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# At Mnemosyne Middle School, there are 700 students: all the students a

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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28 Feb 2017, 11:25
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10
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Difficulty:

95% (hard)

Question Stats:

61% (03:37) correct 39% (03:48) wrong based on 116 sessions

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At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4th or 5th grade. There are 320 students in the 4th grade, and there are 210 girls in the 5th grade. Fifty percent of the 5th graders and 40% of the 4th graders take Mandarin Chinese. Ninety 5th grade boys do not take Mandarin Chinese. The number of 4th grade girls taking Mandarin Chinese is less than half of the number of 5th grade girls taking Mandarin Chinese. Which of the following could be the number of 4th grade boys in Mandarin Chinese?

(A) 10
(B) 40
(C) 70
(D) 100
(E) 130

This is one of a set of fifteen challenging GMAT Quant problems. To see the whole collection, as well as the OE for this question, go to:
Challenging GMAT Math Practice Questions

Mike

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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Posts: 8589
Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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02 Mar 2017, 05:55
2
mikemcgarry wrote:
At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4th or 5th grade. There are 320 students in the 4th grade, and there are 210 girls in the 5th grade. Fifty percent of the 5th graders and 40% of the 4th graders take Mandarin Chinese. Ninety 5th grade boys do not take Mandarin Chinese. The number of 4th grade girls taking Mandarin Chinese is less than half of the number of 5th grade girls taking Mandarin Chinese. Which of the following could be the number of 5th grade boys in Mandarin Chinese?

(A) 10
(B) 40
(C) 70
(D) 100
(E) 130

This is one of a set of fifteen challenging GMAT Quant problems. To see the whole collection, as well as the OE for this question, go to:
Challenging GMAT Math Practice Questions

Mike

Hi

A point..
Either the Q has some typo error or it contains unnecessary info and wrong choices

At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4th or 5th grade. There are 320 students in the 4th grade -- So 5th grade has 700-320=380 students
, and there are 210 girls in the 5th grade. --- So total boys in 5th grade are 380-210=170
Fifty percent of the 5th graders and 40% of the 4th graders take Mandarin Chinese. --- In present scenario, nothing comes out of this
Ninety 5th grade boys do not take Mandarin Chinese. ---- So remaining read mandarin Chinese. That is 170-90=80
The number of 4th grade girls taking Mandarin Chinese is less than half of the number of 5th grade girls taking Mandarin Chinese. --Not required
Which of the following could be the number of 5th grade boys in Mandarin Chinese? We have already found it as 80..

80 is not in ANSWER ???
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Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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02 Mar 2017, 06:42
1
According to OA from Magoosh website - answer is about 4th grade boys taking Mandarin Chinese, not 5th...
https://magoosh.com/gmat/2017/challengi ... questions/
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Joined: 28 Jul 2011
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Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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02 Mar 2017, 07:01
Attachments

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4485
Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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02 Mar 2017, 10:08
chetan2u wrote:
mikemcgarry wrote:
At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4th or 5th grade. There are 320 students in the 4th grade, and there are 210 girls in the 5th grade. Fifty percent of the 5th graders and 40% of the 4th graders take Mandarin Chinese. Ninety 5th grade boys do not take Mandarin Chinese. The number of 4th grade girls taking Mandarin Chinese is less than half of the number of 5th grade girls taking Mandarin Chinese. Which of the following could be the number of 5th grade boys in Mandarin Chinese?

(A) 10
(B) 40
(C) 70
(D) 100
(E) 130

This is one of a set of fifteen challenging GMAT Quant problems. To see the whole collection, as well as the OE for this question, go to:
Challenging GMAT Math Practice Questions

Mike

Hi

A point..
Either the Q has some typo error or it contains unnecessary info and wrong choices

LeonidK wrote:
According to OA from Magoosh website - answer is about 4th grade boys taking Mandarin Chinese, not 5th...

Dear chetan2u & LeonidK,

Thank you very much to both of you! Yes, these tiny typos sometimes are the hardest things to find and notice. Indeed, the prompt question was supposed to be about the number of 4th grade boys in Mandarin.

I corrected the question above and the blog. Thank you very much for finding this typo!

