Number System-Test 2

Answer: Option E

Explanation

Let the First odd number be 'x'

Then, 8 consecutive odd numbers are as

x-8, x-6, x-4, x-2, x

x+2, x+4, x+6

Now, (x-8)+(x-6)+(x-4)+(x-2)+x+(x+2)+(x+4)+(x+6)=656

⇒ 8x-8=656

⇒ 8x=656+8

⇒ 8x=664

⇒ x=83

Now, let four consecutive even numbers be y-2, y, y+2 and y+4

Now, 4y+4=87×4

⇒ 4y+4=348

⇒ 4y=348

⇒ y=86

Now, smallest even number =86-8= 78

Second largest even number =88

∴ Sum of both the numbers =88+78=166

Hence, Option E is correct.

Answer: Option E

Explanation

Let the three consecutive odd numbers be x-2, x and x+2 and three even numbers be y-2, y and y+2

Now,

⇒ x-2+x+x+2+y-2+y+y+2=231

⇒ 3x+3y=231

⇒ x+y=77

Again, y-2-(x-2)=11

⇒ y-2-x+2=11

⇒ y-x=77  ---Eq(1)

⇒ x+y=11  ---Eq(2)

By adding Eq(1) and Eq(2), we get 

⇒ 2y=88

⇒ y=44, x=33

∴ Largest odd number =35

and largest even number =46

∴ Sum of these two numbers =81

Hence, Option E is correct.

Answer: Option E

Explanation

Let the five conseutive numbers be

⇒ x-2, x-1, x, x+1, x+2

Again, 

⇒ x-2+x-1+x+x+1+x+2=270

⇒ 5x=270

⇒ x=54

Second number= 54-1=53

and fifth number= 54+2=56

∴ Required sum = 56+53=109

Hence, Option E is correct.

Answer: Option E

Explanation

Let the original fraction be $\frac{x}{y}$

Then,

$$\begin{gathered} =\frac{x\times 500}{y\times 600}=\frac{20}{27} \\ =\frac{x}{y}=\frac{120}{135} \\ =\frac{x}{y}=\frac{8}{9} \end{gathered}$$

 Hence, Option E is correct.

Answer: Option E

Explanation

Let the original fraction be $\frac{x}{y}$

Then,

$$\begin{gathered} =\frac{x+{\displaystyle \frac{x}{4}}}{y-{\displaystyle \frac{y}{3}}}=\frac{33}{64} \\ =\frac{{\displaystyle \frac{4x+x}{4}}}{{\displaystyle \frac{2y}{3}}}=\frac{33}{64} \\ =\frac{x}{y}=\frac{33\times 8}{320\times 3} \\ =\frac{x}{y}=\frac{11}{40} \end{gathered}$$

Hence, Option E is correct.