The following table shows the number of employees and their median age in eight companies located in a district.
Company
Number of employees
Median age
A
32
24
B
28
30
C
43
39
D
39
45
E
35
49
F
29
54
G
23
59
H
16
63
It is known that the age of all employees are integers. It is known that the age of every employee in A is strictly less than the age of every employee in B, the age of every employee in B is strictly less than the age of every employee in C, ..., the age of every employee in G is strictly less than the age of every employee in H.
The highest possible age of an employee of company A is:
Enter your answer to attempt
The Setup: Think of these companies as sorted C++ arrays. We need to maximize the final element of array A without throwing a logic error when it's compared to the very first element of array B. It's a strict inequality check, so we need to min-max the data to push Company A's ceiling as high as possible.
Step 1: Decode the median mechanics for Company B. Company B has 28 employees (an even number). The median age (30) is the average of the two middle elements. If we use standard 1-based math indexing, that's the 14th and 15th employees:
2b14+b15=30Step 2: Find the lowest possible starting age for Company B. To give array A the most room to scale up, we must push B's values as low as the rules allow. We can initialize the first 15 elements in B to exactly 30 without breaking the median requirement: b1=b2=⋯=b14=b15=30.
Thus, the absolute minimum age for the youngest employee in B is 30.
Step 3: Lock in Company A's max age. The constraint dictates that *every* employee in A must be strictly younger than *every* employee in B. In code terms, a32<b1. Since ages are strictly typed integers, if b1=30, the absolute maximum allowed for a32 is 29.
Step 4: Verify this doesn't break Company A's own median constraint. Company A has 32 employees with a median of 24. This requires the average of a16 and a17 to be 24. We can easily assign a16=24 and a17=24, which leaves plenty of capacity for elements a18 through a32 to cap out at 29. The backend logic runs with zero lag, and the max age holds up perfectly.
Final Answer: 29
In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituen … read passage
The constituency in which B got lower number of votes compared to A and C is
AS3
BS4
CS2
DS1
Pick an option to attempt
The Setup: This is a logical reasoning Data Interpretation problem based on an election matrix. We must deduce the exact vote distribution for parties A, B, and C across 5 constituencies using their total vote counts, win conditions, and numerical sequence constraints.
Step 1: Analyze Party C's winning constraints.
Every constituency has exactly 20 voters and a clear winner (no ties for first place). To guarantee a win without tying, a party must secure a minimum of 8 votes (since the remaining 12 could be split 6−6; a score of 7 allows a 7−7−6 tie).
Party C won *only* S2 and S3. Thus, c2≥8 and c3≥8.
Party C's total votes across all constituencies is 16.
Therefore, C must have obtained exactly 8 votes in S2, 8 votes in S3, and 0 votes in S1, S4, and S5.
Step 2: Analyze Party B's winning constraints.
Party A won only S1, and C won only S2 and S3. By elimination, Party B must be the winner of S4 and S5.
In S4 and S5, C has 0 votes, meaning A and B split the 20 votes entirely. For B to win clearly, B must secure more than half the votes: b4≥11 and b5≥11.
Step 3: Apply Party B's sequence constraints.
B's votes across S1 to S5 are distinct natural numbers in increasing order: b1<b2<b3<b4<b5.
Since b4≥11, and b5 must be strictly greater than b4, b5≥12.
B's total votes equal 35. To leave enough votes for the first three constituencies, we must minimize b4 and b5.
Let b4=11 and b5=12.
The remaining votes for the first three constituencies are: b1+b2+b3=35−11−12=12.
Step 4: Determine Party B's exact sequence.
In S2 and S3, C wins with 8 votes. Therefore, A and B must each have fewer than 8 votes (b2≤7,b3≤7,a2≤7,a3≤7).
Since ai+bi=20−8=12 in these constituencies, the only valid integer pairs for (ai,bi) bounded by 7 are (7,5),(6,6), and (5,7).
Thus, B's votes in S2 and S3 must be chosen from the set {5,6,7}.
Maintaining the strictly increasing sequence b2<b3, we test combinations to satisfy b1+b2+b3=12:
If (b2,b3)=(5,6), then b1=12−11=1. (Valid natural number)
If (b2,b3)=(5,7), then b1=12−12=0. (Invalid, natural numbers begin at 1)
Therefore, B's exact vote sequence across S1-S5 is 1,5,6,11,12.
