (New Pattern) MCQs are made for Commerce 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for IPMAT Mock Test - 6 (New Pattern) below.
Solutions of IPMAT Mock Test - 6 (New Pattern) questions in English are available as part of our IPMAT Mock Test Series for Commerce & IPMAT Mock Test - 6 (New Pattern) solutions in Hindi for IPMAT Mock Test Series course. Download more important topics, notes, lectures and mock test series for Commerce Exam by signing up for free. Attempt IPMAT Mock Test - 6 (New Pattern) | 100 questions in 90 minutes | Mock test for Commerce preparation | Free important questions MCQ to study IPMAT Mock Test Series for Commerce Exam | Download free PDF with solutions
IPMAT Mock Test - 6 (New Pattern) - Question 1
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What is the value of k for which the system of equations kx + 2y = 5 and 3x + y = 1 have no solution?

Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 1
The given system of equation may be written as

kx + 2y − 5 = 0

3x + y − 1 = 0

It is of the form:

a1x + b1y + c1 = 0

a2x + b2y + c2 = 0

Where a1 = k, b1 = 2, c1 = −5

And a2 = 3, b2 = 1, c2 = −1

The given system will have no solution, if:

We have,

So, the given system of equations will have no solution, if:

a1/a2 = b1/b2

⇒ k/3 = 2/1

⇒ k = 6

So, the given system of equations will have no solution if k = 6.

Hence, the correct option is (c)

IPMAT Mock Test - 6 (New Pattern) - Question 2
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How many different words can be formed using all the letters the word HONOLULU if no two alike letters are together?

Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 2
H = 1 ; N = 1 ; O, L, U = 2

Total permutations

With both O together (7 items)

Similarly for both L together

also for

Now with both O and L together = 6!/2! = β

With both O and U together = 6!/2!

with U and L together = 6!/2!

All three together = 5! = y

Total 3α − 3β + y

Words with none together = 7! − (3α − 3β + y)

Hence, the correct option is (C).

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IPMAT Mock Test - 6 (New Pattern) - Question 3
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Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 3

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 4
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To get an entry into NTS examination a student has to score an average of score 60% or above in 5 terminal tests having maximum marks 100 in each. He has scored 70% in 1st two tests but failed to score 60% in third. What should be his score in last two tests so that he must get the entry into the NTS Examination?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 4

According to question

Score in first two terminal = 70 x 2 = 140

Let score in third term is K which is less than 60. If average score in last two be x than = 140 + 2x + k = 60% of 500

⇒ 140 + 2x + k = 300

⇒ 2x + k = 160

As k may be zero, so to must get entry in the NTS Examination a student has to score 160 marks in the last two-term of which the average is 80%.

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 5
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A player has scored 5929 runs in his entire career. Find the number of matches played by him, if it is the same as the average number of runs scored per match.
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 5
Let the number of matches played be x. So, the average runs scored per match will also be x. According to the question,

Hence, the number of matches played by him is 77.

IPMAT Mock Test - 6 (New Pattern) - Question 6
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When a clock shows 4 : 30, the minute hand points in North. In which direction does the hour hand point?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 6
Realising the following figure

From the figure, the hour hand points in North-West direction.

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 7
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Each question is followed by two statements P and Q. Mark your answer using the following instructions.

In a party how many people ordered both ice cream and soup?

P: Number of people who ordered soup is 35 and number of people who ordered at least one of the two items is 55.

Q: Number of people who ordered the ice cream is 25.
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 7
Let the number of people who ordered only soup, only ice cream and both the items be ‘a’, V and V respectively. Using statement P: a + c = 35 and a + b + c = 55 We cannot find the value of c.

This statement is insufficient to answer the question.

Using statement Q : b + c = 25

Nothing can be concluded for value of c on the basis of this statement alone

Using both statements together: c = 5 Therefore, number of people who ordered both the items is 5.

IPMAT Mock Test - 6 (New Pattern) - Question 8
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There are 20 points in a plane, how many triangles can be formed by these points if 5 are colinear?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 8
Number of points in plane n = 20.

Number of colinear points m = 5.

Number of triangles from by joining n points of which m are colinear = nC3 – mC3

Therefore the number of triangles = 20C3 – 5C3 = 1140-10 = 1130.

Hence, the correct option is (A).

IPMAT Mock Test - 6 (New Pattern) - Question 9
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If then which of the following statement is true?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 9
Given series

Series can be rewritten as:

Therefore, the value of x will be between 4 and 5.

