Question

The table below gives data collected for an online job portal, InfiniteJobs.com, for the Technical and Managerial candidate categories in 2004 and 2005.

Year	Category	Registrations	CVs Posted	Shortlisted by Employers	Offered Jobs
2004	Technical	61,205	59,981	684	181
	Managerial	19,236	15,389	138	48
2005	Technical	63,298	60,133	637	115
	Managerial	45,292	40,763	399	84

Statement X: In 2004, the number of candidates offered jobs as a proportion of the number of CV's posted was higher for Technical than for Managerial candidates.

Statement Y: In 2004, among those short-listed by Employers, the Technical category had a higher success rate in securing jobs than the Managerial category.

• A. Only [X] is True
• B. Only [Y] is True
• C. Both [X] and [Y] are True
• D. Neither [X] nor [Y] is True

Hint:

Turn each statement into a ratio (offers over CV's, and offers over shortlisted) for both categories in 2004, then compare the two ratios directly instead of assuming which one should be bigger.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
Both statements are comparisons of two fractions. Instead of converting each fraction to a decimal, we can compare $\frac{a}{b}$ and $\frac{c}{d}$ directly by cross multiplying, since $\frac{a}{b} > \frac{c}{d}$ exactly when $a \times d > c \times b$. This avoids any rounding error.

Step 2: Key Formula or Approach:
Apply cross multiplication once for the CV based ratio (Statement X) and once for the shortlist based ratio (Statement Y).

Step 3: Detailed Explanation.
For Statement X, compare Technical's $\frac{181}{59981}$ with Managerial's $\frac{48}{15389}$.
Cross multiply: $181 \times 15389 = 2785409$ and $48 \times 59981 = 2879088$.
Since $2879088 > 2785409$, the Managerial fraction is the larger one, so Technical's proportion is not higher and Statement X fails.
For Statement Y, compare Technical's $\frac{181}{684}$ with Managerial's $\frac{48}{138}$.
Cross multiply: $181 \times 138 = 24978$ and $48 \times 684 = 32832$.
Since $32832 > 24978$, Managerial again has the larger ratio, so Technical does not have the higher success rate either, and Statement Y fails.

Step 4: Final Answer:
Cross multiplication shows Managerial wins both comparisons, so neither X nor Y is correct.
\[\boxed{\text{Neither X nor Y is True}}\]