Mike McGarry
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Status: Profile 1
Joined: 20 Sep 2015
Posts: 56
GMAT 1: 690 Q48 V37
GPA: 3.2
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Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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21 Apr 2017, 10:30
At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4th or 5th grade. There are 320 students in the 4th grade, and there are 210 girls in the 5th grade. Fifty percent of the 5th graders and 40% of the 4th graders take Mandarin Chinese. Ninety 5th grade boys do not take Mandarin Chinese. The number of 4th grade girls taking Mandarin Chinese is less than half of the number of 5th grade girls taking Mandarin Chinese. Which of the following could be the number of 4th grade boys in Mandarin Chinese?

(A) 10
(B) 40
(C) 70
(D) 100
(E) 130

with all the corrections given above in the question...

210 Girls in 5th & 90 Boys in 5th do not take bla bla... = 5th grade is having mix of Girls and Boys

The number of 4th grade girls taking Mandarin Chinese is less than half bla bla..(less than half could be 0) +
all the students are boys or girls in the 4th or 5th grade +
question asked for number of boys in 4th grade (non zero ans option so) = 4th grade is having only Boys (320 Boys)

40% of the 4th graders take Mandarin Chinese + number of 4th grade boys in Mandarin Chinese = 320*(4/10) =128

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Posts: 936
Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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27 Apr 2017, 07:11
mikemcgarry wrote:
chetan2u wrote:
mikemcgarry wrote:
At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4th or 5th grade. There are 320 students in the 4th grade, and there are 210 girls in the 5th grade. Fifty percent of the 5th graders and 40% of the 4th graders take Mandarin Chinese. Ninety 5th grade boys do not take Mandarin Chinese. The number of 4th grade girls taking Mandarin Chinese is less than half of the number of 5th grade girls taking Mandarin Chinese. Which of the following could be the number of 5th grade boys in Mandarin Chinese?

(A) 10
(B) 40
(C) 70
(D) 100
(E) 130

This is one of a set of fifteen challenging GMAT Quant problems. To see the whole collection, as well as the OE for this question, go to:
Challenging GMAT Math Practice Questions

Mike

Hi

A point..
Either the Q has some typo error or it contains unnecessary info and wrong choices

LeonidK wrote:
According to OA from Magoosh website - answer is about 4th grade boys taking Mandarin Chinese, not 5th...

Dear chetan2u & LeonidK,

Thank you very much to both of you! Yes, these tiny typos sometimes are the hardest things to find and notice. Indeed, the prompt question was supposed to be about the number of 4th grade boys in Mandarin.

I corrected the question above and the blog. Thank you very much for finding this typo!

Mike McGarry

mikemcgarry

Please make above question correct as said earlier
thanks
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Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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27 Apr 2017, 07:56
2
2
The correct question written on blog as below.

Quote:
At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4th or 5th grade. There are 320 students in the 4th grade, and there are 210 girls in the 5th grade. Fifty percent of the 5th graders and 40% of the 4th graders take Mandarin Chinese. Ninety 5th grade boys do not take Mandarin Chinese. The number of 4th grade girls taking Mandarin Chinese is less than half of the number of 5th grade girls taking Mandarin Chinese. Which of the following could be the number of 4th grade boys in Mandarin Chinese?

(A) 10
(B) 40
(C) 70
(D) 100
(E) 130

Here is the table I've made for easier view.
Attachment:

Table.PNG [ 4.47 KiB | Viewed 3470 times ]

First, there are 320 4th grade students, so there are 700 - 320 = 380 students in 5th grade.

There are 210 girls in 5th grade so there are 380 - 210 = 170 boys in 5th grade.

50% of the 5th graders take MC, or 50% * 380 = 190 students in 5th grade take MC.

40% of the 4th graders take MC, or 40% * 320 = 128 students in 4th grade take MC.

90 boys in 5th grade don't take MC => the remaining 170 - 90 = 80 boys in 5th grade take MC.

Hence there are 190 - 80 = 110 girls in 5th grade take MC.

The number of 4th grade girls taking MC is less than 1/2 of the number of 5th grade girls taking MC. There are 110 girls in 5th grade take MC, so the number of 4th grade girls taking MC is less than 1/2 * 110 = 55

Note that there are 128 students in 4th grade taking MC, so the number of boys in 4th grade taking MC must greater than 128 - 55 = 73.

