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04 May 2022, 07:15
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
75%
(hard)
Question Stats:
61% (03:28) correct
39%
(03:18)
wrong
based on 117
sessions
History
Date
Time
Result
Not Attempted Yet
In a high school with 500 students, 40% of the seniors play a musical instrument, while 30% of the non-seniors do not play a musical instrument. In all, 46.8% of the students do not play a musical instrument. How many non-seniors play a musical instrument?
(A) 66
(B) 154
(C) 186
(D) 220
(E) 266
Are You Up For the Challenge: 700 Level Questions
(A) 66
(B) 154
(C) 186
(D) 220
(E) 266
Are You Up For the Challenge: 700 Level Questions
06 May 2022, 00:12
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Number of students who do not play a musical instrument = 46.8% of 500 = 234. Number who do play is 266.
Let 'x' be the total number of Non-seniors (NS) and 'y' the total number of Seniors (S).
Of the 266 students who play, 7x/10 are NS and 4y/10 are S. (1)
Of the 234 students who do not play, 3x/10 are NS and 6y/10 are S. (2)
From (1), we can formulate the following equation:
7x + 4y = 2660
From (2), we get:
3x + 6y +2340...> x + 2y = 780
Solving for 'x' , we get x=220.
Number of NS who play is 7x/10= (7/10)*220 = 154
ANS: B
Let 'x' be the total number of Non-seniors (NS) and 'y' the total number of Seniors (S).
Of the 266 students who play, 7x/10 are NS and 4y/10 are S. (1)
Of the 234 students who do not play, 3x/10 are NS and 6y/10 are S. (2)
From (1), we can formulate the following equation:
7x + 4y = 2660
From (2), we get:
3x + 6y +2340...> x + 2y = 780
Solving for 'x' , we get x=220.
Number of NS who play is 7x/10= (7/10)*220 = 154
ANS: B
06 May 2022, 06:59
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This question can be solved easily by drawing a 2 x 2 grid / table, since the data here is mutually exclusive – a student could be a senior or non-senior, not both; he/she plays a musical instrument or doesn’t, not both.
We take two of these parameters for the columns and two others for the rows and draw a table like the one below:
6th May 2022 - Post 6.png [ 8.62 KiB | Viewed 3579 times ]
Since the number of seniors and non-seniors is not given and we have to apply certain percentages on these unknowns, taking numbers like 100x and 100y is a good idea, so that decimal values can be avoided.
From the table, we see that we have two independent linear equations in two variables.
40x + 70y = 266
60x + 30y = 234
Solving the equations, we have y = 2.2.
From the table, the number of non-seniors who play a musical instrument = 70y; substituting and simplifying, we get 154.
The correct answer option is B.
We take two of these parameters for the columns and two others for the rows and draw a table like the one below:
Attachment:
6th May 2022 - Post 6.png [ 8.62 KiB | Viewed 3579 times ]
Since the number of seniors and non-seniors is not given and we have to apply certain percentages on these unknowns, taking numbers like 100x and 100y is a good idea, so that decimal values can be avoided.
From the table, we see that we have two independent linear equations in two variables.
40x + 70y = 266
60x + 30y = 234
Solving the equations, we have y = 2.2.
From the table, the number of non-seniors who play a musical instrument = 70y; substituting and simplifying, we get 154.
The correct answer option is B.
