Question

In the following pattern, each letter

represents some number:
P Q G R S T 10
The sum of any three consecutive number
In the pattern is 21. Then


A) Q is 11.
B) Q is 10.
C) Q is 6
D) Q is 5
E) there is more than one possible value for Q.

Answer 1

Answer:Let's analyze the given pattern to determine the value of Q.

From the information provided, we know that the sum of any three consecutive numbers in the pattern is 21. Let's assign values to the letters based on this rule:

P Q G R S T 10

Now, we can write the equation for the sum of three consecutive numbers:

Q + G + R = 21

To solve for Q, we need more information. Let's examine the given options:

A) Q is 11.

B) Q is 10.

C) Q is 6.

D) Q is 5.

E) There is more than one possible value for Q.

Let's substitute each value of Q into the equation and see if it satisfies the rule:

A) Substituting Q = 11:

11 + G + R = 21

G + R = 10

B) Substituting Q = 10:

10 + G + R = 21

G + R = 11

C) Substituting Q = 6:

6 + G + R = 21

G + R = 15

D) Substituting Q = 5:

5 + G + R = 21

G + R = 16

From the above equations, we can see that only option B) Q is 10 satisfies the rule, where the sum of G and R is 11. Thus, the correct answer is B) Q is 10.

Therefore, based on the given information, we can conclude that Q is 10.

Explanation:

Answer 2

D) Q is 5

Explanation:

In the following pattern, we are told that each letter represents some number:

• P Q 6 R S T 10

Given that the sum of any three consecutive numbers in the pattern is 21, we can write the following 5 equations:

(1) P + Q + 6 = 21

(2) Q + 6 + R = 21

(3) 6 + R + S = 21

(4) R + S + T = 21

(5) S + T + 10 = 21

Subtract equation 5 from equation 4 to find the value of R:

`\begin{aligned}\sf (R + S + T) - (S + T + 10) &= \sf 21 - 21\\\sf R - 10 &= \sf 0\\\sf R - 10 + 10 &= \sf 0 + 10\\\sf R &= \sf 10\end{aligned}`

Substitute the found value of R into equation 2 and solve for Q:

`\begin{aligned}\sf Q + 6 + R &= \sf 21\\\sf Q + 6 + 10 &= \sf 21\\\sf Q + 16 &= \sf 21\\\sf Q + 16 - 16 &= \sf 21 - 16\\\sf Q &= \sf 5\end{aligned}`

Therefore, the value of Q is 5.

`\hrulefill`

Additional information

To find the value of P, substitute the found value of Q into equation 1:

`\begin{aligned}\sf P + 5 + 6 &= \sf 21\\ \sf P + 11 &= \sf 21\\ \sf P + 11 -11 &= \sf 21-11\\ \sf P &= \sf 10\end{aligned}`

To find the value of S, substitute the found value of R into equation 3:

`\begin{aligned}\sf 6 + 10 + S &= \sf 21\\\sf S + 16 &= \sf 21\\\sf S+16-16&= \sf 21-16\\\sf S &= \sf 5\end{aligned}`

To find the value of T, substitute the found value of S into equation 5:

`\begin{aligned}\sf 5 + T + 10 &= \sf 21\\\sf T + 15 &= \sf 21\\\sf T+15-15&= \sf 21-15\\\sf T &= \sf 6\end{aligned}`

Therefore, the pattern is:

• P Q 6 R S T 10 = 10 5 6 10 5 6 10