Question

P,Q and R are friends. Q's height is 5/6 times the height of P. R's height is 11/5 times that of Q.


WHICH OF THESE STATEMENTS ARE TRUE?

A) The ratio of P's height to that of Q is 5:6
B) P is shorter than Q
C) Q is taller than R
D) P and R are of the same height

Answer 1

Answer:

Sentence C is true from all

Step-by-step explanation:

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Answer 2

Given:

Q's height is 5/6 times the height of P.

R's height is 11/5 times the height of Q.

To Find:

1. If the ratio of P's height to Q's height is 5 : 6

2. If B is shorter than Q

3. If Q is taller than R

4. If P and R are of the same height

Solution

Define x:

Let the height of P be x

Find the height of Q in term of x:

Q's height is 5/6 times the height of P.

$\text{Height of Q} = \dfrac{5}{6} \times x$

$\text{Height of Q} = \dfrac{5}{6} x$

Find the height of R in term of x:

R's height is 11/5 times the height of Q.

$\text{Height of R} = \dfrac{11}{5} \times \dfrac{5}{6}x$

$\text{Height of R} = \dfrac{11}{6}x$

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A) Find the ratio of P : Q:

$P : Q = x : \dfrac{5}{6}x$

Multiply both sides of the ratio by 6:

$P : Q = 6x : 5x$

Divide both sides by x:

$P : Q = 6 : 5$

Statement A is false

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B) Check if P is shorter than Q

$P = x$

$Q = \dfrac{5}{6}x$

$P > Q \Rightarrow \text{P is taller than Q}$

Statement B is false

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C) Check if Q is taller than R

$Q = \dfrac{5}{6}x$

$R = \dfrac{11}{6}x$

$R > Q \Rightarrow \text{R is taller than Q}$

Statement C is false

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D) P and R are of the same height

$P = x$

$R = \dfrac{11}{6}x$

$R > P \Rightarrow \text{R is taller than P}$

Statement D is false

Answer: None of the statements are true.