Miss Prism, being duly sworn, was asked her age but remained stubbornly silent. Come, come, my good woman," snapped the judge. "You must answer the court's questions." Counsel intervened smoothly. "I understand, M’Lord that she is certainly over 40 and under 50, if it pleases you, M'Lord." "It does not please me, Sir Ambrose. I am thinking of finding her in contempt." This threat overcame some of Miss Prism's reticence, and she hastily deposed as follows: "When I stop speaking, I shall have made exactly two true statements. My age is divisible by 2. It is a perfect square. It is not 42. It is a prime number. It is divisible by 3". At this point, she stopped speaking. 'Perjury, I fancy," snapped the judge. "With respect, M’Lord, I fancy she has answered the question, if your Lordship will attend carefully to the various possibilities." How old is the lady?

42 years

Step-by-step explanation:

Let x be Miss Prism's Age

From the Statement.

"I understand, M’Lord that she is certainly over 40 and under 50"

Therefore: 40<x<50

The possible values of x are:

41,42,43,44,45,46,47,48,49.

The Statements spoken by Miss Prism are:

1.My age is divisible by 2.

2.It is a perfect square.

3.It is not 42.

4.It is a prime number.

5.It is divisible by 3.

Out of these, only two are true.

Consider Statement 2: It is a perfect square.

The only perfect square in the set of numbers is 49 and this invalidates all other statements. Therefore, her age cannot be 49 and this statement is false.

We are left with:

41,42,43,44,45,46,47,48

Consider Statement 4: It is a prime number.

The prime numbers present are 41,43,47. However, there is no other statement to back these choices, Therefore these numbers are out.

We are left with:

42,44,45,46,48

In the other three statements

1.My age is divisible by 2.

3.It is not 42.

5.It is divisible by 3.

Since we are looking for one result, we consider out of the numbers that which is solely satisfied by two of the rules.

If:

1.My age is divisible by 2. (True)

3.It is not 42. (True)

5.It is divisible by 3. (False)

The possible results are:

44,46

If:

1.My age is divisible by 2. (False)

3.It is not 42. (True)

5.It is divisible by 3. (True)

The following results are possible

45,48

If:

1.My age is divisible by 2. (True)

3.It is not 42. (False)

5.It is divisible by 3. (True)

The only possible result is 42

Therefore the Woman's age is 42.

y=−9/2x+10

step-by-step explanation:

let's solve for y.

0−9x−2y=−20

step 1: add 9x to both sides.

−9x−2y+9x=−20+9x

−2y=9x−20

step 2: divide both sides by -2.

−2y

−2

=

9x−20

−2

y=

−9

2

x+10