Read the following information carefully and answer the given questions. Some recruitment is done by three companies, i.e., P, Q and R. The number of vacancies in company P, Q, and R are 6, 12 and 2 respectively. The number of candidates, who got interview call for per vacancy in company P, Q and R are 60, 6x and 4x respectively. The total number of candidates applied in company R is 25% of the total number of candidates, applied in the company Q and three fifth of the total number of candidates applied in the company P. The difference between the number of candidates, who got interview calls in the company Q and R is 320. If the difference between the total number of candidates applied in company P and company R is 160, then find the number of candidates, who did not get interview call from company Q.

### Concept & Logic Leverage the newly provided absolute difference to find the exact number of applied candidates using their predefined ratios. Then, use the interview calls equation to find $x$ and subtract total calls from total applicants. ### Step-by-Step Solution 1. Establish the ratio of applicants: $A_R = \frac{3}{5} A_P \implies A_P = \frac{5}{3} A_R$. 2. Use the given difference to find $A_R$: $A_P - A_R = 160$. Substituting $A_P$, we get $\frac{5}{3} A_R - A_R = 160 \implies \frac{2}{3} A_R = 160 \implies A_R = 240$. 3. Find applied candidates for Q ($A_Q$): Since $A_R = 25\%$ of $A_Q$, we know $A_Q = 4 \times A_R = 4 \times 240 = 960$. 4. Calculate $x$ from the interview calls difference: Interview calls for Q = $12 \times 6x = 72x$. Interview calls for R = $2 \times 4x = 8x$. The difference is $320$. So, $72x - 8x = 320 \implies 64x = 320 \implies x = 5$. 5. Find actual interview calls for Q: $72 \times 5 = 360$. 6. Calculate candidates who did not get a call from Q: Total Applied - Interviewed = $960 - 360 = 600$. ### Exam Strategy & Shortcut Instead of fractions, work directly with unit ratios. The applicant ratio is $A_P : A_Q : A_R = 5 : 12 : 3$. The difference between P and R is $5 - 3 = 2$ units. We are told $2 \text{ units} = 160$, so $1 \text{ unit} = 80$. Total applied in Q is $12 \text{ units} = 12 \times 80 = 960$. This simplifies calculation heavily. ### Common Pitfall Forgetting to calculate $x$ based on the general directions and instead using a wrong assumption for the number of interview calls. ### Final Answer Therefore, the correct answer is **600**.