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 10
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Find the total number of ways in which letters of the word ’SUCEEDS’ can be arranged such that S or E is neither at the first place nor at the last place.
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 10
Apart from 2S and 2E there are three letters that can be placed at the end places. Hence, both ends can be filled in 3C2 × 2! ways while rest letters can be filled in ways.

∴ Required number of ways

Hence, the correct option is (C).

IPMAT Mock Test - 6 (New Pattern) - Question 11
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751 + 752 + 753 + 754 is always divisible by?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 11
751 + 752 + 753 + 754

= 751(1 + 7 + 72 + 73)

= 751 × 400 = 750 × 2800

Hence, it is always divisible by 2800.

IPMAT Mock Test - 6 (New Pattern) - Question 12
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Two trains travel in the same direction at 55 km/hr and 91 km/hr. A person sitting in the slower train observes that the faster train crosses him in 20 second. Then what is the length of the faster train?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 12
Relative speed = (91 - 55)km/hr

= 36 km/hr = 10 m/s

.*. The length of the faster train

= 20 x 10 = 200 m

IPMAT Mock Test - 6 (New Pattern) - Question 13
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If 85 % of a number is added to 75, then the result is the number itself. The number is:
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 13
Let the number be x.

We are given that, 85% of x + 75 = x

Hence, the correct option is (C).

IPMAT Mock Test - 6 (New Pattern) - Question 14
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Two pipes P and Q can fill a tank in 24 minutes and 16 minutes respectively. If both the pipes are opened simultaneously, after how much time Q should be closed so that the tank will be filled completely in 12 minutes?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 14
Let the pipe Q be closed after x minutes

Part filled by P in 12 minutes + part filled by Q in x minutes = 1

12 /24 + x /16 = 1

x = 8 minutes

Hence, pipe Q must be closed after 8 minutes.

IPMAT Mock Test - 6 (New Pattern) - Question 15
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A sells an article to B at a profit of 10% sells the article back to A at a loss of 10%. In this transaction:
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 15

Let CP was 100 for A originally

A sells article to B at 10% profit,

CP for B = 100 + 10% of 100 = 110

Now, B sells it A again with loss 10%

Now, CP for A this time = 110 − 10% of 110 = 99

A makes profit = 110 − 99 = 11%

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 16
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In how many ways, a committee of 7 members can be formed from 6 males and 5 females, consisting of at most 3 males?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 16
Possible ways are

3 males and 4 females or 2 males and 5 females

∴ Total number of ways = 6C3 × 5C4 + 6C2 × 5C5

= 100 + 15 = 115.

IPMAT Mock Test - 6 (New Pattern) - Question 17
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Direction: Answer the following question based on the given information.

The table given below shows the number of employees in five companies - A, B, C, D and E in five different departments - HR, Marketing, Operation, Finance and Other.

The total number of employees in company C is what percent of the total number of employees in company E?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 17
Total employees in C company = 50 + 75 + 41 + 58 + 55 = 279

Total employees in E company = 70 + 70 + 28 + 48 + 72 = 288

Required percent

= 96.9%

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 18
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Direction: Answer the following question based on the given information.

The table given below shows the number of employees in five companies - A, B, C, D and E in five different departments - HR, Marketing, Operation, Finance and Other.

The ratio of the total number of the employees in HR & Operations in the company D to the total number of the employees in Finance and others in the company E is?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 18
A number of employees in HR in the company D = 45.

A number of employee Operations in the company D = 19.

The total number of employees in HR & Operations in the company D = 45 + 19 = 64.

A number of employees in Finance in the company E = 48.

A number of the employees in others in the company E = 72.

A total number of employees in Finance and others in the company E = 48 + 72 = 120.

The ratio of the total number of the employees in HR & Operations in the company D to the total number of the employees in Finance and others in company E is = 64/120 = 8 : 15.

Hence the correct option is C.

IPMAT Mock Test - 6 (New Pattern) - Question 19
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The pie chart given below shows the distribution of sales of seven different companies and bar graph shows percentage profit of the respective companies. Study the graphs given below and answer the following questions.

If total stiles of company E is Rs. 310.8 thousands, then profit earned by the company A (in thousands) is?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 19
Let Total sale = 100

The profits of the different companies are tabulated below:

Total sale of company E = 28x

∴ 28x = 310.8

⇒ x = 310.8/28 = 11.1

So, the profit earn by 22.2 thousands

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 20
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If what is the value of the x?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 20

IPMAT Mock Test - 6 (New Pattern) - Question 21
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What should come in place of '?' in the following number series?

