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09 Jul 2025, 08:00
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Difficulty:
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77% (02:28) correct
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On Monday, Elena had a certain amount of money in her savings account. On Tuesday, she increased that amount by m percent. On Wednesday, she withdrew n percent of her Tuesday's closing balance, leaving her with exactly 50 percent of what she had on Monday. What is the value of n in terms of m?
A. \(\frac{100(m + 50)}{m + 100}\)
B. \( \frac{100(m - 50)}{m + 100}\)
C. \( \frac{100(m + 50)}{100 - m}\)
D. \( \frac{100m}{m + 100}\)
E. \( \frac{100(50 - m)}{m - 100}\)
A. \(\frac{100(m + 50)}{m + 100}\)
B. \( \frac{100(m - 50)}{m + 100}\)
C. \( \frac{100(m + 50)}{100 - m}\)
D. \( \frac{100m}{m + 100}\)
E. \( \frac{100(50 - m)}{m - 100}\)
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09 Jul 2025, 08:30
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GMAT Club Official Explanation:
Assuming she had $x on Monday, then:
On Tuesday, she’d have \(x(1 + \frac{m}{100})\)
On Wednesday, she’d have \(x(1 + \frac{m}{100}) (1 - \frac{n}{100})\)
Since that amount was 50 percent of what she had on Monday, then:
\(x(1 + \frac{m}{100}) (1 - \frac{n}{100}) =\frac{x}{2}\)
\((1 + \frac{m}{100}) (1 - \frac{n}{100}) =\frac{1}{2}\)
\((\frac{100 + m}{100}) (1 - \frac{n}{100}) =\frac{1}{2}\)
\((1 - \frac{n}{100}) =\frac{50}{100 + m }\)
\(\frac{100 - n}{100} =\frac{50}{100 + m }\)
\(100 - n =\frac{5,000}{100 + m }\)
\(n = 100 - \frac{5,000}{100 + m }\)
\(n = \frac{10,000 + 100m - 5,000}{100 + m }\)
\(n = \frac{5,000 + 100m}{100 + m }\)
\(n = \frac{100(50 + m)}{100 + m }\)
Answer: A.
General Discussion
09 Jul 2025, 08:11
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Monday: T (Money deposited)
Tuesday: T(1+m/100) ......(increased by m%)
Wednesday balance : (1-n/100) X T(1+m/100)
Since,50% of T = Wednesday balance
T/2=(1-n/100) X T(1+m/100)
Solving this would give answer D
Tuesday: T(1+m/100) ......(increased by m%)
Wednesday balance : (1-n/100) X T(1+m/100)
Since,50% of T = Wednesday balance
T/2=(1-n/100) X T(1+m/100)
Solving this would give answer D
