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All questions of Rational & Irrational Numbers for EmSAT Achieve Exam
Direction: Read the following text and answer the following questions on the basis of the same:A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
According to Fundamental Theorem of Arithmetic 13915 is a- a)Composite number
- b)Prime number
- c)Neither prime nor composite
- d)Even number
Correct answer is option 'A'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
According to Fundamental Theorem of Arithmetic 13915 is a
a)
Composite number
b)
Prime number
c)
Neither prime nor composite
d)
Even number
 | Naina Sharma answered |
The prime factorization of 13,915 is 5 × 112 × 23.
Since it has a total of 4 prime factors, 13,915 is a composite number.
Direction: Read the following text and answer the following questions on the basis of the same:A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
What will be the value of z?- a)22
- b)23
- c)17
- d)19
Correct answer is option 'B'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
What will be the value of z?
a)
22
b)
23
c)
17
d)
19
 | Anita Menon answered |
253 = 11 × z
z = 253/11
z = 23
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
Find the sum of exponents of the prime factors of total number of plants.- a)2
- b)3
- c)5
- d)6
Correct answer is option 'D'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
Find the sum of exponents of the prime factors of total number of plants.
a)
2
b)
3
c)
5
d)
6
| | Arun Sharma answered |
Total number of plants = 135 + 225 = 360
The prime factors of 360 = 2 × 2 × 2 × 3 × 3 × 5
= 23 × 32 × 51
∴ Sum of exponents = 3 + 2 + 1 = 6.
Direction: Read the following text and answer the following questions on the basis of the same:A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
What will be the value of x?- a)15005
- b)13915
- c)56920
- d)17429
Correct answer is option 'B'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
What will be the value of x?
a)
15005
b)
13915
c)
56920
d)
17429
 | Vivek Rana answered |
X = 2783 × 5
x = 13915
Direction: Read the following text and answer the following questions on the basis of the same:A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
What is the minimum number of rooms required during the event?- a)11
- b)31
- c)41
- d)21
Correct answer is option 'D'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
What is the minimum number of rooms required during the event?
a)
11
b)
31
c)
41
d)
21
 | Radha Iyer answered |
Minimum no. of rooms required are total number of students divided by number of students in each room.
= 21
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
What is the maximum number of columns in which they can be planted ?- a)45
- b)40
- c)15
- d)35
Correct answer is option 'A'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
What is the maximum number of columns in which they can be planted ?
a)
45
b)
40
c)
15
d)
35
 | Krishna Iyer answered |
No. of rose plants = 135
No. of marigold plants = 225
The maximum number of columns in which they can be planted
= HCF of 135 and 225
∴ Prime factors of 135 = 3 × 3 × 3 × 5
and 225 = 3 × 3 × 5 × 5
∴ Prime factors of 135 = 3 × 3 × 5 = 45.
Direction: Read the following text and answer the following questions on the basis of the same:A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are- a)14
- b)12
- c)16
- d)18
Correct answer is option 'B'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
In each room the same number of participants are to be seated and all of them being in the same subject, hence maximum number participants that can accommodated in each room are
a)
14
b)
12
c)
16
d)
18
 | Pooja Shah answered |
No. of participants seated in each room would be HCF of all the three values above.
60 = 2 × 2 × 3 × 5
84 = 2 × 2 × 3 × 7
108 = 2 × 2 × 3 × 3 × 3
Hence, HCF = 12.
Direction: Read the following text and answer the following questions on the basis of the same:A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
The product of HCF and LCM of 60,84 and 108 is- a)55360
- b)35360
- c)45500
- d)45360
Correct answer is option 'D'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
The product of HCF and LCM of 60,84 and 108 is
a)
55360
b)
35360
c)
45500
d)
45360
| | Amit Sharma answered |
60 = (22 × 3 × 5)
84 = (22 × 3 × 7)
108 = (22 × 33)
HCF(60, 84,108) = (22 × 3) = 12
LCM =
LCM of 60, 84, and 108 is 3780.
Product of HCF x LCM = 3780 x 12 = 45360
Direction: Read the following text and answer the following questions on the basis of the same:To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
7 × 11 × 13 × 15 + 15 is a- a)Prime number
- b)Composite number
- c)Neither prime nor composite
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
7 × 11 × 13 × 15 + 15 is a
a)
Prime number
b)
Composite number
c)
Neither prime nor composite
d)
None of the above
| | Ayush kumar..🥀❤ answered |
As we know that composite numbers are numbers that have more than two factors(1 nd itself) .
And the solution of 7×11×13×15+15= 15,030 which have more than two factors so it's a composite number.
(btw what's the need of upper question in this...?)
And the solution of 7×11×13×15+15= 15,030 which have more than two factors so it's a composite number.
(btw what's the need of upper question in this...?)
Direction: Read the following text and answer the following questions on the basis of the same:To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is- a)2
- b)4
- c)6
- d)8
Correct answer is option 'B'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
If the product of two positive integers is equal to the product of their HCF and LCM is true then, the HCF (32 , 36) is
a)
2
b)
4
c)
6
d)
8
| | Pooja Shah answered |
Prime factor 32 is 2 x 2 x 2 x 2 x 2
Prime factor 36 is 2 x 2 x 3 x 3
HCF is 2 x 2 i.e 4
HCF of 32 and 36 is 4.
