12. 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
Correct 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
x/3xy + y/3xy = 12/105
⇒ 1/3y + 1/3x = 4/35
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13. The LCM of two numbers is 12 times their HCF. The sum of the HCF and the LCM is 403. If one of the numbers is 93, then the other number is
a) 124 b) 134 c) 128 d) 138
Correct 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 x 31 x 12)/93 = 124
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14. The LCM of the 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
Correct 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 – x2
→ x2 – 55x – 45x – 2475 = 0
→ (x – 45) (x – 55) = 0
→ x = 45 or x = 55
Then, difference = 55 – 45 = 10
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15. If the product of three consecutive numbers is 210 than the sum of the smaller number is:
a) 3 b) 5 c) 4 d) 11
Correct Answer: (d)
2 210 — divide by 2
3 105 — divide by 3
5 35 — divide by 5
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