Number System-Test 1

Answer: Option B

Explanation

Let the number be x.

Hence,

 $$\begin{gathered} \frac{3}{4}\times \frac{4}{5}\times x-\frac{1}{6}\times \frac{2}{5}\times x=648 \\ \frac{3x}{5}-\frac{x}{15}=648 \\ 8x=648\times 15 \\ x=\frac{648\times 15}{8} \\ x=81\times 15=1215 \end{gathered}$$

 Hence, Option B is correct.

Answer: Option B

Explanation

Let the number be 'x'

Then, 

$$\begin{gathered} \Rightarrow x-\frac{x}{7}=180˚ \\ \Rightarrow \frac{6x}{7}=180 \\ \Rightarrow x=210 \end{gathered}$$

Hence, Option B is correct.

Answer: Option C

Explanation

Let the first even number be 'x'

Then, second even number is x+6.

Now, x+x+6=2x+6

or 2x+6=2x+6 

Hence, data provided is not sufficient.

Answer: Option A

Explanation

Let the one even number be x'

Then, another even number is (x+2)

Now, x(x+2)=3248

or x²+2x-3248=0

⇒ x²+58x-56x-3248=0    (by splitting the middle term)

⇒ x(x-56)+58(x-56)=0

⇒ (x-58)(x-56)=0

⇒ x=56

∴ Larger nummber is x+2 or 56+2=58

Hence, Option A is correct.

Answer: Option D

Explanation

Let the first even number be 'x'

Then, second number is x+2

Again, x²+(x+2)²=6500

or x²+(x+2)²+4+4x=6500

⇒ 2x²+4x+4=6500

⇒ x²+2x+2=3250

⇒ x²+2x-3250=0

⇒ x²+58x-56x-3250=0   (by splitting the middle term)

⇒ x(x-56)+58(x-56)=0

⇒ x=56

∴ smaller number is 56.

Hence, Option d is correct.