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The people eating in a certain cafeteria are either faculty members or
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01 Feb 2018, 23:23
Question Stats:
54% (02:26) correct 46% (02:21) wrong based on 118 sessions
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The people eating in a certain cafeteria are either faculty members or students, and the number of faculty members is 15 percent of the total number of people in the cafeteria. After some of the students leave, the total number of persons remaining in the cafeteria is 50 percent of the original total. The number of students who left is what fractional part of the original number of students? (A) 17/20 (B) 10/17 (C) 1/2 (D) 7/17 (E) 7/20
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Re: The people eating in a certain cafeteria are either faculty members or
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01 Feb 2018, 23:27
C 1/2 85 students +15 faculty =100 Students left and remaining total is 50 X+15=50 So x is 35 Number of students left is 8535=50 50/100 =1/2 Sent from my Redmi Note 3 using GMAT Club Forum mobile app



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The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 00:04
+1 D
Assume,
Total number of Faculty=F Total number of Students=S After some students left,New number of students=S1
Now, we get F=.15(F+S)(1) > F=3/17S
Now After some of the students left, the total number of persons remaining is 50 percent of the original total
i.e, F+S1=.5(F+S)(2)
Solving 1 and 2 we get
S1=7/17 S
Hence, answer is D.



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Re: The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 01:31
Let x be the total number of people.therefore number of faculty =0.15x No of students =0.85x Let students who left be y then 0.15x+0.85x y=0.5x solving we get x=2y y/x=1/2 Please let me know if i m wrong somewhere Sent from my MotoG3 using GMAT Club Forum mobile app



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Re: The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 01:33
jrk23 wrote: C 1/2 85 students +15 faculty =100 Students left and remaining total is 50 X+15=50 So x is 35 Number of students left is 8535=50 50/100 =1/2 Sent from my Redmi Note 3 using GMAT Club Forum mobile appSorry 50/85 question is asking students left to original students... So 10/17 answer is B Sent from my Redmi Note 3 using GMAT Club Forum mobile app



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Re: The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 01:38
surbhipuri wrote: Let x be the total number of people.therefore number of faculty =0.15x No of students =0.85x Let students who left be y then 0.15x+0.85x y=0.5x solving we get x=2y y/x=1/2 Please let me know if i m wrong somewhere Sent from my MotoG3 using GMAT Club Forum mobile appSorry didnt readthe question properly i guess Student left / total students =x/2×0.85x =10/17 Is the answer Sent from my MotoG3 using GMAT Club Forum mobile app



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Re: The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 01:38
surbhipuri wrote: Let x be the total number of people.therefore number of faculty =0.15x No of students =0.85x Let students who left be y then 0.15x+0.85x y=0.5x solving we get x=2y y/x=1/2 Please let me know if i m wrong somewhere Sent from my MotoG3 using GMAT Club Forum mobile appYou should not use x in denominator, you should use .85x in denominator Sent from my Redmi Note 3 using GMAT Club Forum mobile app



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Re: The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 01:39
Corrected the same sir Sent from my MotoG3 using GMAT Club Forum mobile app



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Re: The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 04:02
let The Total no of students =100 then no of faculty = 15 no of student =85 let p no of student left so , 100p=50*100/100 p=50 students left so, No of student left /total no of student = 35/85=7/17



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The people eating in a certain cafeteria are either faculty members or
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Updated on: 02 Feb 2018, 04:41
let The Total no of students =100 then no of faculty = 15 no of student =85 let p no of student left so , 100p=50*100/100 p=50 students left so, No of student left /total no of student = 50/85=10/17
Originally posted by CharuSingh26 on 02 Feb 2018, 04:03.
Last edited by CharuSingh26 on 02 Feb 2018, 04:41, edited 1 time in total.



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Re: The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 04:28
CharuSingh26 wrote: let The Total no of students =100 then no of faculty = 15 no of student =85 let p no of student left so , 100p=50*100/100 p=50 students left so, No of student left /total no of student = 35/85=7/17 No of student left is 50 as you calculated So answer should be 50/85=10/17 Sent from my MotoG3 using GMAT Club Forum mobile app



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The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 09:05
The people eating in a certain cafeteria are either faculty members or students, and the number of faculty members is 15 percent of the total number of people in the cafeteria. After some of the students leave, the total number of persons remaining in the cafeteria is 50 percent of the original total. The number of students who left is what fractional part of the original number of students?
(A) 17/20 (B) 10/17 (C) 1/2 (D) 7/17 (E) 7/20
Answer is B. Picking smart numbers start with 85 students and 15 teachers. After some students leave there is half as many people, meaning 50 students have left. 50/85 = 10/17 when simplified.



