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

Answer: (d)

Let the two numbers be x and (x + 2).

Then, $x^2 + (x + 2)^2 = 6500$

⇒ $x^2 + x^2 + 4x + 4 = 6500$

⇒ $2x^2 + 4x – 6496 = 0$

⇒ $x^2 + 2x – 3248 = 0$

⇒ $x^2 + 58x – 56x – 3248 = 0$

⇒ $(x + 58) (x – 56) = 0$

⇒ $x$ = 56

Again, using options, it is clear that $(56)^2 + (58)^2 = 6500$

Answer: (b)

Let total number of goats be x.

Then, total number of hens = (90 – x)

So, x × 4 + (90 – x) × 2 = 248

4x – 2x = 248 – 180

$x = 68/2$ = 34

Answer: (a)

A number divisible by 16, 36, 45, 48,

= L.C.M of 16, 36, 45 and 48 = 720

Highest four-digits number = 9999

Now, highest 4 digit number divisible by 720

Completely = 720 × 13 = 9360 < 9999

Answer: (b)

Unit digit in $(3127)^173$ = Unit digit in $(7)^173$.

Now, $7^4$ gives unit digit 1.

∴ $(7)^173 = (7^4)^43 × 7^1$.

Thus, $(7)^173$ gives unit digit 7.

Answer: (a)

Third number = $265/5 = 53$

∴ Smallest number = 49

Largest number = 57

∴ Required value

= 57 + 2 × 49

= 57 + 98 = 155