Now, A, B, C are out.

Note that there are 128 students in 4th grade taking MC, so the number of boys in 4th grade taking MC cannot greater than 128, so E is out.

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Posts: 4485
Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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27 Apr 2017, 11:02
rohit8865 wrote:
mikemcgarry

Please make above question correct as said earlier
thanks

Dear rohit8865

Done.

Mike
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Mike McGarry
Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Status: I am not giving up. Not yet.
Joined: 23 Jul 2015
Posts: 38
Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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03 May 2017, 00:56
mikemcgarry wrote:
At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4th or 5th grade. There are 320 students in the 4th grade, and there are 210 girls in the 5th grade. Fifty percent of the 5th graders and 40% of the 4th graders take Mandarin Chinese. Ninety 5th grade boys do not take Mandarin Chinese. The number of 4th grade girls taking Mandarin Chinese is less than half of the number of 4th 5th grade girls taking Mandarin Chinese. Which of the following could be the number of 4th grade boys in Mandarin Chinese?

(A) 10
(B) 40
(C) 70
(D) 100
(E) 130

This is one of a set of fifteen challenging GMAT Quant problems. To see the whole collection, as well as the OE for this question, go to:
Challenging GMAT Math Practice Questions

Mike

Wonderful question ruined by typos.
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Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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03 May 2017, 01:35
No of students in 4th grade=320
No of students in 5th grade=380 (boys=170, girls=210)

Students taking Mandarin Chinese:
4th grade: 0.4*128=128 (boys=x, girls= less than 55 (half of girls in 5th grade)

A, B, C are crossed out because their sum will not reach 128
E is crossed out because it will exceed 130

D IMO

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Joined: 28 Dec 2011
Posts: 4485
Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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03 May 2017, 12:15
PKay wrote:
mikemcgarry wrote:
At Mnemosyne Middle School, there are 700 students: all the students are boys or girls in the 4th or 5th grade. There are 320 students in the 4th grade, and there are 210 girls in the 5th grade. Fifty percent of the 5th graders and 40% of the 4th graders take Mandarin Chinese. Ninety 5th grade boys do not take Mandarin Chinese. The number of 4th grade girls taking Mandarin Chinese is less than half of the number of 4th 5th grade girls taking Mandarin Chinese. Which of the following could be the number of 4th grade boys in Mandarin Chinese?

(A) 10
(B) 40
(C) 70
(D) 100
(E) 130

This is one of a set of fifteen challenging GMAT Quant problems. To see the whole collection, as well as the OE for this question, go to:
Challenging GMAT Math Practice Questions

Mike

Wonderful question ruined by typos.

Dear PKay,

I corrected this in the entry at the top. Thanks for pointing this out.

Mike
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Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)
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Joined: 14 May 2015
Posts: 45
At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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03 May 2017, 16:10
total student=700
4th student=320
5th student=380 [G=210 B=170]

Chinese:
5th student(B+G)=190
4th student(B+G)=128

5th student:
B not chn=90
B chn=170-90=80
G chn=190-80=110

4th G chn<(5th G chn)/2
4th G chn<110/2
4th G chn<55

if 4th G chn=54
then, 4th B chn=128-54=74

if 4th G chn=0
then, 4th B chn=128-0=128

74<= 4th B chn <=128

Only possible answer is D (100)
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Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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05 May 2017, 07:18
Given:
Total 700
90 5th grade boys do not take MC
4th grade girls taking MC < half of 5th grade girls taking MC
Find 4th grade boys taking MC?
Analysis:
5th grade has 210 girls so number of boys = 380-210=170
Out of these 170 boys, 90 do not take MC so 80 take MC
Girls in 5th grade taking MC = (50% of 380) - 80=110
4th grade MC = 40% of320=128
Maximum girls taking MC in 4th grade should be atleast one less than half of 5th grade girls taking MC = 110/2-1=54
So number of 4th grade boys taking MC is atleast 128-54=74.
Answer D matches(100>74) as it can not be E(130>128)
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Re: At Mnemosyne Middle School, there are 700 students: all the students a  [#permalink]

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Re: At Mnemosyne Middle School, there are 700 students: all the students a   [#permalink] 28 Mar 2020, 21:58