Step 5: Calculate Party A's vote distribution.
Using the formula ai=20−bi−ci:
S1: a1=20−1−0=19 (A wins)
S2: a2=20−5−8=7 (C wins)
S3: a3=20−6−8=6 (C wins)
S4: a4=20−11−0=9 (B wins)
S5: a5=20−12−0=8 (B wins)
Checking the total: 19+7+6+9+8=49, which perfectly matches A's given total.
Step 6: Answer the specific prompt.
We must find the constituency where B got fewer votes than both A and C.
In S2, B has 5 votes, A has 7 votes, and C has 8 votes. 5<7 and 5<8.
Final Answer: S2
In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituen … read passage
The number of votes obtained by B in S2 is
A6
B7
C5
D4
Pick an option to attempt
The Setup: We must identify the specific number of votes obtained by Party B in constituency S2, using the comprehensive election matrix derived from the logical constraints.
Step 1: Reference the derived election matrix.
As established through the total vote counts and sequence constraints:
Party C's votes across S1-S5: 0,8,8,0,0
Party B's votes across S1-S5: 1,5,6,11,12
Party A's votes across S1-S5: 19,7,6,9,8Step 2: Isolate the requested data point.
We look at Party B's vote sequence (b1,b2,b3,b4,b5) and identify the value for S2 (b2).
b2=5.
Final Answer: 5
In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituen … read passage
The number of votes obtained by A in S5 is
A6
B9
C8
D7
Pick an option to attempt
The Setup: We must identify the specific number of votes obtained by Party A in constituency S5, utilizing the completed election matrix.
Step 1: Reference the derived election matrix.
The calculated vote distribution for Party A across the five constituencies (S1 through S5) is 19,7,6,9, and 8.
Step 2: Isolate the requested data point.
We evaluate Party A's sequence (a1,a2,a3,a4,a5) and extract the specific value corresponding to S5 (a5).
a5=8.
Final Answer: 8
In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituen … read passage
Comparing the number votes obtained by A across different constituencies, the lowest number of votes were in constituency
AS4
BS2
CS5
DS3
Pick an option to attempt
The Setup: We need to compare Party A's vote counts across all five constituencies to determine which constituency yielded their lowest performance.
Step 1: Retrieve Party A's vote distribution.
From our derived election matrix, the votes obtained by Party A in constituencies S1, S2, S3, S4, and S5 are respectively:
19,7,6,9,8Step 2: Identify the minimum value.
Comparing the integers in the set {19,7,6,9,8}, the lowest number is 6.
Step 3: Map the minimum value back to its constituency.
The vote count of 6 corresponds to constituency S3.
Final Answer: S3
In an election there were five constituencies S1, S2, S3, S4, and S5 with 20 voters each all of whom voted. Three parties A, B, and C contested the elections. The party that gets the maximum number of votes in a constituency wins that seat. In every constituen … read passage
Assume that A and C had formed an alliance and any voter who voted for either A or C would have voted for this alliance. Then the number of seats this alliance would have won is
A4
B2
C3
D5
Pick an option to attempt
The Setup: We must model a hypothetical political alliance between Party A and Party C, combining their votes in each constituency to see how many total seats the new alliance would win against Party B.
Step 1: Calculate the alliance's combined votes per constituency.
We sum the individual votes of A and C for each constituency (ai+ci):
S1: 19+0=19
S2: 7+8=15
S3: 6+8=14
S4: 9+0=9
S5: 8+0=8Step 2: Compare the alliance's votes against Party B's votes.
To win a seat, the alliance's combined votes must exceed Party B's votes in that constituency.
S1: Alliance (19) vs Party B (1) ⇒ Alliance wins.
S2: Alliance (15) vs Party B (5) ⇒ Alliance wins.
S3: Alliance (14) vs Party B (6) ⇒ Alliance wins.
S4: Alliance (9) vs Party B (11) ⇒ Party B wins.
S5: Alliance (8) vs Party B (12) ⇒ Party B wins.
Step 3: Total the seats won by the alliance.
The alliance successfully wins constituencies S1, S2, and S3, totaling 3 seats.
Final Answer: 3