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In a school of 150 students, 75 study Latin, 110 study Spani
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05 Aug 2018, 14:41
05 Aug 2018, 14:41
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Expert Reply
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Question Stats:
67% (01:02) correct
32% (01:14) wrong based on 183 sessions
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In a school of 150 students, 75 study Latin, 110 study Spanish, and 11 study neither.
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Quantity A |
Quantity B |
The number of students who study only Latin |
46 |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: In a school of 150 students, 75 study Latin, 110 study Spani
[#permalink]
07 Aug 2018, 16:48
07 Aug 2018, 16:48
3
Expert Reply
Explanation
Use the overlapping sets formula for two groups: Total = Group 1 + Group 2 – Both + Neither. (Adding the two groups—in this case Latin and Spanish—double-counts the students who
study both languages, so the formula subtracts the “both” students.)
Set up your equation:
150 = 75 + 110 – B + 11
150 = 196 – B
46 = B
Careful! This is not the value of Quantity A. Since 46 students study both Latin and Spanish, subtract 46 from the total who study Latin to find those who study only Latin:
75 – 46 = 29
Thus, Quantity A is 29. Therefore Quantity B is greater.
Use the overlapping sets formula for two groups: Total = Group 1 + Group 2 – Both + Neither. (Adding the two groups—in this case Latin and Spanish—double-counts the students who
study both languages, so the formula subtracts the “both” students.)
Set up your equation:
150 = 75 + 110 – B + 11
150 = 196 – B
46 = B
Careful! This is not the value of Quantity A. Since 46 students study both Latin and Spanish, subtract 46 from the total who study Latin to find those who study only Latin:
75 – 46 = 29
Thus, Quantity A is 29. Therefore Quantity B is greater.
Re: In a school of 150 students, 75 study Latin, 110 study Spani
[#permalink]
10 Jan 2019, 00:31
10 Jan 2019, 00:31
2
Expert Reply
Just make a table
The numbers written in black is what were given
The numbers written in red are the calculations based on what was given
If there are 150 students in total, but 110 taking spanish, then there are 40 people not taking Spanish
Also, if there are 150 students, and 75 students take Latin, then 75 Students dont take latin
Out of 75 students who dont take Latin, 11 take neither latin nor spanish, which means there are 75-11=64 students who take spanish but not latin
out of the 110 studetns that take spanish, there are 110-64=46 students who also take latin
Out of the 75 students that take latin, 75-46 =29 that take only latin.
This table, on paper, takes about 50 seconds to complete if you are good with simple math, and don't want to learn anything
that may seem too complicated.
The numbers written in black is what were given
The numbers written in red are the calculations based on what was given
If there are 150 students in total, but 110 taking spanish, then there are 40 people not taking Spanish
Also, if there are 150 students, and 75 students take Latin, then 75 Students dont take latin
Out of 75 students who dont take Latin, 11 take neither latin nor spanish, which means there are 75-11=64 students who take spanish but not latin
out of the 110 studetns that take spanish, there are 110-64=46 students who also take latin
Out of the 75 students that take latin, 75-46 =29 that take only latin.
This table, on paper, takes about 50 seconds to complete if you are good with simple math, and don't want to learn anything
that may seem too complicated.
Attachments
latin.PNG [ 119.8 KiB | Viewed 10323 times ]
