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

Question

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

please correct me...

broall · Accepted Answer

The correct question written on blog as below.
mikemcgarry: Please make sure your question correct.

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 14779 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.

The answer is D.

chetan2u · Answer

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 ???

LeonidK · Answer

According to OA from Magoosh website - answer is about 4th grade boys taking Mandarin Chinese, not 5th... https://magoosh.com/gmat/2017/challengi ... questions/

FieryLeo · Answer

Is the answer 100? (D)

mikemcgarry · Answer

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 :-)

jokschmer · Answer

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 :-)

(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

please correct me...

rohit8865 · Answer

mikemcgarry Please make above question correct as said earlier

thanks

mikemcgarry · Answer

Dear rohit8865 Done. :-)

Mike

PKay · Answer

Wonderful question ruined by typos.

jxav · Answer

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)

5th grade: 0.5*380=190 (boys=80, girls=110)

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

D IMO

Sent from my SM-G935F using  GMAT Club Forum mobile app

mikemcgarry · Answer

Dear PKay , I corrected this in the entry at the top. Thanks for pointing this out. Mike :-)

ishaan.wares · Answer

total student=700
4th student=320
5th student=380

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)

dabhishek87 · Answer

Given:
Total 700
4th grade 320
5th grade girls- 210
50% 5th grade and 40th % 4th grade takes MC
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:
4th grade has 320 so 5th grade has 700-320=380
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)

Kartik2121 · Answer

I dare anyone to solve this question within 2 minutes.

Posted from my mobile device

KarishmaB · Answer

We can use a matrix here to arrange the data properly. The ticks show the people who take Chinese and crosses (x) show those who do not. We need the value of n. Total there are 700 students, 320 in 4th grade so 380 in 5th grade. Since there are 210 5th grader girls, there are 170 5th grader boys. 90 of them do not have Chinese so 80 do have. Then 110 5th grader girls have chinese. So 4th grader girls taking Chinese must be less than 55. But this number is less than 55 only if n is 100. n cannot be 130 since it must be less than 128. Screenshot 2023-08-20 at 1.15.09 PM.png Answer (D).

rak08 · Answer

How i worked through it was

eliminated A & E first because max Boys = 128 and minimum = 24
so left with B,C,D

now if Girls (M) < 105
Boys (M)>23
in total for 4th grade

Girls < 210
Boys >46
but the sum of the least of two is 209+47 = 256
the total is 320
so 320-256 = 84
now we need at least -> 23+84 = 107 ish
so thats why i picked D = 100

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards