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All questions of Fractions, Decimals and Approximations for JAMB Exam

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  • a)
    2.5
  • b)
    0.25
  • c)
    0.0025
  • d)
    0.025
Correct answer is option 'D'. Can you explain this answer?

Sun Ray Institute answered
Mistake Points:
In this type of question, in the numerator, there are 6.75 and 4.25, while in the denominator there is 67.5, and 42.5 is present in multiplication.
From the denominator, we can write 67.5 × 67.5 as 6.75 × 10 × 6.75 × 10 = 100 × (6.75), and similarly for other terms.
Therefore we take 100 as common from the denominator.
Identity used:
a3 - b3 = (a - b) (a2 + b2 + ab)
Calculation:
⇒ ? = 2.5/100
⇒ ? = 0.025
∴ ? = 0.025

  • a)
    11/7
  • b)
    2
  • c)
    4/7
  • d)
    7/11
Correct answer is option 'A'. Can you explain this answer?

Sun Ray Institute answered
Given:

Calculation:
On picking fractions one by one,
⇒ 1 - 1/2 = 1/2
⇒ 2 + 1 = 3
⇒ 1 + 1/3 = 4/3
⇒ 1 + 4/3 = 7/4
⇒ 1 + 4/7 = 11/7

Solve:
(?)3 × 10 = 13230 ÷ (9.261 ÷ 7)
  • a)
    10
  • b)
    25
  • c)
    125
  • d)
    0.5
Correct answer is option 'A'. Can you explain this answer?

Sun Ray Institute answered
Given expression is,
⇒ (?)3 × 10 = 13230 ÷ (9.261 ÷ 7)
⇒ (?)3 × 10 = 13230 ÷ (1.323)
⇒ (?)3 × 10 = 10000
⇒ (?)3 = 1000
⇒ (?)3 = (10)3
⇒ ? = 10

The closest approximation of the solution product
0.3333 × 0.25 × 0.499 × 0.125 × 24 is:
  • a)
    1/8
  • b)
    3/4
  • c)
    3/8
  • d)
    2/5
Correct answer is option 'A'. Can you explain this answer?

Sun Ray Institute answered
0.3333 × 0.25 × 0.499 × 0.125 × 24
⇒ 1 / 3 × 1 / 4 ×  499/1000 × 1/8 × 24
⇒ 1 /3 × 1 / 4 × 499 / 1000 × 3
⇒  1 / 4 × 499 / 1000
⇒  499/4000
⇒  0.12475 ~ 0.125
⇒  0.125 = 1/8
Hence the correct answer is "1/8".

In a group of students, 1/5 are aged below 8 years. Of the remaining 2/5 are above 8 years. What fraction of the students are exactly 8 years of age?
  • a)
    12/25
  • b)
    2/5
  • c)
    3/5
  • d)
    4/25
Correct answer is option 'A'. Can you explain this answer?

Sun Ray Institute answered
Let the total number of students in the group be 1
Number of students who are below age 8 = 1 × 1/5 = 1/5
Remaining students = 1 – 1/5 = 4/5
Number of students who are above age 8 = 4/5 × 2/5 = 8/25
Number of students who are exactly 8 years old = 1 – 1/5 – 8/25 = 12/25
Short trick:
Let the total number of students be 25
Number of student who are below age 8 = 25 × 1/5 = 5
Remaining students = 25 – 5 = 20
Number of students who are above age 8 = 20 × 2/5 = 8
Number of students who are exactly age 8 = 25 – 5 – 8 = 12
Required fraction = 12/25

The sum of all proper fractions whose denominators are less than or equal to 100 is:
  • a)
    2124
  • b)
    2475
  • c)
    2575
  • d)
    1925
Correct answer is option 'B'. Can you explain this answer?

Sun Ray Institute answered
Formula used :
(1 + 2 + 3 + 4 +     ......... + 99) = [ n ( n + 1 ) ] ÷ 2
Solution :
We can write all proper fractions whose denominators are less than or equal to 100 in given form :
⇒ 1/2 + (1/3 + 2/3) + (1/4 + 2/4 + 3/4) + ...  (1/100 + 2/100 + .. ..  99/100)
⇒ 1/2 + 3/3 + 6/4 + ..... + 4950/100
⇒ 1/2 + 1 + 3/2 + 2 + ........ + 99/2
We can also write this equation in following way :
⇒ 1/2 + 2/2 + 3/2 + ...... + 99/2
⇒ 1/2 ( 1 + 2 + 3 + ..... + 99 )
⇒  /2 [ ( 99 × 100) ÷ 2 ]
⇒ 99 × 25
⇒ 2475
Hence the correct answer is "2475".