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Re: The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 12:47
CanCanuck90 wrote: The people eating in a certain cafeteria are either faculty members or students, and the number of faculty members is 15 percent of the total number of people in the cafeteria. After some of the students leave, the total number of persons remaining in the cafeteria is 50 percent of the original total. The number of students who left is what fractional part of the original number of students?
(A) 17/20 (B) 10/17 (C) 1/2 (D) 7/17 (E) 7/20
Answer is B. Picking smart numbers start with 85 students and 15 teachers. After some students leave there is half as many people, meaning 50 students have left. 50/85 = 10/17 when simplified. 50 students do not leave. 50 people leave. Your scenario has to go from 15/100 people are teachers to 15/50 teachers. This means you go from 85 students to 35 students. D. 7/17 It also easier if you pick 30/200 teachers and then after kids leave its 30/100 teachers. 170 students down to 70 students. 70/170 =7/17



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Re: The people eating in a certain cafeteria are either faculty members or
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02 Feb 2018, 13:53
IdiomSavant wrote: CanCanuck90 wrote: The people eating in a certain cafeteria are either faculty members or students, and the number of faculty members is 15 percent of the total number of people in the cafeteria. After some of the students leave, the total number of persons remaining in the cafeteria is 50 percent of the original total. The number of students who left is what fractional part of the original number of students?
(A) 17/20 (B) 10/17 (C) 1/2 (D) 7/17 (E) 7/20
Answer is B. Picking smart numbers start with 85 students and 15 teachers. After some students leave there is half as many people, meaning 50 students have left. 50/85 = 10/17 when simplified. 50 students do not leave. 50 people leave. Your scenario has to go from 15/100 people are teachers to 15/50 teachers. This means you go from 85 students to 35 students. D. 7/17 It also easier if you pick 30/200 teachers and then after kids leave its 30/100 teachers. 170 students down to 70 students. 70/170 =7/17 Reread the question, it says "after some students leave".... I agree with everything else. Sent from my iPhone using GMAT Club Forum mobile app



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Re: The people eating in a certain cafeteria are either faculty members or
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05 Feb 2018, 10:18
Bunuel wrote: The people eating in a certain cafeteria are either faculty members or students, and the number of faculty members is 15 percent of the total number of people in the cafeteria. After some of the students leave, the total number of persons remaining in the cafeteria is 50 percent of the original total. The number of students who left is what fractional part of the original number of students?
(A) 17/20 (B) 10/17 (C) 1/2 (D) 7/17 (E) 7/20 If we let the total people = n, then 0.15n = faculty and 0.85n = students. If we let x = the number of students who leave, we can create the equation: [0.15n + (0.85n  x)]/n = 1/2 (n  x)/n = 1/2 2(n  x) = n 2n  2x = n n = 2x n/2 = x Thus, the number of students who left is (n/2)/(85n/100) = 100n/170n = 10/17 of the original number of students. Answer: B
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Re: The people eating in a certain cafeteria are either faculty members or
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05 Feb 2018, 10:40
techiesam wrote: +1 D
Assume,
Total number of Faculty=F Total number of Students=S After some students left,New number of students=S1
Now, we get F=.15(F+S)(1) > F=3/17S
Now After some of the students left, the total number of persons remaining is 50 percent of the original total
i.e, F+S1=.5(F+S)(2)
Solving 1 and 2 we get
S1=7/17 S
Hence, answer is D. Sorry guys...the answer should be B I did the calculation right but didnot read the question properly. The question asks (SS1)/S=? ITS 10/17. So its B



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The people eating in a certain cafeteria are either faculty members or
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05 Feb 2018, 10:57
Let total number of people in cafteria be 100.
Given  15% of total are faculty members  15 85 % would be students  85 2 ] After some students leave the total number of people becomes 50% of what was at the start  50% of 100  50 Number of students who left = 50  15 = 35
The number of students who left is what fractional part of the original number of students = 35/85 = 7/17. [D]



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Re: The people eating in a certain cafeteria are either faculty members or
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11 Feb 2018, 22:11
this question definitely calls for test it so draw a table total student teachers 100 85 15 ........as 15 percent are teacher 50 35 15 ............ as total number reduce to half but teachers are same so only students reduce
required ratio = no of students left/total no of students =8535/85=50/85=10/17 (B)



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Re: The people eating in a certain cafeteria are either faculty members or
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19 Feb 2018, 17:53
Really nice trap in answer C (students to overall total, not original students.)




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