OSSSC / OSSC MATH AND REASONING
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网络:📈 Telegram 频道 OSSSC / OSSC MATH AND REASONING 的分析概览
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🔴𝐄𝐧𝐠𝐥𝐢𝐬𝐡- @BLACKBOOK_ENGLISH”
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𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
The Least Common Multiple and Highest Common Factor of two numbers are 60 and 3 respectively. If their difference is 3, then what will be the sum of these two numbers?
Ans. (c) :
The L.C.M of two numbers is always divisible by H.C.F.
The number 72, 24, 48 are divisible by 8, while 68 is not divisible.
Hence 68 can not be the L.C.M of these two numbers. ✅
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
If Highest Common Factor of two numbers is 8, then which of the following cannot be their Least Common Multiple?
Ans. (c) :
First number × Second number = LCM × HCF
=> 390 × 420 = 5460 × HCF.
HCF = 30 ✅
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
If LCM of two numbers 390 and 420 is 5460, then the HCF of two numbers is:
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
The H.C.F. and L.C.M of two numbers is 20 and 120 respectively. If a number is 50% more than the second number, the smaller number is?
Ans. (b) : Let the two numbers be 7x and 11x.
HCF of two numbers × LCM of two numbers = Product of numbers
13 × LCM = 7x × 11x
(HCF = x, then x = 13)
13× LCM = 7×13×11×13
LCM = 1001 ✅
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
If the ratio of two numbers is 7 : 11 and their HCF is 13 then their L.C.M. is:
Ans. (c)
165 = 3 × 5 × 11
176 = 2 × 2 × 2 × 2 × 11
385 = 5 × 7 × 11
495 = 3 × 3 × 5 × 11
LCM = k = 3 × 3 × 5 × 11 × 7 × 2 × 2 × 2 × 2...(i) HCF = 11 ....... (ii)
According to the question
∴ p = equation (i) ÷ equation (ii)
p = 5040 ✅
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
The LCM of 165, 176, 385 and 495 is k. When k is divided by the HCF of the numbers, the quotient is p. What is the value of p?
Ans. (d) : Let the numbers be 2x and 3x respectively.
Formula –
Product of the numbers = HCF × LCM
2x × 3x = 8 × 48
x² = 8 × 8
x = 8
The larger of the two number
= 3x = 3 × 8 = 24 ✅
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
The HCF and LCM of two numbers are 8 and 48 respectively. If the ratio of the two numbers is 2:3, then the larger of the two numbers is:
Ans. (b) : Let those two numbers
a = 21x b = 21 y
LCM = 21 × 221
21xy = 21 × 221
xy = 221 = 13 × 17
∴ a = 21x = 21 × 13 = 273
b = 21 × 17 = 357
Hence the sum of the digits of the other number = 3 + 5 + 7 = 15 ✅
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
The HCF of two numbers is 21 and their LCM is 221 times the HCF. If one of the numbers lies between 200 and 300, then the sum of the digits of the other number is :
Ans. (b) : Let, the two numbers are a, b.
HCF of two numbers = 12
LCM of two numbers = 48
Accoding to the question,
Product of two numbers = HCF × LCM
⇒ a × b = 12 × 48
⇒ a × b = 576
On taking square root of both sides,
√ ab = 24 ✅
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
If the HCF of two numbers is 12 and LCM of the same two numbers is 48, then the square root of the product of these numbers is:
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
What is the HCF of 2³ × 3⁴ and 2⁵× 3² ?
Ans. (d) :
Given– Highest Common Factor (HCF) = 28
Hence, the number · 7×28, 11×28
= 196, 308
Sum of the numbers · (196+308)
= 504 ✅
𝐎𝐃𝐈𝐒𝐇𝐀 𝐕𝐈𝐑𝐓𝐔𝐀𝐋 𝐋𝐈𝐁𝐑𝐀𝐑𝐘
Two numbers are in the ratio 7:11. If their HCF is 28, then find the sum of the two numbers :