5,6,22,103,359,?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 21
The series follows the below pattern,

5 + 12 = 6

6 + 42 = 22

22 + 92 = 103

103 + 162 = 359

359 + 252 = 984

∴ The next term in the series is 984.

Hence, the correct option is (A).

IPMAT Mock Test - 6 (New Pattern) - Question 22
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In ∆LMN, medians MX and NY are perpendicular to each other and intersect at Z. If MX = 8 cm, NY = 12 cm, what is the area of ∆LMN?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 22

Since Z is the centroid, so it divides triangle in the ratio 2:1, therefore NZ = 2YZ

⇒ NZ = 8 and YZ = 4

Since the median divides the triangle into two equal areas, area ∆LMN = 2 x ∆ NMX

= 64 cm2

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 23
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Find the area of the equilateral triangle (in cm2) each of whose sides measure 18cm.
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 23
Area of equilateral triangle

Where b is the side of the triangle.

Area = 140.29 cm2

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 24
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Sum of two natural numbers is 4 less than the difference of their squares. Find the ratio of the squares of the numbers.
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 24
Let the two numbers be x and y

x + y + 4 = x2 − y2

x + y + 4 = (x + y)(x − y)

⇒ (x + y)(x − y − 1) = 4

⇒ x + y = 4

and x−y−1=1

(since, x + y > x − y − 1, as both x and y are natural numbers.)

Solving above equations, we get x = 3 and y = 1. the ratio of the squares of the numbers

= 32 : 12 = 9 : 1

Hence, the correct option is (C).

IPMAT Mock Test - 6 (New Pattern) - Question 25
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Kamal started a business investing Rs. 9000. After five months, Sameer joined with a capital of Rs. 8000. If at the end of the year, they earn a profit of Rs. 6970, then what will be the share of Sameer in the profit?
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 25
It is given that, Kamal invested for 12 months and Sameer invested for 7 months.

So, Kamal : Sameer = (9000 × 12) : (8000 × 7)

= 108 : 56

= 27 : 14

At the end of the year, they earn a profit of Rs. 6970.

Therefore, Sameer's ratio in profit will be:

Hence, the correct option is (A).

IPMAT Mock Test - 6 (New Pattern) - Question 26
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Each question is followed by two statements P and Q. Mark your answer using the following instructions.

If LCM of two numbers is 90, then what are the numbers?

P: One of the numbers is 18.

Q: HCF of the numbers is 3.
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 26
Either of the statements alone is not sufficient to answer the question.

Using both the statements: Let the other number be x

90 × 3 = 18 × x

(Since, product of two numbers is equal to the product of their LCM and HCF) x = 15.

Hence the correct option is (a).

IPMAT Mock Test - 6 (New Pattern) - Question 27
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Direction: The question is followed by two statements P and Q. Mark your answer using the following instructions.

Which of the number among A, B and C is the greatest?

P: B is not less than A

Q: C is less than A
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 27
Combining both the statements:-

B ≥ A > C,

B may or may not be the greatest.

So, both the statements together are not sufficient to answer the question.

Hence, the correct option is (B).

IPMAT Mock Test - 6 (New Pattern) - Question 28
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If p, q and r in A.P., then the value of the following determinant is
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 28
∵ p, q and r are in A.P

∴ p + r = 2 q

IPMAT Mock Test - 6 (New Pattern) - Question 29
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If length, breadth and height of a cube is increased by 10%, 20% and 30% respectively, then find the percentage increase in its volume.
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 29
Let the length, breadth and height (in units) of original cube be x.

∴ Volume of the original cube = x3 New volume = 1.1x × 1.2x × 1.3x = 1.716 x3

∴ Required percentage

= 71.6%

IPMAT Mock Test - 6 (New Pattern) - Question 30
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If the matrix does not have its inverse, then find the value of x.
Detailed Solution for IPMAT Mock Test - 6 (New Pattern) - Question 30
∵ Inverse of A does not exist.

∴ |A| = 0

⇒ x(2 − 0) − 2 (−3 −0) + 5(6 − 6) = 0

⇒ 2x + 6 + 0 = 0 ⇒ 2x + 6 = 0 ⇒ x = −3

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