Lenas grade was in the 80th percentile out of 120 grades in

Question

Lena’s grade was in the 80th percentile out of 120 grades in her class. In another class of 200 students there were 24 grades higher than Lena’s. If nobody had Lena’s grade, then Lena was what percentile of the two classes combined?

A. 72nd
B. 80th
C. 81st
D. 85th
E. 92nd

Bunuel · Accepted Answer

ORIGINAL QUESTION IS: Lena’s grade was in the 80th percentile out of 120 grades in her class. In another class of 200 students there were 24 grades higher than Lena’s. If nobody had Lena’s grade, then Lena was what percentile of the two classes combined? If someone's grade is in x_{th} percentile of the n grades, this means that x% of people out of n has the grades less than this person. So, being in 80th percentile out of 120 grades means Lena outscored 120*0.8=96 classmates. In another class she would outscored 200-24=176 students. So, in combined classes she outscored 96+176=272 . As there are total of 120+200=320 students, so Lena is in \frac{272}{320}=0.85=85% , or in 85th percentile. The concept is explained here: math-number-theory-percents-91708.html Hope it helps.

LalaB · Answer

(120*80%+200-24)/(120+200)=85

manwiththeharmonica · Answer

Nitpicking, but if 24 students scored better then Lena, then wouldnt she have scored better than 200 - 25 = 175 students?

We should count her score as well?

Posted from my mobile device

EvaJager · Answer

There are two categories: one, the students who scored better than Lena, so their scores are definitely greater than her scores; two, those who didn't score better then Lena, so their scores are less than or equal to Lena's scores. Lena, herself is in the second category. The information that nobody has Lena's score is not relevant. What is important is how many outscored her:
on the first test - 0.2*120 = 24
on the second test - 24
In total, 24 + 24 = 48 out of 120 + 200 = 320 outscored Lena, and represent 48/320 = 15%. Therefore, Lena's score is in the 100 - 15 = 85th percentile.

154238 · Answer

Hi Eva, I am still not convinced with the above explanaton. Can you please explain again? Its clearly written in the question that 24 students out of 200 scored better than Lena means she scored better than 175 students !! (Please correct me) Thanks

EvaJager · Answer

There were two tests. What is important is how many outscored her on  both  tests:
on the first test - 0.2*120 = 24
on the second test - 24
In total, 24 + 24 = 48 out of 120 + 200 = 320 outscored Lena, and they represent 48/320 = 15%. Therefore, Lena's score is in the 100 - 15 = 85th percentile.

154238 · Answer

Got it thanks :-D

!! Kudos for you

!!

pacifist85 · Answer

Hi,

Great, but did the problem also give answer options? It is quite good to see what the offered answers are in order to get an idea of how test makers would trick you into giving the wrong answer!

HardWorkBeatsAll · Answer

Sorry, but there still seems to be some discrepancy. If xth percentile means that x%people score BELOW you then with that explanation, EITHER (1) should be - 96 scored below so Leena was 97th and thus 23 people outscored her.
OR that Leena was 175th and she outscored 174, so overall percentile will be (174+96)/320.

Bunuel or EvaJager, can you help me understand this/confirm if my reasoning is right?

anox · Answer

Hi  Bunuel ,

In reference to number of students she outscored in second class (highlighted in red), shouldn't that number be 175 instead? (because 24 students scored more than her, she herself is 25th highest scorer and the remaining class of 175 student are the ones who scored less then her).

Although, working with  176  makes calculation easier by quickly reducing the fraction to 17/20 which is clearly .85

I am just trying to understand the correct logic for working with percentile. Will really appreciate your help.

Thanks!

stonecold · Answer

Students with score greater than Lena in class A=> 20/100 *120 => 24

Students with score greater than Lena in class B => 24

Combined class strength = 120+200 = 320

Students with score greater than Lena in class A=> 20/100 *120 => 24

Students with score greater than Lena => 24+24 = 48

48 is 15 percent of 320
Hence Lena's percentile rank => 85

Shruti0805 · Answer

If Lena's score is 80%, then she has outscored : (80*120)/100 people, i.e., 96 people.
Thus, 24 people have a score greater than her in her own class.

Also, in the other class there are another 24 people who would outscore her, making it a total of 48 people to outscore her.

(48*100)/320 = 15 % people to outscore her.

Thus, Lena's score would be 85% overall.

B.

VIGHNESHKAMATH · Answer

But doesn't this question assume that 120 grades = 120 students, couldn't there be more than one student with the same grade?

Regards
Vighnesh

bumpbot · Answer

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Lenas grade was in the 80th percentile out of 120 grades in

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