Directions: The given pie chart shows the number of total voters registered…
2019
Directions: The given pie chart shows the number of total voters registered from 4 different villages, and all registered voters from these four villages cast their votes.
Total number of valid voters in village Z3 is one-third more than the difference of the valid voters of village Z1 and Z2.
Difference of valid voters from village Z4 and Z2 is 480. Ratio of total voters from village Z2 and that of Z4 is 3 : 7 respectively.
Total voters in village Z3 are more than that of Z2. Total invalid voters from all the villages together are 20% of total registered voters from all the villages.
If valid voters from Z4 are more than that of Z2, and valid voters from Z2 are 3600, and total valid voters from Z1 and Z4 are 10800, how many valid voters are from Z3?
- A.
5300
- B.
3120
- C.
4160
- D.
None of these
- E.
4080
Show answer & explanation
Correct answer: C
Concept
In a multi-clue voters problem, not every given clue bears on the specific quantity being asked. Identify the chain of relations that links the asked quantity to the known values, and set aside any clue that concerns a different quantity (for instance, a ratio of total registered voters when the target and the knowns are all about valid voters) rather than treating it as inconsistent. Each relation here is linear in the number of valid voters, so substitute one known value into the next.
Application (step by step)
Valid voters in Z2 are given directly as 3600.
The difference of valid voters between Z4 and Z2 is 480, with Z4 greater than Z2, so valid voters in Z4 = 3600 + 480 = 4080.
Valid voters in Z1 and Z4 together are 10800, so valid voters in Z1 = 10800 − 4080 = 6720.
The difference of valid voters between Z1 and Z2 = 6720 − 3600 = 3120.
Valid voters in Z3 are one-third more than this difference = 3120 × 4/3 = 4160.
Cross-check
The total-voters ratio Z2 : Z4 = 3 : 7 is about total registered voters, while the steps above use only counts of valid voters, so that ratio is not needed for this particular sub-question and is left aside. The chain used is self-consistent and yields 4160 valid voters in Z3, which is a positive figure consistent with the data; note that the invalid percentage (20%) is given for all villages together, not per village, so per-village totals are not separately required here.