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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Mon Apr 13, 2020 4:36 pm

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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

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Source: Beat The GMAT — Data Sufficiency | Mon Apr 13, 2020 4:36 pm

swerve: Legendary Member; Posts: 2539; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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

by swerve » Wed Apr 15, 2020 2:44 pm

BTGmoderatorDC wrote: ↑
Mon Apr 13, 2020 4:36 pm
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

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deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

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

by deloitte247 » Thu Apr 16, 2020 2:57 am

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

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