The sum of two even numbers is six more than twice of the smaller number. If the difference between these two numbers is 6, If the larger number lies between 15 to 25 Which is the smaller number?

a)
16

b)
6

c)
24

d)
12

e)
Can not be determined

Correct answer is option 'D'. Can you explain this answer?

Question

The sum of two even numbers is six more than twice of the smaller number. If the difference between these two numbers is 6, If the larger number lies between 15 to 25 Which is the smaller number?

a)
16
b)
6
c)
24
d)
12
e)
Can not be determined

Correct answer is option 'D'. Can you explain this answer?

Answer

Smaller no = x.
x + y = 2x + 6 ----eq 1
y - x = 6. y - 6 = x ---eq 2
from eq2 and eq1
Difference between smaller and larger value is 6. Option B, C and A not possible. Last Option D satisfy every equation.

Answer

Option a is also correct
smaller no = 16
larger no = 16+6 = 22 (<25 and=''>12)
now 16+22= 38 and 16*2+6 = 32+6= 38

Answer

Why not option a edurev should look into this

Answer

**Problem Analysis:**

Let's assume the smaller even number is x and the larger even number is y.

According to the given information,

x + y = 2x + 6 (The sum of two even numbers is six more than twice of the smaller number)

y - x = 6 (The difference between these two numbers is 6)

We are also given that the larger number lies between 15 to 25.

**Solution:**

Let's solve the given equations to find the values of x and y.

1) x + y = 2x + 6

Rearranging the equation, we get:

y = x + 6

2) y - x = 6

Rearranging the equation, we get:

y = x + 6

Since both equations have the same expression for y, it means that the value of y is constant and does not depend on x.

Therefore, the larger number y will always be 6 more than the smaller number x.

Now, let's consider the range of values for y.

Given: 15 ≤ y ≤ 25

Substituting y = x + 6 in the range inequality, we get:

15 ≤ x + 6 ≤ 25

Subtracting 6 from all sides of the inequality, we get:

9 ≤ x ≤ 19

Therefore, the possible values for the smaller number x lie between 9 and 19.

But since x is an even number, the possible values for x are:

x = {10, 12, 14, 16, 18}

Out of these values, the only option present in the answer choices is 12.

Therefore, the correct answer is option 'D' (12).

**Conclusion:**

The smaller number in this problem is 12.

Answer

Let's assume the smaller even number to be x.

Given, the sum of two even numbers (x and y) is 6 more than twice the smaller number (2x+6).
So, x+y=2x+6 ----(1)

Also given, the difference between the two numbers is 6.
So, y-x=6 ----(2)

We need to find the smaller number which is x.

Now, we have two equations (1) and (2) with two variables (x and y).
We can solve these equations to find the values of x and y.

From equation (2), we get y=6+x.

Substituting this value of y in equation (1), we get:

x+y=2x+6
x+6+x=2x+6
2x+6=2x+6
2x=0
x=0/2
x=0

But the given condition is that the larger number lies between 15 to 25. So, x cannot be zero.

Let's try another value of x.
If we take x=12, then y=18 (from equation (2)).

Now, we need to check if y lies between 15 to 25.

As y=18 which is between 15 to 25, we can say that the smaller number is 12 (option D).

Hence, the correct answer is option D (12).

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