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) 2
(b) 4
(c) 3
(d) 5
The correct answers to the above question in:
Answer: (b)
Let the numbers be 21x and 21y
where x and y are prime to each other.
21x + 21y = 336
21 (x + y) = 336
x + y = $336/21$ = 16
∴ Possible pairs = (1, 15), (5, 11), (7, 9), (3, 13)
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Question : 1
HCF and LCM of two numbers are 7 and 140 respectively. If the numbers are between 20 and 45, the sum of the numbers is :
a) 70
b) 63
c) 77
d) 56
Answer »Answer: (b)
Let the numbers be 7x and 7y
where x and y are co-prime.
Now, LCM of 7x and 7y = 7xy
∴ 7xy = 140 ⇒ xy = $140/7$ = 20
Now, required values of x and y whose product is 50 and are coprime, will be 4 and 5.
∴ Numbers are 28 and 35 which lie between 20 and 45.
∴ Required sum = 28 + 35 = 63.
Question : 2
The product of the LCM and the HCF of two numbers is 24. If the difference of the numbers is 2, then the greater of the number is
a) 3
b) 6
c) 4
d) 8
Answer »Answer: (b)
Using Rule 1,
1st number × 2nd number = L.C.M. × H.C.F
Let the larger number be x.
Smaller number = x – 2
First number × Second number = HCF × LCM
→ x (x – 2) = 24
→ $x^2$ – 2x – 24 = 0
→ $x^2$ – 6x + 4x – 24 = 0
→ x (x – 6) + 4 (x – 6) = 0
→ (x – 6) (x + 4) = 0
→ x = 6 because x ≠ – 4
Question : 3
The sum of two numbers is 84 and their HCF is 12. Total number of such pairs of number is
a) 2
b) 4
c) 3
d) 5
Answer »Answer: (c)
HCF = 12
∴ Numbers = 12x and 12y where x and y are prime to each other.
∴ 12x + 12y = 84
⇒ 12 (x + y) = 84
⇒ x + y = $84/12$ = 7
∴ Possible pairs of numbers satisfying this condition
= (1,6), (2,5) and (3,4). Hence three pairs are of required numbers.
Question : 4
A number between 1000 and 2000 which when divided by 30, 36 and 80 gives a remainder 11 in each case is
a) 1451
b) 1712
c) 1641
d) 1523
Answer »Answer: (a)
We find LCM of 30, 36 and 80.
2 | 30, | 36, | 80 |
2 | 15, | 18, | 40 |
3 | 15, | 9, | 20 |
5 | 5, | 3, | 20 |
1, | 3, | 4 |
LCM = 2 × 2 × 3 × 3 × 4 × 5 = 720
∴ Required number = 2 × 720 + 11
= 1440 + 11 = 1451
Question : 5
If A and B are the H.C.F. and L.C.M. respectively of two algebraic expressions x and y, and A + B = x + y, then the value of A3 + B3 is
a) x3 – y3
b) y3
c) x3
d) x3 + y3
Answer »Answer: (d)
Let no. are x and y and HCF = A, LCM = B
Using Rule, we have
xy = AB
⇒ x + y = A + B (given) ...(i)
$(x–y)^2$ = $(x+y)^2$ – 4xy
or, $(x–y)^2$ = $(A+B)^2$ – 4 AB
$(x–y)^2$ = $(A–B)^2$
(x–y) = A – B ...(ii)
Using (i) and (ii), we get
x = A and y = B
∴ $A^3 + B^3 = x^3 + y^3$
Question : 6
The smallest five digit number which is divisible by 12,18 and 21 is :
a) 10224
b) 10080
c) 30256
d) 50321
Answer »Answer: (b)
2 | 12, | 18, | 21 |
3 | 6, | 9, | 21 |
2, | 3, | 7 |
LCM of 12, 18 and 21
= 2 × 3 × 2 × 3 × 7 = 252
Of the options, 10080 ÷ 252 = 40
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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