The average of 5 positive integers is 436. The average of the first two numbers is 344 and the average of the last two numbers is 554. What is the third number ?
(a) 482 (b) 346 (c) 556 (d) 384 (e) None of these
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Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy
Correct answer is option (C) 0 ≤ r < b
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If two positive integers x and y are expressible in terms of primes as x = p^2q^3 and y = p^3q, what can you say about their LCM and HCF.
Solution: x = p2q3 and y = p3q HCF(x, y) = p2 x q LCM(x, y) = p3 x q3 LCM(x, y) = (p x q2) x HCF(x, y) => LCM is a multiple of HCF.
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If two positive integers a and b are written as a = x^3y^2 and b = xy^3; x, y are prime numbers, then HCF (a, b) is
Correct answer is (B) xy2
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Three consecutive integers add up to 51. What are these integers?
Let the three consecutive integers bex, x+1and x+2. According to the question, x+x+1+x+2 = 51 => 3x+3=51 => 3x+3-3=51-3 [Subtracting 3 from both sides] => 3x=48 => 3x/3 = 48/3 [Dividing both sides by 3] X=16 Hence, first...
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If a and b are two odd positive integers such that a > b, then prove that one of the two numbers (a+b)/2 and (a-b)/2 is odd and the other is even.
Let, a = 2p+1, p∈N and b = 2q+1 , q∈N\(\cup\){0} \(\because\) a > b ⇒ 2p+1 > 2q+1 ⇒ p > q \(\frac{a+b}{2}\) = \(\frac{2p+1+2q+1}{2}\) = p+q+1 \(\frac{a-b}{2}\) = \(\frac{2p+1-(2q+1)}{2}\) = p-q Case-I: \(\frac{a+b}{2}\) is odd which implies p+q+1 is odd \(\Rightarrow\) p+q is even (\(\because\) odd - 1 = even) \(\Rightarrow\) p+q-2q...
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Define HOE of two positive integers and find the HCF of the following pairs of numbers: (i) 32 and 54 (ii) 18 and 24 (iii) 70 and 30 (iv) 56 and 88
By applying Euclid’s division lemma (i) 54 = 32 × 1 + 22 Since remainder ≠ 0, apply division lemma on division of 32 and remainder 22. 32 = 22 × 1 +...
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Two positive integers p and q can be expressed as = ab^2 and q =a^2b, a and b are prime numbers. what is the LCM Of p and q ?
The correct answer is a2 b2
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The average of five numbers is 281. The average of the first two numbers is 280 and the average of the last two numbers is 178.5.
(a) Assume the third number = x According to question 2 × 280 + x + 178.5 × 2 = 281 × 5 or, 560 + x + 357 = 1405 or, x +...
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The sum of five numbers is 290. The average of the first two numbers is 48.5 and the average of last two numbers is 53.5.
(e) Third number = 290 – (48.5 × 2) – (53.5 × 2) = 290 – 97 – 107= 86
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The average of 15 numbers is 18. The average of first 8 is 19 and that last 8 is 17, then the 8th number is
(C) The 8th number is 18.
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