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mrmba11
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The GMAT is scored on a scale of 200 to 800 in 10 point incr 12 Aug 2022, 08:31
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This guy hit the NAIL.


IanStewart
enigma123
The GMAT is scored on a scale of 200 to 800 in 10 point increments. (Thus 410 and 760 are real GMAT scores but 412 and 765 are not). A first-year class at a certain business school consists of 478 students. Did any students of the same gender in the first-year class who were born in the same-named month have the same GMAT score?
(1) The range of GMAT scores in the first-year class is 600 to 780.
(2) 60% of the students in the first-year class are male.

Bowtie's solution above is perfect, but I'll go into a bit more detail in case it's unclear:

This question (and another I responded to yesterday) is based on something called the 'pigeonhole principle'. That principle is usually explained as follows: if a postal worker has 4 envelopes which she will place in 3 pigeonholes, then it must be true that (at least) 2 envelopes will end up in the same pigeonhole, since even if the first 3 envelopes go into different pigeonholes, the 4th will need to go in a pigeonhole already containing an envelope. Changing the numbers to mimic the question above, say you have 20 people who take a test consisting of 19 questions. Then it must be true that two people answered the same number of questions correctly, since even if the first 19 people all had a different number of correct answers, that uses up all of the possibilities from 1 to 19, so the last person would need to have answered the same number of questions correctly as one of the first nineteen people.

We have a similar situation here. From Statement 1, there are only 19 possible GMAT scores in the class. So if we know we have 20 students of the same gender who were born in the same month, we could then be sure that (at least) two of them must have the same GMAT score. We have 478 students in total. At least half of these, or 239 students, must be of the same gender (you couldn't have less than 239 men *and* less than 239 women in the class). Further, it is impossible that there are only 19 students of the same gender born in *every* month of the year (since then you'd only have at most 12*19 = 228 students of that gender), so we must have at least 20 students of the same gender born in the same month. So two of these students must have the same GMAT score, and the answer is A.
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rahulbanka
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The GMAT is scored on a scale of 200 to 800 in 10 point incr 29 Jan 2023, 02:05
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enigma123
The GMAT is scored on a scale of 200 to 800 in 10 point increments. (Thus 410 and 760 are real GMAT scores but 412 and 765 are not). A first-year class at a certain business school consists of 478 students. Did any students of the same gender in the first-year class who were born in the same-named month have the same GMAT score?

(1) The range of GMAT scores in the first-year class is 600 to 780.
(2) 60% of the students in the first-year class are male.

Can someone please let me know how to solve this? I tried it this way:
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Considering Statement 1

Range of scores will be 600, 610, 620.........770, 780 and there are 12 months in a year so 12 distinct possibilities for a birth month of a student. I struggled from here to solve.

Considering Statement 2 --> Is clearly insufficient as range for GMAT scores is not provided.
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Statement 1
Let's find the maximum score possibilities.
Since range of scores is 600 - 780, the maximum number of different scores possible = 19 (since scores are in increments of 10)
There are 12 months and 2 genders
Hence, maximum score possibilities = 19 x 2 x 12 = 456
Since, 456 < 478 (total students), there are students of the same gender who were born in the same-named month have the same GMAT score
Hence, sufficient

Statement 2
Male - female ratio gives us no further information

Hence, answer is A
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The GMAT is scored on a scale of 200 to 800 in 10 point incr 19 May 2026, 10:20
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🎯 What are we trying to prove?
👉 Do at least 2 students share ALL 3:
  • same gender
  • same birth month
  • same GMAT score

🧠 Build the “boxes”
Each student is classified by:
  • Gender → 2
  • Months → 12
  • Scores → from 200 to 800 in steps of 10 → 61 possible scores
👉 Total distinct combinations:
2 × 12 × 61 = 1464 boxes

👀 Compare with students
  • Students = 478
  • Boxes = 1464
👉 478 < 1464 → NOT forced
So overall, duplicates are not guaranteed.

🔍 Statement (1)
Range = 600 to 780
Count scores:
(780 − 600)/10 + 1 = 19 scores
New boxes:
2 × 12 × 19 = 456
Now compare:
  • Students = 478
  • Boxes = 456
👉 478 > 456 → collision MUST happen
✅ Sufficient

🔍 Statement (2)
60% male → 40% female
  • Male ≈ 287
  • Female ≈ 191
But nothing about score range → still 61 scores.
Boxes per gender:
12 × 61 = 732
Compare:
  • Males: 287 < 732 → no guarantee
  • Females: 191 < 732 → no guarantee
❌ Not sufficient

✅ Final Answer:
👉 (1) alone is sufficient
👉 (2) alone is not
Answer: A
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