At a certain high school, there are 20 more female sophomores than male sophomores. How many of the female sophomores

[BTGmoderatorDC]

At a certain high school, there are 20 more female sophomores than male sophomores. How many of the female sophomores are studying geometry?

(1) 20 percent of all the sophomores are studying geometry
(2) 15 percent of the male sophomores are studying geometry


OA E

Source: GMAT Prep

[swerve]

At a certain high school, there are 20 more female sophomores than male sophomores. How many of the female sophomores are studying geometry?

(1) 20 percent of all the sophomores are studying geometry
(2) 15 percent of the male sophomores are studying geometry


OA E

Source: GMAT Prep

\(f=20+m\) (a)
Call \(x\) is the percent the female sophomores are studying geometry.
Combining (1) & (2)
\(15\%m + x\% f = 0.2 (m+f)\) (b)
We have 2 equations \((a,b)\) for 3 variables \((x, m, f)\). Can't solve for \(x \Longrightarrow\) Answer is E

[deloitte247]

Let the no. of males = m
Let the no. of females = f
f=20fm
Question=> How many of the female sophomores are studying geometry?
Total sophomores = m + f = m + (20 + m)
= 2m + 20
Statement 1: 20 percent of all the sophomores are studying geometry.
Total sophomores in geometry = 20% of (2m + 20)
Percentage/value of female and male sophomores is unknown, hence, the target question cannot be answered; thus, statement 1 is NOT SUFFICIENT.

Statement 2: 15 percent of the male sophomores are studying geometry.
Total sophomores in geometry = 'm' in geometry + 'f' in geometry
Where 'm' in geometry = 15% of m
Percentage/value of male and female sophomores is unknown, hence, the target question cannot be answered; thus, statement 2 is NOT SUFFICIENT.

Combining both statements together:
None of the statement provides information on the percentage/value of male and female sophomores. So, the target cannot be answered. Hence, both statements combined together ARE NOT SUFFICIENT.

ANSWER = OPTION E