Question

If the sum and difference of two numbers are respectively $4x-2$ and $2x+4$, then the larger number is and the smaller number is .

• A. $x-3$
• B. $6x+2$
• C. $3x+1$
• D. $x+3$

Answer 1

Answer: (A), (C)

The correct options are
A $x-3$
C $3x+1$

Let the larger and smaller numbers be $a$ and $b$.
According to the question,
$a+b=4x-2$ and $a-b=2x+4.$

Adding both the numbers we get
$(a+b)+(a-b)=(4x-2)+(2x+4)\Rightarrow a+b+a-b=4x-2+2x+4\Rightarrow 2a=6x+2\Rightarrow 2a=2(3x+1)\Rightarrow a=3x+1$

Now, subtracting one number from another we have
$(a+b)-(a-b)=(4x-2)-(2x+4)\Rightarrow a+b-a+b=4x-2-2x-4\Rightarrow 2b=2x-6\Rightarrow 2b=2(x-3)\Rightarrow b=x-3$

Therefore, the larger number is $3x+1$ and the smaller number is $x-3$.