Directions: Study the table carefully and answer the given questions.
Number of pages printed by 5 printers during 5 days
| Printers $\rightarrow$
Days $\downarrow$ | A | B | C | D | E |
| :--- | :--- | :--- | :--- | :--- | :--- |
| Monday | 139 | 147 | 211 | 141 | 184 |
| Tuesday | 141 | 189 | 164 | 189 | 151 |
| Wednesday | 115 | 141 | 159 | 156 | 136 |
| Thursday | 89 | 223 | 120 | 147 | 113 |
| Friday | 187 | 93 | 257 | 160 | 124 |
The number of pages printed by printer E on Monday is what percent more than the number of pages printed by printer C on Thursday?
Aptitude
Statistics
Difficulty: Medium
Choose an option
-
A$60\frac{1}{3}$
-
B$51\frac{2}{3}$
-
C$45\frac{2}{3}$
-
D$53\frac{1}{3}$
-
E$55\frac{1}{3}$
Answer
Correct Answer: $53\frac{1}{3}$
Explanation
### Concept & Percentage Increase
To find how much more one value is than another in percentage terms, divide the difference by the base value (the "than" value) and multiply by 100.
$$ \text{Percentage More} = \left( \frac{\text{Difference}}{\text{Base Value}} \right) \times 100 $$
### Step-by-Step Solution
1. **Extract the relevant values:**
- Printer E on Monday = $184$
- Printer C on Thursday = $120$
2. **Calculate the difference:**
- $\text{Difference} = 184 - 120 = 64$
3. **Calculate the percentage relative to C on Thursday:**
- $\text{Percentage} = \left(\frac{64}{120}\right) \times 100$
4. **Simplify the fraction:**
- Divide by $8$: $\frac{64}{120} = \frac{8}{15}$
- Calculate: $\frac{8}{15} \times 100 = \frac{800}{15} = \frac{160}{3}$
5. **Convert to mixed fraction:**
- $160 \div 3 = 53$ with a remainder of $1$.
- The percentage is $53\frac{1}{3}\%$.
### Exam Strategy & Shortcut
Simplify the ratio first: $184 : 120 = 46 : 30 = 23 : 15$. The difference in ratio units is $23 - 15 = 8$. The percentage more is $\frac{8}{15} \times 100$. Knowing $\frac{1}{15} \approx 6.66\%$, then $8 \times 6.66\% \approx 53.33\%$, which corresponds to $53\frac{1}{3}\%$.
### Common Pitfall
Using the wrong base value. The phrase "more than ... C on Thursday" means the value for C on Thursday ($120$) must be the denominator.
### Final Answer
Therefore, the correct answer is **$53\frac{1}{3}$**.