GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 20 Jan 2020, 23:13

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

In a certain class, 1/5 of the boys are shorter than the shorter

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60517
In a certain class, 1/5 of the boys are shorter than the shorter  [#permalink]

Show Tags

New post 08 May 2018, 00:42
1
17
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

38% (02:59) correct 62% (03:17) wrong based on 103 sessions

HideShow timer Statistics

In a certain class, \(\frac{1}{5}\) of the boys are shorter than the shortest girl in the class, and \(\frac{1}{3}\) of the girls are taller than the tallest boy in the class. If there are 16 stu­dents in the class and no two people have the same height, what percent of the students are taller than the shortest girl and shorter than the tallest boy?

A. 25%

B. 50%

C. 62.5%

D. 66.7%

E. 75%

_________________
Most Helpful Community Reply
Manager
Manager
avatar
P
Joined: 01 Aug 2017
Posts: 220
Location: India
Concentration: General Management, Leadership
GMAT 1: 500 Q47 V15
GPA: 3.4
WE: Information Technology (Computer Software)
Reviews Badge CAT Tests
Re: In a certain class, 1/5 of the boys are shorter than the shorter  [#permalink]

Show Tags

New post 08 May 2018, 01:45
3
3
Total number of students is 16. Boys + Girls = 16.

1/5 of the boys are shorter than the shortest girl in the class.
This implies number of boys should be multiple of 5. It can be 5,10,15.

1/3 of the girls are taller than the tallest boy in the class.
This implies number of girls should be multiple of 3. It can be 3,6,9,12,15.

Let's find the number of boys and girls:
If number of boys is 5, then we can have 11 girls but 11 is not divisible by 3.
If number of boys is 15, then we can have 1 girls but 1 is not divisible by 3.
So we get No of boys is 10 and No. of Girls is 6.

Let's solve to find the answer:-

1/5 of the boys are shorter than the shortest girl in the class - No of boys = 1*10/5 = 2

And 1/3 of the girls are taller than the tallest boy in the class - No of Girls = 1*6/3 = 2.

what percent of the students are taller than the shortest girl and shorter than the tallest boy?

This can be found as given below.
16 - (2 + 2 ) - (1 + 1 ) = 10
(1 + 1 ) is for the shortest girl and the tallest boy.

Percentage = 10*100/16 = 62.5.

Ans - C
General Discussion
examPAL Representative
User avatar
P
Joined: 07 Dec 2017
Posts: 1155
Re: In a certain class, 1/5 of the boys are shorter than the shorter  [#permalink]

Show Tags

New post 08 May 2018, 01:39
1
2
Bunuel wrote:
In a certain class, \(\frac{1}{5}\) of the boys are shorter than the shortest girl in the class, and \(\frac{1}{3}\) of the girls are taller than the tallest boy in the class. If there are 16 stu­dents in the class and no two people have the same height, what percent of the students are taller than the shortest girl and shorter than the tallest boy?

A. 25%

B. 50%

C. 62.5%

D. 66.7%

E. 75%


We'll draw out our data so it is easier to understand.
This is an Alternative approach.

1/5 of boys < shortest girl
tallest boy > 1/3 of girls

We need to find
shortest girl < ?? % students < tallest boy

all the girls except 1 are taller than the shortest girl and 1 -1/3 = 2/3 of them are shorter than the tallest boy
all the boys except 1 are shorter than the tallest boy and 1 -1/5 = 4/5 of them are taller than the shortest girl

so we need 2/3 of the girls and 4/5 of the boy - 2.
Let's find the number of girls and boys:
The number of boys is divisibly by 5 so it can be 5, 10 or 15.
If it is 5 there are 11 girls which is not divisible by 3. If it is 15 there is 1 girl which is not divisible by 3.
So there are 10 boys and 6 girls.

So, 2/3 of girls is 4 students and 4/5 of boys is 8 students.
Our percentage is (4+8-2)/16 = 10/16 = 5/8 = 0.625

(C) is our answer.
_________________
CrackVerbal Quant Expert
User avatar
G
Joined: 12 Apr 2019
Posts: 351
Re: In a certain class, 1/5 of the boys are shorter than the shorter  [#permalink]

Show Tags

New post 08 Jun 2019, 10:44
3
1
This is a very good question which can be solved by simple calculations and pure logic. Beware of the trick element though, which can get you into trouble. Answer option E seems to be a very common trap answer, therefore.

The class has a total of 16 students, all of whom have distinct heights. The question mentions 1/5th of the boys and 1/3rd of the girls. This is a clear indication that the number of boys and girls should be multiples of 5 and 3 respectively. The only possible combination turns out to be 10 boys and 6 girls.

Therefore, as per the question, 2 boys are shorter than the shortest girl and 2 girls are taller than the tallest boy.

Let the shortest girl be Q and the tallest boy be M. Then, the entire question can be represented diagrammatically, like this:

Attachment:
08th June 2019 - Reply 1.JPG
08th June 2019 - Reply 1.JPG [ 21.85 KiB | Viewed 2712 times ]


The 2 boys who are shorter than the shortest girl will be shorter than the other girls too. Similarly, the 2 girls who are taller than the tallest boy will be taller than the other boys too.

How many boys are we left with who are taller than the shortest girl? 8, correct? But one of these 8 boys is M himself. So, there are 7 boys taller than the shortest girl, but shorter than the tallest boy.

How many girls are shorter than the tallest boy? 4, right? But, one of these 6 girls is Q herself. So, there are 3 girls who are shorter than the tallest boy but taller than the shortest girl.

