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08 May 2018, 00:42
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
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Question Stats:
47% (02:49) correct
53%
(03:11)
wrong
based on 406
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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%
A. 25%
B. 50%
C. 62.5%
D. 66.7%
E. 75%
SSM700plus
Joined: 01 Aug 2017
Last visit: 08 Aug 2022
Posts: 164
Given Kudos: 420
Location: India
Concentration: General Management, Leadership
Schools: ISB '20 (S) IIMA PGPX"20 (S)
GMAT 1: 500 Q47 V15
GPA: 3.4
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08 May 2018, 01:45
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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
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
08 Jun 2019, 10:44
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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:
08th June 2019 - Reply 1.JPG [ 21.85 KiB | Viewed 22216 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!
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 [ 21.85 KiB | Viewed 22216 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!
