Number System-Test 2

Answer: Option B

Explanation

Let the first even number be 'x'

Then, second even number is (x+2)

And,   x(x+2)=9408

or x²+2x-9408=0     [by splitting the middle term]

⇒  x²+98x-96x-9408=0

⇒  x(x-96)+98(x-96)=0

⇒  (x+98)+(x-96)=0

⇒ x=96

∴ The greater number is 98.

Hence, Option B is correct.

Answer: Option E

Explanation

Let the first even number be 'x'

Then, second even number is (x+2)

And,   x(x+2)=6888

or       x²+2x=6888

⇒ x²+84x-82x-6888=0  [by splitting the middle term]

⇒ x(x-82)+84(x-82)=0

⇒ (x+84)(x-82)=0

⇒ x=82

and second number is 84.

∴ Greater number is 84.

Hence, Option E is correct.

Answer: Option B

Explanation

Let the first odd number be 'x'

Then, Second odd number is 'y'

Then, x+y=38    ---Eq(1)

And   x×y=325

(x-y)²=(x+y)²-4xy

(x-y)²⇒ (38)²-4×325

(x-y)²⇒ 1444-1300

x-y⇒ √144

or x-y=12         ---Eq(2)

By solving Eq(1) and Eq(2), we get

⇒ 2x=50

⇒ x=25, y=13

∴ Required number =3×25=75

Hence, Option B is correct.

Answer: Option E

Explanation

Let the first odd number be 'x'

Second odd number is x+2

Third odd number is x-2

Fourth Odd number is x+4

Now, x+x+2+x-2+x+4=4×36

or 4x+4=4×36

⇒ x+1=36

⇒ x=35

∴ smallet odd number  is (x-2)=0

⇒ (35-2)=33.

Hence, Option E is correct.

Answer: Option D

Explanation

Let the five consecutive odd numbers be x, x-2, x-4, x+2 and x+4

And,

⇒ x+x+2+x-2+x+4+x-4=575

⇒ 5x=575

⇒ x=115

So, from this, five odd numbers are 111, 113, 115, 117, 119.

By this, we cannot determine the next set of odd numbers.

Hence Option D is correct.