number systems Model Questions & Answers, Practice Test for ibps clerk mains

Answer: (c)

Let the integer be x.

Integer + Its reciprocal = $10/3$

⇒ $x + 1/x = 10/3$

⇒ ${x^2 + 1}/x = 10/3$

⇒ $3x^2 + 3 = 10x$

⇒ $3x^2 – 10x + 3$ = 0

⇒ $3x^2 – 9x – x + 3$ = 0 (by splitting middle term)

⇒ 3x (x – 3) – 1(x – 3) = 0

⇒ (x – 3) (3x – 1) = 0

∴ x = 3 (since 1/3 is not an integer)

Alternative Method:

By Hook or by Crook.

From option (a),

$3 + 1/3 = {9 + 1}/3 = 10/3$

Answer: (b)

So, prime factors of 30030 are 2, 3, 5, 11, 7, and 13

So, number of prime factors of 30030 is 6.

Answer: (d)

Amount received by each person

= $72128/46$ = Rs.1568

Answer: (d)

Amount received by each person

= $172850/25 = Rs. 6914$

Answer: (c)

${17^23 + 23^23 + 29^23}/23$

= ${17^23 + (0)^23 + 29^23}/23$

= ${17^23 + 29^23}/23 = {(17)^23 + (6)^23}/23$

Here ${a^n + b^n}/n$

So remainder is always zero.