Which of the following is true?
  • a)
    9/16 < 13/24
  • b)
    9/16 = 13/24
  • c)
    9/16 > 13/24
  • d)
    9/16 ≤ 13/24
Correct answer is option 'C'. Can you explain this answer?

Sun Ray Institute answered
Concept Used:
a/b and c/d are two numbers,
then (a × d) and (b × c) are need to be compared.
Calculation:
We have, 9/16 and 13/24 
⇒ 9 × 24 = 216
⇒ 13 × 16 = 208
⇒ 216 > 208
⇒ 9/16 > 13/24.

Which of the following fractions is the largest?
  • a)
    13/19
  • b)
    25/31
  • c)
    28/31
  • d)
    70/79
Correct answer is option 'C'. Can you explain this answer?

Sun Ray Institute answered
Given:
The fractions are 13/19, 25/ 31, 28/31, 70/79.
Calculation:
The values are-
13/19 = 0.68
25/31 = 0.80
28/31 = 0.90
70/79 = 0.88
∴ Option C is correct.

 then the value of x is
  • a)
    1/3
  • b)
    1
  • c)
    2/3
  • d)
    None of the above
Correct answer is option 'C'. Can you explain this answer?

Sun Ray Institute answered
⇒ 2x = 2 - x
⇒ 3x = 2
⇒ x = 2/3
∴ The value of x is 2/3
The correct option is 3 i.e. 2/3

Directions: What will come in place of the question mark (?) in the following questions?
? = {(2.5)3 + (1.5)3}/{(2.5)3 – (1.5)3}
  • a)
    3/5
  • b)
    6233/2000
  • c)
    6233/1000
  • d)
    1. 76/49
Correct answer is option 'D'. Can you explain this answer?

Sun Ray Institute answered
Given:
{(2.5)3 + (1.5)3}/{(2.5)3 – (1.5)3}
Calculation:
⇒ ? = {(2.5)3 + (1.5)3}/{(2.5)3 – (1.5)3}
⇒ ? = (15.625 + 3.375)/(15.625 - 3.375)
⇒ ? = 19/12.25
⇒ ? = 1900/1225 = 76/49

Solve:
(81.84 + 118.16) ÷ 53 = 1.2 × 2 + ?
  • a)
    0.8
  • b)
    -0.8
  • c)
    0.6
  • d)
    -0.6
Correct answer is option 'B'. Can you explain this answer?

Sun Ray Institute answered
Given expression,
(81.84 + 118.16) ÷ 53 = 1.2 × 2 + ?
⇒ 200 ÷ 53 = 1.2 × 2 + ?
⇒ 200 ÷ 125 = 1.2 × 2 +?
⇒ 1.6 = 2.4 + ?
⇒ ? = -0.8

If the fractions 7/13, 2/3, 4/11, 5/9 are arranged in ascending order, then the correct sequence is?
  • a)
    2/3, 7/13, 4/11, 5/9
  • b)
    7/13, 4/11, 5/9, 2/3
  • c)
    4/11, 7/13, 5/9, 2/3
  • d)
    5/9, 4/11, 7/13, 2/3
Correct answer is option 'C'. Can you explain this answer?

Sun Ray Institute answered
(7/13) = 0.538
(2/3) = 0.666
(4/11) = 0.3636
(5/9) = 0.5555
Out of 2/3, 7/13, 4/11, 5/9
2/3 is the largest number followed by 5/9 then 7/13 and the smallest is 4/11.
∴ The ascending order will be 4/11, 7/13, 5/9, 2/3.

The positive square root of
  • a)
    3
  • b)
    4
  • c)
    1
  • d)
    2
Correct answer is option 'D'. Can you explain this answer?

