Aptitude  Number series  Practice Q&A

Answer: 114345
Explanation:

99 = 11 x 9, where 11 and 9 are co-prime.

By hit and trial, we find that 114345 is divisible by 11 as well as 9. So, it is divisible by 99.

Answer: 18
Explanation:

This is an A.P. in which $ a $ = 6, $ d $ = 6 and S_n = 1800

Then,$ \dfrac{n}{2} $[2$ a $ +$\left ( n - 1\right)$$ d $] = 1800

$\Rightarrow$ $ \dfrac{n}{2} $[2 x 6 + $\left( n - 1\right)$ x 6] = 1800

$\Rightarrow$ 3$ n $ $\left(n + 1\right)$ = 1800

$\Rightarrow n \left(n + 1\right)$ = 600

$\Rightarrow n $² + $ n $ - 600 = 0

$\Rightarrow n $² + 25$ n $ - 24$ n $ - 600 = 0

$\Rightarrow n $$\left( n + 25\right)$ - 24$\left( n + 25\right)$ = 0

$\Rightarrow$ $\left( n + 25\right)$$\left( n - 24\right)$ = 0

$\Rightarrow n $ = 24

Number of terms = 24.

Answer: 2975
Explanation:

This is an A.P. in which $ a $ = 51, $ l $ = 100 and $ n $ = 50.

$\therefore$Sum =$ \dfrac{n}{2} $$\left( a + l \right)$=$ \dfrac{50}{2} $x (51 + 100)   = 25 x 151   = 3775.

Answer: 3625216
Explanation:

1904 x 1904= (1904)²

= (1900 + 4)²

= (1900)² + (4)² + $\left(2 \times 1900 \times 4\right)$

= 3610000 + 16 + 15200.= 3625216.

Answer: 6
Explanation:

Unit digit in 7⁹⁵ = Unit digit in [(7⁴)²³ x 7³]

= Unit digit in [Unit digit in 2401 ²³] x (343)]

= Unit digit in (1²³ x 343)
= Unit digit in (343)
= 3

Unit digit in 3⁵⁸ = Unit digit in [(3⁴)¹⁴ x 3²]
= Unit digit in [Unit digit in (81)¹⁴ x 3²]
= Unit digit in [(1)¹⁴ x 3²]
= Unit digit in 1 x 9
= Unit digit in 9
= 9

Unit digit in (7⁹⁵ - 3⁵⁸) = Unit digit in (343 - 9) = Unit digit in (334) = 4.

So, Option b is the answer.

Answer: 820
Explanation:

Sum of first n natural numbers = $\dfrac{n × (n + 1)}{2}$
Sum of first 40 natural numbers = $\dfrac{40 × 41}{2}$
= 20 × 41
= 820

Answer: 153
Explanation:

Sum of first n natural numbers = $\dfrac{n × (n + 1)}{2}$
Sum of first 17 natural numbers = $\dfrac{17 × 18}{2}$
= 17 × 9
= 153

Answer: 6084
Explanation:

Sum of the cubes of first n natural numbers = $\left[\dfrac{n × (n + 1)}{2}\right]^{2}$
Sum of the cubes of first 12 numbers = $\left[\dfrac{12 × (12 + 1)}{2}\right]^{2}$
= $\left[\dfrac{12 × 13}{2}\right]^{2}$
= $(6 × 13)^{2}$
= $78^{2}$
= 6084

Answer: a = 1; x = 10
Explanation:

Plug in the values of each option in the equation and check.
Option 4: 1 + 2 + 3 + 4 = 10.

Answer: 105625
Explanation:

Sum of the cubes of first 25 natural numbers = $\left[\dfrac{n × (n + 1)}{2}\right]^{2}$
= $\left[\dfrac{25 × (25 + 1)}{2}\right]^{2}$
= $\left[\dfrac{25 × 26}{2}\right]^{2}$
= $(25 × 13)^{2}$
= $325^{2}$
= 105625