model 4 addition, subtraction, multiplication and division with lcm & hcf Section-Wise Topic Notes With Detailed Explanation And Example Questions
MOST IMPORTANT quantitative aptitude - 5 EXERCISES
The following question based on LCM & HCF topic of quantitative aptitude
(a) 3
(b) 5
(c) 4
(d) 11
The correct answers to the above question in:
Answer: (d)
2 | 210 |
3 | 105 |
5 | 35 |
7 |
210 = 2 × 3 × 5 × 7 = 5 × 6 × 7
∴ Required answer = 5 + 6 = 11
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Read more with math operations Based Quantitative Aptitude Questions and Answers
Question : 1
Let x be the least number, which when divided by 5, 6, 7 and 8 leaves a remainder 3 in each case but when divided by 9 leaves no remainder. The sum of digits of x is
a) 21
b) 18
c) 22
d) 24
Answer »Answer: (b)
LCM of 5, 6, 7 and 8 = 840
2 | 5, | 6, | 7, | 8 |
5, | 3, | 7, | 4 |
∴ LCM = 2 × 5 × 3 × 7 × 4 = 840
Required number = 840x + 3
which is divisible by 9 for a certain least value of x.
Now, 840x + 3 = 93x × 9 + 3x + 3
3x + 3, is divisible by 9 for x = 2
Required number = 840 × 2 + 3
= 1680 + 3 = 1683
∴ Sum of digits = 1 + 6 + 8 + 3 = 18
Question : 2
Three numbers which are coprime to one another are such that the product of the first two is 551 and that of the last two is 1073. The sum of the three numbers is :
a) 75
b) 85
c) 81
d) 89
Answer »Answer: (b)
Let the numbers be x, y and z which are prime to one another.
Now, xy = 551 yz = 1073
∴ y = HCF of 551 and 1073
y = 29
x = $551/29$ = 19
and z = $1073/29$ = 37
∴Sum = 19 + 29 + 37 = 85
Question : 3
The greatest four digit number which is exactly divisible by each one of the numbers 12, 18, 21 and 28 is
a) 9828
b) 9882
c) 9288
d) 9928
Answer »Answer: (a)
Using Rule 1,
1st number × 2nd number = L.C.M. × H.C.F
2 | 12, | 18, | 21, | 28 |
2 | 6, | 9, | 21, | 14 |
3 | 3, | 9, | 21, | 7 |
7 | 1, | 3, | 7, | 7 |
1, | 3, | 1, | 1 |
LCM = 2 × 2 × 3 × 3 × 7= 252
The largest 4-digit number = 9999
∴ Required number = 9999 – 171 = 9828
Question : 4
The LCM of two numbers is 495 and their HCF is 5. If the sum of the numbers is 100, then their difference is :
a) 10
b) 70
c) 46
d) 90
Answer »Answer: (a)
Using Rule 1,
Suppose 1st number is x then, 2nd number = 100 – x
∴ LCM × HCF = 1st number × 2nd number
→ 495 × 5 = x × (100 – x)
→ 495 × 5 = 100x – $x^2$
→ $x^2$ – 55x – 45x – 2475 = 0
→ (x – 45) (x – 55) = 0
→ x = 45 or x = 55
Then, difference = 55 – 45 = 10
Question : 5
The LCM of two numbers is 12 times their HCF. The sum of the HCF and the LCM is 403. If one of the number is 93, then the other number is
a) 124
b) 134
c) 128
d) 138
Answer »Answer: (a)
Using Rule 1,
Let the HCF of numbers = H
Their LCM = 12H
According to the question,
12H +H = 403
⇒ 13H = 403
⇒ H = $403/13$ =31
⇒ LCM = 12 × 31
Now, First number × second number
= HCF × LCM
= 93 × Second Number
= 31 × 31 × 12
Second number = ${31 × 31 × 12}/93$ = 124
Question : 6
The sum of two numbers is 36 and their H.C.F and L.C.M. are 3 and 105 respectively. The sum of the reciprocals of two numbers is
a) $2/35$
b) $4/35$
c) $3/25$
d) $2/25$
Answer »Answer: (b)
Let the numbers be 3x and 3y.
∴ 3x + 3y = 36
⇒ x + y = 12 ... (i)
and 3xy = 105 ... (ii)
Dividing equation (i) by (ii), we have
$\text"x"/ \text"3xy" + \text"y"/ \text"3xy" = 12/105$
⇒ $1/\text"3y" + 1/\text"3x" = 4/35$
LCM & HCF Shortcuts and Techniques with Examples
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model 1 Basic formula of LCM & HCF
Defination & Shortcuts … -
model 2 find lcm of numbers
Defination & Shortcuts … -
model 3 find hcf of numbers
Defination & Shortcuts … -
model 4 addition, subtraction, multiplication and division with lcm & hcf
Defination & Shortcuts … -
model 5 lcm & hcf vs ratios
Defination & Shortcuts …
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