Direction: Read the following text and answer the following questions on the basis of the same:To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
If p and q are positive integers such that p = ab2 and q = a2b, where a, b are prime numbers, then the LCM (p, q) is- a)ab
- b)a3b3
- c)a3b2
- d)a2b2
Correct answer is option 'D'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
If p and q are positive integers such that p = ab2 and q = a2b, where a, b are prime numbers, then the LCM (p, q) is
a)
ab
b)
a3b3
c)
a3b2
d)
a2b2
| | Anita Menon answered |
Given, p = ab2 = a × b × b
q = a2b = a × a × b
LCM of (p, q) = a2b2
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
Find the sum of exponents of the prime factors of the maximum number of columns in which they can be planted.- a)5
- b)3
- c)4
- d)6
Correct answer is option 'B'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
Find the sum of exponents of the prime factors of the maximum number of columns in which they can be planted.
a)
5
b)
3
c)
4
d)
6
 | Gaurav Kumar answered |
We have proved that the maximum number of columns = 45
So, prime factors of 45
= 3 × 3 × 5 = 32 × 51
∴ Sum of exponents = 2 + 1 = 3.
Direction: Read the following text and answer the following questions on the basis of the same:A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
The LCM of 60, 84 and 108 is- a)3780
- b)3680
- c)4780
- d)4680
Correct answer is option 'A'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
The LCM of 60, 84 and 108 is
a)
3780
b)
3680
c)
4780
d)
4680
| | Kiran Mehta answered |
LCM = 2 x 2 x 3 x 3 x 3 x 5 x 7
LCM = 3780
Therefore, LCM of 60, 84, and 108 is 3780.
Direction: Read the following text and answer the following questions on the basis of the same:A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
What will be the value of y?- a)23
- b)22
- c)11
- d)19
Correct answer is option 'C'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
What will be the value of y?
a)
23
b)
22
c)
11
d)
19
| | Naina Sharma answered |
2783 = y × 253
y = 2783/253
y = 11
Direction: Read the following text and answer the following questions on the basis of the same:To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?- a)144
- b)128
- c)288
- d)272
Correct answer is option 'C'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
What is the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B?
a)
144
b)
128
c)
288
d)
272
| | Avinash Patel answered |
We have to find the LCM of 32 and 36.
LCM(32, 36) = 25 × 9 = 288
Hence, the minimum number of books required to distribute equally among students of section A and section B are 288.
Direction: Read the following text and answer the following questions on the basis of the same:A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
108 can be expressed as a product of its primes as- a)23 × 32
- b)23 × 33
- c)22 × 32
- d)22 × 33
Correct answer is option 'D'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A seminar is being conducted by an Educational Organisation, where the participants will be educators of different subjects. The number of participants in Hindi, English and Mathematics are 60, 84 and 108 respectively.
108 can be expressed as a product of its primes as
a)
23 × 32
b)
23 × 33
c)
22 × 32
d)
22 × 33
| | Rohit Sharma answered |
All even numbers except 2 are composite numbers, so 108 is a composite number.
Therefore, we can conclude that 108 can be expressed as a product of prime factors by 22 × 33.
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
Find the total number of plants- a)135
- b)225
- c)360
- d)45
Correct answer is option 'C'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same: A garden consists of 135 rose plants planted in certain number of columns. There are another set of 225 marigold plants, which is to be planted in the same number of columns.
Find the total number of plants
a)
135
b)
225
c)
360
d)
45
 | Abhigyan Shukla answered |
Total number of plants = 135 of rose + 225 of marigold
Total number of plants = 360 plants
So , correct option is C i.e. 360
Direction: Read the following text and answer the following questions on the basis of the same:To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
36 can be expressed as a product of its primes as- a)22 × 32
- b)21 × 33
- c)23 × 31
- d)20 × 30
Correct answer is option 'A'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
To enhance the reading skills of grade X students, the school nominates you and two of your friends to set up a class library. There are two sections- section A and section B of grade X. There are 32 students in section A and 36 students in section B.
36 can be expressed as a product of its primes as
a)
22 × 32
b)
21 × 33
c)
23 × 31
d)
20 × 30
| | Rohan Jain answered |
Solution : Given :
There are two sections- section A and section B of grade X.
There are 32 students in section A and 36 students in section B
the product of two positive integers is equal to the product of their HCF and LCM is true
Solution:
To find the minimum number of books you will acquire for the class library, so that they can be distributed equally among students of Section A or Section B
we need to find LCM of 32 and 36
32 = 2 x 2 x 2 x 2 x 2
36 = 2 x 2 x 3 x 3
LCM = 2 x 2 x 2 x 2 x 2 x 3 x 3
= 288
288 minimum number of books
LCM * HCF = Product of numbers
288 x HCF = 32 x 36
=> HCF = 4
HCF (32 , 36) is 4
Direction: Read the following text and answer the following questions on the basis of the same:A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
The prime factorisation of 13915 is- a)5 × 113 × 132
- b)5 × 113 × 232
- c)5 × 112 × 23
- d)5 × 112 × 232
Correct answer is option 'C'. Can you explain this answer?
Direction: Read the following text and answer the following questions on the basis of the same:
A Mathematics Exhibition is being conducted in your School and one of your friends is making a model of a factor tree. He has some difficulty and asks for your help in completing a quiz for the audience.
The prime factorisation of 13915 is
a)
5 × 113 × 132
b)
5 × 113 × 232
c)
5 × 112 × 23
d)
5 × 112 × 232
 | Meera Rana answered |
Using the prime factorization tree, we have
∴ 13915 = 5 × 11 × 11 × 23 = 5 × 112 × 23
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