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74%
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Schwartz Bank has more than 100 interns. Of the m male interns, 70 percent speak French, and of the f female interns, 40 percent speak French. Do more than half of the interns speak French?
(1) Most of the interns who speak French are male.
(2) The number of female interns is 10 less than three-fourths of the total number of interns.
(1) Most of the interns who speak French are male.
(2) The number of female interns is 10 less than three-fourths of the total number of interns.
kittiponrw
20 Mar 2026, 07:40
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The Core Setup
We want to know if the total number of French speakers is strictly greater than 50% of the total interns.
Total Interns = m + f > 100
Total French Speakers = 0.7m + 0.4f
The Target Question:
- Is 0.7m + 0.4f > 0.5(m + f)?
- or is 2m > f? (simplified)
If a statement guarantees that f is less than 2m, the answer is definitively Yes. Otherwise No.
Evaluating Statement (1) "Most of the interns who speak French are male."
Translation: Male French speakers > Female French speakers. (0.7m > 0.4f) => (7/4)m > f which satisfy our condition then Statement (1) is Sufficient.
Evaluating Statement (2) "The number of female interns is 10 less than three-fourths of the total number of interns."
Translation: f = 0.75(m + f) - 10 => f = 3m - 40
Substitute our $f$ equation into the total intern constraint:
m + (3m - 40) > 100
4m > 140
m > 35
Because $m$ only needs to be greater than 35, we have a split scenario.
- if m = 36, then m < 40 is true (meaning Yes, more than half speak French).
- if m = 50, then m < 40 is false (meaning No, less than half speak French).
Because we can yield both a Yes and a No, Statement (2) is Insufficient.
We want to know if the total number of French speakers is strictly greater than 50% of the total interns.
Total Interns = m + f > 100
Total French Speakers = 0.7m + 0.4f
The Target Question:
- Is 0.7m + 0.4f > 0.5(m + f)?
- or is 2m > f? (simplified)
If a statement guarantees that f is less than 2m, the answer is definitively Yes. Otherwise No.
Evaluating Statement (1) "Most of the interns who speak French are male."
Translation: Male French speakers > Female French speakers. (0.7m > 0.4f) => (7/4)m > f which satisfy our condition then Statement (1) is Sufficient.
Evaluating Statement (2) "The number of female interns is 10 less than three-fourths of the total number of interns."
Translation: f = 0.75(m + f) - 10 => f = 3m - 40
Substitute our $f$ equation into the total intern constraint:
m + (3m - 40) > 100
4m > 140
m > 35
Because $m$ only needs to be greater than 35, we have a split scenario.
- if m = 36, then m < 40 is true (meaning Yes, more than half speak French).
- if m = 50, then m < 40 is false (meaning No, less than half speak French).
Because we can yield both a Yes and a No, Statement (2) is Insufficient.
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