Sun Ray Institute answered
⇒ [ ( 0.75 × 0.75 × 0.75 ) / 0.25 ] + [ 1.75 + 0.5625 ]
⇒ [ ( 3 × 0.5625 ) ] + [ 2.3125 ]
⇒ [ 1.6875 + 2.3125 ]
⇒ 4
Now √4 = 2 
Hence the correct answer is "2".

Correct expression of 
  • a)
    1/55
  • b)
    18/100
  • c)
    18/1000
  • d)
    1/66
Correct answer is option 'A'. Can you explain this answer?

Sun Ray Institute answered
Calculation:
Let x = 0.0181818....
⇒ 10x = 0.1818.... ----eq (1)
⇒ 1000x = 18.1818.... ----eq (2)
Now, eq (2) - eq (1)
⇒ 1000x - 10x = 18.1818... - 0.1818...
⇒ 990x = 18
⇒ x = 18/990
⇒ x = 1/55
∴ The fraction of  is 1/55

The value of  is equal to:
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?

Sun Ray Institute answered
Formula used:

Calculation:

By using the above formula
Alternate Method
Calculation:
By subtracting eq.1 from eq.2: 
99x = 122
⇒ x = 122/99
By subtracting eq.3 from eq.4:
99y = 86
⇒ y = 86/99
By subtracting eq.5 from eq.6:
99z = 29
⇒ z = 29/99

7/9 of the people present in a hall are sitting in 9/13 of the chairs available and the rest are standing. If there are 28 empty chairs, how many chairs would have been still empty if everyone in the hall was sitting?
  • a)
    15
  • b)
    12
  • c)
    18
  • d)
    10
Correct answer is option 'D'. Can you explain this answer?

Sun Ray Institute answered
Let the number of people be x and number of the chair be y.
Number of available chair = y × (9/13) = 9y/13
Number of empty chair = y - (9y/13) = 4y/13
Given, Number of empty chairs = 28
According to the question
4y/13 = 28
y = 28 × (13/4) = 91
Total number of chairs = 91
Number of chairs in which people are sitting = 91 - 28 = 63
Number of people who sit = x × (7/9) = 7x/9
According to the question
7x/9 = 63
x = 63 × (9/7) = 81
Total number of people are = 81
Chairs would have been still empty if everyone in the hall was sitting = 91 - 81 = 10

What will come in place of question mark ‘?’ in the following question?
  • a)
    1
  • b)
    100
  • c)
    0.1
  • d)
    0.01
Correct answer is option 'A'. Can you explain this answer?

Sun Ray Institute answered
Given:
Concept used:
a2 - b2 = (a + b) × (a - b)
Calculation:
⇒ [(4.22 - 1.92) + 2.3]/(2.3 × 7.1) = ?
⇒ [(4.2 + 1.9) × (4.2 - 1.9) + 2.3]/((2.3 × 7.1) = ?
⇒ (2.3 × 6.1 + 2.3)/(2.3 × 7.1) = ?
⇒ 2.3 × (6.1 + 1)/(2.3 × 7.1) = ?
⇒ (2.3 × 7.1)/(2.3 × 7.1) = ?
? = 1

What is the value of 
  • a)
    36
  • b)
    37
  • c)
    39
  • d)
    38
Correct answer is option 'B'. Can you explain this answer?

Sun Ray Institute answered
= 25/2 + 37/3 + 73/6
= (75 + 74 + 73)/6
= 222/6
= 37
Shortcut Trick:

= 12 + 12 + 12 + (1/2 + 1/3 + 1/6)
= 36 + 1 = 37

Find the value of {(.98)3 + (0.02)3 + 3 × 0.98 × 0.02 – 1}
  • a)
    1.98
  • b)
    1.09
  • c)
    1.562
  • d)
    0
Correct answer is option 'D'. Can you explain this answer?

Sun Ray Institute answered
Given:
 {(.98)3 + (0.02)3 + 3 × 0.98 × 0.02 – 1}
Concept used:
(a + b)3 = a3 + b3 + 3ab(a + b)
Calculation:
{(.98)3 + (0.02)3 + 3 × 0.98 × 0.02 – 1
⇒ [(.98)3 + (0.02)3 + 3 × 0.98 × 0.02(0.98 + 0.02)} – 1]
Now, first term is of the form (a + b)3 where a = .98 and b = 0.02
⇒ (0.98 + 0.02)3 – 1 = 1 – 1 = 0
∴ The value is 0.

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