In all, we have 10 students in between Q and M. 10 as a percentage of 16 is nothing but

\(\frac{10}{16}\) * 100 = 62.5%

So, the correct answer option is C.

If you forget to exclude M and Q from your calculation, you will end up marking 75% as the answer, which as we mentioned, could be a very common trap answer in this question.

Hope this helps!
_________________
Manager
Manager
User avatar
B
Joined: 16 Dec 2018
Posts: 66
Re: In a certain class, 1/5 of the boys are shorter than the shorter  [#permalink]

Show Tags

New post 04 Dec 2019, 12:35
GMATPrepNow better if u explain it, and advance thanks
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 12 Sep 2015
Posts: 4217
Location: Canada
Re: In a certain class, 1/5 of the boys are shorter than the shorter  [#permalink]

Show Tags

New post 04 Dec 2019, 12:58
1
Top Contributor
Bunuel wrote:
In a certain class, \(\frac{1}{5}\) of the boys are shorter than the shortest girl in the class, and \(\frac{1}{3}\) of the girls are taller than the tallest boy in the class. If there are 16 stu­dents in the class and no two people have the same height, what percent of the students are taller than the shortest girl and shorter than the tallest boy?

A. 25%

B. 50%

C. 62.5%

D. 66.7%

E. 75%


GIVEN: There are 16 students and 1/5 of them are boys.
This means the number of boys must be a multiple of 5.
There are 3 possible cases:
i) 5 boys and 11 girls
ii) 10 boys and 6 girls
iii) 15 boys and 1 girl

GIVEN: There are 16 students and 1/3 of them are girls.
This means the number of girls must be a multiple of 3.
When we check the three possible cases above, we see that only one case (case ii) is such that the number of girls is divisible by 3.

So we now know that there are 10 boys and 6 girls

Let A, B, C, D, E, F represent the heights of the 6 girls arranged in ASCENDING order
Let Q, R, S, T, U, V, W, X, Y, Z represent the heights of the 10 boys arranged in ASCENDING order

1/5 of the boys are shorter than the shortest girl in the class
1/5 of 10 = 2
So, 2 boys are shorter than the shortest girl in the class
We have: Q, R, A [ these 3 heights must be arranged in ascending order]


1/3 of the girls are taller than the tallest boy in the class
1/3 of 2 = 2
So, 2 girls are taller than the tallest boy in the class
We have: Z, E, F [ these 3 heights must be arranged in ascending order]

NOTE: The remaining students must lie BETWEEN A and Z, however there is no way to determine the relationships between each boy and each girl within this range.

So one possible configuration is as follows: Q, R, A, S, T, U, V, W, X, Y, B, C, D, Z, E, F


What percent of the students are taller than the shortest girl and shorter than the tallest boy?
Shortest girl is A and the tallest boy is Z
As we can see from the above diagram, there are 10 such students

10/16 = 5/8 = 62.5%

Answer: C

Cheers,
Brent
_________________
Test confidently with gmatprepnow.com
Image
Manager
Manager
User avatar
B
Joined: 16 Dec 2018
Posts: 66
Re: In a certain class, 1/5 of the boys are shorter than the shorter  [#permalink]

Show Tags

New post 04 Dec 2019, 13:36
GMATPrepNow wrote:
Bunuel wrote:
In a certain class, \(\frac{1}{5}\) of the boys are shorter than the shortest girl in the class, and \(\frac{1}{3}\) of the girls are taller than the tallest boy in the class. If there are 16 stu­dents in the class and no two people have the same height, what percent of the students are taller than the shortest girl and shorter than the tallest boy?

A. 25%

B. 50%

C. 62.5%

D. 66.7%

E. 75%


GIVEN: There are 16 students and 1/5 of them are boys.
This means the number of boys must be a multiple of 5.
There are 3 possible cases:
i) 5 boys and 11 girls
ii) 10 boys and 6 girls
iii) 15 boys and 1 girl

GIVEN: There are 16 students and 1/3 of them are girls.
This means the number of girls must be a multiple of 3.
When we check the three possible cases above, we see that only one case (case ii) is such that the number of girls is divisible by 3.

So we now know that there are 10 boys and 6 girls

Let A, B, C, D, E, F represent the heights of the 6 girls arranged in ASCENDING order
Let Q, R, S, T, U, V, W, X, Y, Z represent the heights of the 10 boys arranged in ASCENDING order

1/5 of the boys are shorter than the shortest girl in the class
1/5 of 10 = 2
So, 2 boys are shorter than the shortest girl in the class
We have: Q, R, A [ these 3 heights must be arranged in ascending order]


1/3 of the girls are taller than the tallest boy in the class
1/3 of 2 = 2
So, 2 girls are taller than the tallest boy in the class
We have: Z, E, F [ these 3 heights must be arranged in ascending order]

NOTE: The remaining students must lie BETWEEN A and Z, however there is no way to determine the relationships between each boy and each girl within this range.

So one possible configuration is as follows: Q, R, A, S, T, U, V, W, X, Y, B, C, D, Z, E, F


What percent of the students are taller than the shortest girl and shorter than the tallest boy?
Shortest girl is A and the tallest boy is Z
As we can see from the above diagram, there are 10 such students

10/16 = 5/8 = 62.5%

Answer: C

Cheers,
Brent


thank u so much. :heart :heart
GMAT Club Bot
Re: In a certain class, 1/5 of the boys are shorter than the shorter   [#permalink] 04 Dec 2019, 13:36
Display posts from previous: Sort by

In a certain class, 1/5 of the boys are shorter than the shorter

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne