Multiple choice

Read the data carefully and answer the following question. 20, p, q, r, s, 165 p - 5 = (A + 3)2 + B q - p = (A + 2)2 + B r - q = (A + 4)2 + B s - r = (A + 5)2 + B Given, A = HCF of P & Q, where P and Q are prime numbers And, B = largest root of w2 - 6w + 8 = 0 How many numbers are not divisible by 5?

  1. p & q Only

  2. p, r & s Only

  3. q, r & s Only

  4. r & s Only

  5. p, q & r Only
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

B is the largest root of w^2 - 6w + 8 = 0, which factors to (w-4)(w-2)=0, so B=4. A is HCF of two primes, which is 1. Substituting: p = (1+3)^2 + 4 + 5 = 25; q = (1+2)^2 + 4 + 25 = 38; r = (1+4)^2 + 4 + 38 = 67; s = (1+5)^2 + 4 + 67 = 107. Numbers not divisible by 5 are q, r, and s.

AI explanation

To determine which numbers are not divisible by 5, we first find A and B from the given series 20, p, q, r, s, 165. The roots of w squared minus 6w plus 8 equals 0 are 2 and 4, so the largest root B is 4. Since A is the highest common factor of two prime numbers P and Q, and we need a valid series, A must be 1. We calculate the gaps using the formulas: p minus 20 equals (1 plus 3) squared plus 4 which is 20, making p equal to 40. Next, q minus p equals (1 plus 2) squared plus 4 which is 13, making q equal to 53. Then, r minus q equals (1 plus 4) squared plus 4 which is 29, making r equal to 82. Finally, s minus r equals (1 plus 5) squared plus 4 which is 40, making s equal to 122. The numbers are 20, 40, 53, 82, 122 and 165, and checking for divisibility by 5 shows that q, r and s are not divisible by 5.

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