model 3 twice, thrice, one third etc. of numbers Practice Questions Answers Test with Solutions & More Shortcuts
average PRACTICE TEST [9 - EXERCISES]
model 1 basic average questions
model 2 average of consecutive numbers
model 3 twice, thrice, one third etc. of numbers
model 4 find nth average from 1st & last number
model 5 find new average from error
model 6 find average of excluded number
model 7 average on ages/weight
model 8 find monthly income
model 9 average on cricket/exam
Question : 6
Of the three numbers, the first is 3 times the second and the third is 5 times the first. If the average of the three numbers is 57, the difference between the largest and the smallest number is
a) 126
b) 135
c) 9
d) 18
Answer »Answer: (a)
Let second number be x
∴ The first number = 3x
and the third number = 15x
Now, x + 3x + 15x = 3 × 57
⇒ 19x = 3 × 57
⇒ x= ${3×57}/19$= 9
∴ Required difference
= 15x – x = 14x
= 14 × 9 = 126
Aliter : Using Rule 15,
From three numbers, first number is 'a’ times of 2nd number, 2nd number is 'b’ times of 3rd number and the average of all three numbers is x, then,
First number = $\text"3ab"/ \text"1+b+ab"$ x ; Second number = $\text"3b"/ \text"1+b+ab"$ x ; Third number = $\text"3b"/ \text"1+b+ab"$ x
a = 3, b = 5, x = 57
First number = $\text"3ab"/ \text"1+b+ab"$x
= ${3×3×5}/{1+3+15}$× 57
= $45/19$ × 57 = 135
Second number = $\text"3ab"/ \text"1+b+ab"$x
= ${3×5}/{19}$× 57
= $15/19$ × 57 = 45
Third number = $3/ \text"1+b+ab"$x
= $3/19$×57 = 9
Required result = 135 – 9 = 126
Question : 7 [SSC CGL Tier-II 2015]
If the arithmetic mean of 3a and 4b is greater than 50, and a is twice b, then the smallest possible integer value of a is
a) 21
b) 19
c) 20
d) 18
Answer »Answer: (a)
$\text"3a+4b"/2$ > 50
⇒ 3a + 4b > 100
⇒ 3a + ${4a}/2$ > 100 [Since a = 2b]
⇒ 3a + 2a > 100
⇒ 5a > 100
⇒ a > 20
∴ Minimum value of a = 21
Question : 8 [SSC CPO 2011]
Of the three numbers, the first number is twice of the second and the second is thrice of the third number. If the average of these 3 numbers is 20, then the sum of the largest and smallest numbers is
a) 54
b) 60
c) 24
d) 42
Answer »Answer: (d)
Let the third number be x.
∴ Second number = 3x
and first number = 6x
∴ 6x + 3x + x = 3 × 20
⇒ 10x = 60 ⇒ x = 6
∴ Required sum = 6x + x = 7x = 7 × 6 = 42
Aliter : Using Rule 15,
From three numbers, first number is 'a’ times of 2nd number, 2nd number is 'b’ times of 3rd number and the average of all three numbers is x, then,
First number = $\text"3ab"/ \text"1+b+ab"$ x ; Second number = $\text"3b"/ \text"1+b+ab"$ x ; Third number = $\text"3b"/ \text"1+b+ab"$ x
Here, a = 2, b = 3, x = 20
Largest Number= $\text"3ab"/ \text"1+b+ab"$ x
= ${3×2×3}/{1+3+2×3}$×20
=$18/10$×20 = 36
Smallest Number = $3/\text"1+b+ab"$ ×x
= $3/{1+3+2×3}$×20
= $3/10$×20 = 6
Sum = 36 + 6 = 42
Question : 9 [SSC CGL Prelim 2005]
The average of first three numbers is thrice the fourth number. If the average of all the four numbers is 5, then find the fourth number.
a) 2
b) 4
c) 4.5
d) 5
Answer »Answer: (a)
Let the numbers be a, b, c,
${\text"a + b + c"}/3$ = 3d
⇒ a + b + c = 9d
Again, ${\text"a + b + c + d"}/4$ = 5
⇒ a + b + c + d = 20
⇒ 9d + d = 20
⇒ 10d = 20 ⇒ d = 2
Question : 10 [SSC CGL Tier-1 2011]
Out of 4 numbers, whose average is 60, the first one is one fourth of the sum of the last three. The first number is
a) 48
b) 60
c) 15
d) 45
Answer »Answer: (a)
Let the first number be x,
then, x = ${240 - x}/4$
⇒ 4x = 240 – x
⇒ 5x = 240
⇒ x = $240/5$ = 48
IMPORTANT quantitative aptitude EXERCISES
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Basic Average Questions Practice Test, Shortcuts, Tricks, PDF »
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New Average Aptitude MCQ Average of Consecutive Numbers »
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Top 99+ Average Aptitude: Twice, One Third of Numbers MCQ »
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Top 99+ Aptitude Average on Ages & Weights MCQ Test Quiz »
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Top Aptitude Average MCQ Find Monthly Income for Average »
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Top 149+ Aptitude Average on Cricket & Exam MCQ Test Quiz »
model 3 twice, thrice, one third etc. of numbers Shortcuts »
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Click to Start..average Shortcuts and Techniques with Examples
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model 1 basic average questions
Defination & Shortcuts … -
model 2 average of consecutive numbers
Defination & Shortcuts … -
model 3 twice, thrice, one third etc. of numbers
Defination & Shortcuts … -
model 4 find nth average from 1st & last number
Defination & Shortcuts … -
model 5 find new average from error
Defination & Shortcuts … -
model 6 find average of excluded number
Defination & Shortcuts … -
model 7 average on ages/weight
Defination & Shortcuts … -
model 8 find monthly income
Defination & Shortcuts … -
model 9 average on cricket/exam
Defination & Shortcuts …
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