GATE Civil 2024 Set 2 | GA | Question: 3

Question

A student was supposed to multiply a positive real number $p$ with another positive real number $q$. Instead, the student divided $p$ by $q$. If the percentage error in the student's answer is $80 \%$, the value of $q$ is

• A. $5$
• B. $\sqrt{2}$
• C. $2$
• D. $\sqrt{5}$

Comments

pq=(p/q)+(80%)pq

so q=sqrt(5)

Answer 1

 

 

 

Answer:

Comments

@Luke Nebula rest everything is fine but the interpretation of $\text{mod}$ function is wrong.

your interpretation:

$\Big|1-\dfrac{1}{q^{2}}\Big| \quad \Rightarrow \quad \Big(1-\dfrac{1}{q^{2}}\Big) = 0.8 \quad \text{and} \quad \Big(1-\dfrac{1}{q^{2}}\Big) = -0.8$

correct interpretation:

$\Big|1-\dfrac{1}{q^{2}}\Big| \quad \Rightarrow \quad \Big(1-\dfrac{1}{q^{2}}\Big) = 0.8 \quad \text{and} \quad -\Big(1-\dfrac{1}{q^{2}}\Big) = 0.8$

$\text{mod}$ function always outputs $+ve$ values. $\Big(1-\dfrac{1}{q^{2}}\Big)$ is the one in question, who can take both $+ve$ and $-ve$ values and when it takes $-ve$ values $\text{mod}$ function outputs $-\Big(1-\dfrac{1}{q^{2}}\Big)$ to make it $+ve$.

Answer 2

Detailed Explanation

 

Answer 3

$\sqrt{2} = 1.41421356 $

$\sqrt{5} = 2.23606798 $

 

the error can be additive or subtractive because $p$ and $q$ are real

 

Case 1:

$pq + 0.8pq = \frac{p}{q}$

$1.8pq = \frac{p}{q}$

$q^2 = \frac{1}{1.8}$

$q = 0.7453559$ no match

 

Case 2:

$pq - 0.8pq = \frac{p}{q}$

$0.2pq = \frac{p}{q}$

$q^2 = \frac{1}{0.2}$

$q = 2.23606798 = \sqrt{5}$

Answer 4

Simple. Since given that 80% of the result is error. That means remaining  20% is valid.  That means 20% of (p*q) = p/q. This gives q = sqrt(5)

Answer 5

d