Question

answer is question in full explanation. ​

Answer 1

Given patterns :

• $\bold{5+3+2= 151022}$
• $\bold{9+2+4=183652}$
• $\bold{8+6+3=482466}$
• $\bold{5+4+5=202541}$

To Find :

• We have to find the pattern followed and also unscramble the pattern $\bold{7+2+5}$

Solution :

Considering the first part,

$\bold{5+3+2=151022}$

So, clearly 15 and 10 can be figured out as 5 times 3 and 5 times 2, respectively. Problem arises to figure out how do we have 22 to the extreme left.

Let's denote the numbers by letter.

Let, 5 = x

Let, 3 = y

Let, 2 = z

Now, we see the first two digit i.e 15 is the product of x and y.

Moving on to the next two digit i.e 10, which is product of x and z.

Now, 22?

For 22, we can say that it is the result obtained after multiplying x and y and adding the product of x and y to the product of x and z and then subtracting y from the result.

Numerically it goes this way,

$\longrightarrow$ $\bold{(5\:\times\:3\:)+\:(5\:\times\:2)\:-\:3}$

$\longrightarrow$ $\bold{(15)+(10)-3}$

$\longrightarrow$ $\bold{25-3}$

$\longrightarrow$ $\bold{22}$

$\bold{\boxed{5+3+2= 151022}}$

So the pattern is :

$\large{\boxed{\bold{\purple{{(x\:\times\:y)(x\:\times\:z)\big[(x\:\times\:y\:)+(x\:\times\:z)\:-y\big]}}}}}$

Now, moving to the next one.

$\bold{9+2+4\:=\:183652}$

Let, x = 9, y = 2 and z = 4.

Following the same pattern, we get :

$\bold{(9\:\times\:2)(9\:\times\:4)\big[(9\:\times\:2)(9\:\times\:4)-2\big]}$

$\longrightarrow$$\bold{(18)(36)\big[(18)+(36)-2\big]}$

$\longrightarrow$ $\bold{1836(54-2)}$

$\longrightarrow$ $\bold{\boxed{183652}}$

Now, similarly the 3rd and 4th will follow the same pattern.

Let's unscramble the solution for the last one using the same pattern.

$\longrightarrow$ $\bold{7+2+5}$

Let, x = 7, y = 2 and z = 5.

$\bold{(7\:\times\:2)(7\:\times\:5)\:\big[(7\:\times\:2)+(7\:\times\:5)-2\big]}$

$\longrightarrow$ $\bold{1435\big[(14)+(35)-2\big]}$

$\longrightarrow$ $\bold{1435(49-2)}$

$\longrightarrow$ $\bold{143547}$

$\large{\boxed{\bold{\red{7+2+5\:=\:143547}}}}$