Question

Madhu has received admission in all schools listed above. She wishes to select the highest overall ranked school whose annual tuition fee does not exceed $23,000 and median starting salary is at least $70,000. Which school will she select?

• A. University of Virginia.
• B. University of Pennsylvania
• C. Northwestern University
• D. University of California - Berkeley
• A. 1
• B. 2
• C. 3
• D. 4
• A. 10
• B. 5
• C. 7
• D. 8

Answer 1

The Correct Option is D

Step 1: Understand what the question asks
Madhu wants one school. It must satisfy two conditions together: annual tuition fee not more than $23,000, and median starting salary at least $70,000.
Among all schools that pass, she picks the one with the best (smallest) overall ranking.
Note the words: fee \(\leq 23{,}000\) and salary \(\geq 70{,}000\). A salary of exactly $70,000 is allowed, but a fee of $23,025 is not.

Step 2: Plan: go down the table in overall-rank order
The list is already sorted by overall ranking. So the first school that passes both tests is the answer, and we can stop there.
We test the fee first, because it removes many schools quickly.

Step 3: Test the top ten schools
Stanford (rank 1): fee $23,100, which is more than $23,000. Rejected.
Harvard (2): fee $23,840. Rejected.
Pennsylvania (3): fee $24,956. Rejected.
MIT (4): fee $23,900. Rejected.
Chicago (5): fee $23,930. Rejected.
Northwestern (6): fee $23,025, only $25 above the limit. Rejected.
Columbia (7): fee $23,830. Rejected.
Dartmouth (8): fee $23,700. Rejected.
Duke (9): fee $24,380. Rejected.
Berkeley (10): fee $18,788, which is below $23,000. Salary is $70,000, which is at least $70,000. Both conditions hold.

Step 4: Why we can stop at Berkeley
Every school ranked above Berkeley has failed, and Berkeley passes. So Berkeley is the highest ranked school that qualifies.
Schools ranked below it may also qualify, but they cannot beat rank 10.

Step 5: Why the other options are wrong
Option (1) University of Virginia: fee $19,627 is fine, but its median salary is $66,000, below $70,000. It also ranks lower (11) than Berkeley.
Option (2) University of Pennsylvania: salary $79,000 is fine, but the fee $24,956 is above $23,000.
Option (3) Northwestern University: salary $70,000 is fine, but the fee $23,025 is just above $23,000, so it fails.

Final Answer:
Berkeley is the best ranked school that meets both limits, which is option (4). \[ \boxed{\text{Option (4): University of California - Berkeley}} \]

Answer 2

Step 1: Understand the comparison
A school is uniformly better than Dartmouth College when it beats Dartmouth on both counts: a higher median starting salary AND a lower tuition fee.
From the table, Dartmouth has a salary of $70,000 and a fee of $23,700.

Step 2: Step through the schools with a lower fee
First list every school whose fee is below $23,700: Stanford 23,100; Northwestern 23,025; Berkeley 18,788; Virginia 19,627; Michigan 23,178; New York University 23,554; Carnegie Mellon 22,200; Yale 23,220; North Carolina 14,333; UCLA 19,431; Texas 11,614; Indiana 15,613; Cornell 23,151.
Harvard (23,840), Pennsylvania (24,956), MIT (23,900), Chicago (23,930), Columbia (23,830) and Duke (24,380) cost more, so they are out.

Step 3: Now keep only the ones with a salary strictly above $70,000
Stanford: $82,000, higher. Counts.
Northwestern: $70,000, equal, not higher. Does not count.
Berkeley: $70,000, equal. Does not count.
New York University: $70,583, higher. Counts.
Virginia 66,000; Michigan 65,000; Carnegie Mellon 67,200; Yale 65,000; North Carolina 60,000; UCLA 65,000; Texas 60,000; Indiana 61,500; Cornell 64,000 are all below $70,000.

Step 4: Count
Only Stanford and New York University beat Dartmouth on both salary and fee. That is 2 schools.

Step 5: Why the other options are wrong
Option (3) would come from counting Northwestern or Berkeley, but their salary is equal to Dartmouth's, and the question needs a higher salary.
Option (1) would miss New York University or Stanford. Option (4) has no support in the table.

Final Answer:
Two schools are uniformly better than Dartmouth, which is option (2). \[ \boxed{\text{Option (2): 2}} \]

Answer 3

Step 1: Understand what a single digit ranking means
A single digit ranking means a rank from 1 to 9. We look at four rank columns: overall, academics, recruiters and placements.
We need schools that have a rank of 9 or better in at least 3 of these 4 columns.

Step 2: Count the single-digit ranks school by school (overall, academics, recruiters, placements)
Stanford 1, 1, 3, 1: all four single digit. Count 4. Qualifies.
Harvard 2, 1, 2, 4: 4. Qualifies.
Pennsylvania 3, 1, 4, 2: 4. Qualifies.
MIT 4, 1, 4, 3: 4. Qualifies.
Chicago 5, 1, 8, 10: three (placements is 10). Qualifies.
Northwestern 6, 1, 1, 11: three. Qualifies.
Columbia 7, 9, 10, 5: three (recruiters is 10). Qualifies.
Dartmouth 8, 12, 11, 6: only two. Does not qualify.
Duke 9, 9, 7, 8: 4. Qualifies.
Berkeley 10, 7, 12, 12: one. No.
Virginia 11, 12, 9, 9: two. No.
Michigan 12, 7, 6, 14: two. No.
New York University 13, 16, 19, 7: one. No.

Step 3: Check the rest
Carnegie Mellon, Yale, North Carolina, Texas, Indiana and Cornell have no single digit rank at all. UCLA 17, 9, 13, 38 has only one.

Step 4: Total
Qualifying schools: Stanford, Harvard, Pennsylvania, MIT, Chicago, Northwestern, Columbia and Duke. That is 8.

Step 5: Why the other options are wrong
Option (2) is 5, which is the number of schools with single digit ranks on all four parameters (Stanford, Harvard, Pennsylvania, MIT, Duke). The question says at least 3, so Chicago, Northwestern and Columbia must be added.
Options (1) and (3) do not match the count of 8 found above.

Final Answer:
Eight schools have a single digit rank on at least three of the four parameters, which is option (4). \[ \boxed{\text{Option (4): 8}} \]