The GMAT is scored on a scale of 200 to 800 in 10 point incr

Question

The GMAT is scored on a scale of 200 to 800 in 10 point increments. (Thus 410 and 760 are real GMAT scores but 412 and 765 are not). A first-year class at a certain business school consists of 478 students. Did any students of the same gender in the first-year class who were born in the same-named month have the same GMAT score?
(1) The range of GMAT scores in the first-year class is 600 to 780.
(2) 60% of the students in the first-year class are male.

(1) The range of GMAT scores in the first-year class is 600 to 780.
(2) 60% of the students in the first-year class are male.

Can someone please let me know how to solve this? I tried it this way:

Considering Statement 1

Range of scores will be 600, 610, 620.........770, 780 and there are 12 months in a year so 12 distinct possibilities for a birth month of a student. I struggled from here to solve.

Considering Statement 2 --> Is clearly insufficient as range for GMAT scores is not provided.

Skywalker18 · Accepted Answer

Total number of students in class = 478
Possible genders = 2
Total possible scores = 61

Number of months = 12

1. Score range = 600 - 780
Therefore , we have 19 possible scores 
Number of combinations =19 *2 * 12 = 456
Since 456< 478 . We will have atleast one repeat of the same gender and birth month.

Sufficient.

2. Number of male = 60 % of 478= 286.8

Not sufficient.
Answer A

IanStewart · Answer

Bowtie's solution above is perfect, but I'll go into a bit more detail in case it's unclear:

This question (and another I responded to yesterday) is based on something called the 'pigeonhole principle'. That principle is usually explained as follows: if a postal worker has 4 envelopes which she will place in 3 pigeonholes, then it must be true that (at least) 2 envelopes will end up in the same pigeonhole, since even if the first 3 envelopes go into different pigeonholes, the 4th will need to go in a pigeonhole already containing an envelope. Changing the numbers to mimic the question above, say you have 20 people who take a test consisting of 19 questions. Then it must be true that two people answered the same number of questions correctly, since even if the first 19 people all had a different number of correct answers, that uses up all of the possibilities from 1 to 19, so the last person would need to have answered the same number of questions correctly as one of the first nineteen people.

We have a similar situation here. From Statement 1, there are only 19 possible GMAT scores in the class. So if we know we have 20 students of the same gender who were born in the same month, we could then be sure that (at least) two of them must have the same GMAT score. We have 478 students in total. At least half of these, or 239 students, must be of the same gender (you couldn't have less than 239 men *and* less than 239 women in the class). Further, it is impossible that there are only 19 students of the same gender born in *every* month of the year (since then you'd only have at most 12*19 = 228 students of that gender), so we must have at least 20 students of the same gender born in the same month. So two of these students must have the same GMAT score, and the answer is A.

rohitkumar77 · Answer

I have always got this question wrong but after a long thinking i finally deduced how to go about these types of questions :-

IN A -

we have 19 ranges - from 600 to 780 ;

total months are 12 - Jan- dec ;

lets start putting the students in one group so that they dont fall in same gender same score same month born category

score 600 - 12 males - 12 different born months - Naming individuals as 600JanM , 600 FEBM , 600marM and so on- we get 12 different males with different score and born month
similarly for females 
score 600 - 12 females - 12 different born months- Naming individuals as 600JanF , 600 FEBF , 600marF and so on- we get 12 different females with different score and born month

doing these for each score we get 24 people ( males and females ) for each score with different gender, score and born month
total til now 24 *19 scores = 456

we are still left with 22 more students and we have to adjust them in one of the either months/scores ; 
So ANswer is A

Hope i was able to explain ; if i am wrong in my approach pls pls correct me

Bowtie · Answer

I got A. so you have 478 students born in 12 different months. so each month has an average of 39.8 kids in them and there is a possiblity of 19 scores. Since 39>19*2 you know that some cases 3 students had the same score in the same month. Since there are 3 students obviously 2 or more had to be the same gender. So the answer should be A.

Now if the question asked specficially if the scores were for a male or female A would not work, or if it was in a given month. But because it asked if any month at all, we can use the average of 39.8 to answer the question.

Hoped this helped

plalud · Answer

To build on Skywalker18 answer.

Total number of students in class = 478.  We need to see if we can fit them all in a case by themselves 
Possible genders = 2
Total possible scores = 61 
Number of months = 12
 Without statements, there are 61*12*2 cases that can be filled. Indeed there are 61*12 different combination of scores and months. Since these combinations can be repeated if the gender differs, and there is a max amount of choice when there are 1/2 female, 1/2 male, we can put two individual on each cases, if they are man and female. Thus we can multiply 61*12 .

1. Score range = 600 - 780
Therefore , we have 19 possible scores 
Number of combinations =19 *2 * 12 = 456
Since 456< 478 . We will have atleast one repeat of the same gender and birth month.

Sufficient.

2. Number of male = 60 % of 478= 286.8

Not sufficient.
Answer A

stonecold · Answer

Great Question.
Here is what i did i this one =>
Number of students =478

Statement 1-->

Number of cases = 19*2*12=456
Hence there must be a repletion.
Hence sufficient => YES

Statement 2-->
No clue of GMAT scores.
Hence Not sufficient

Hence A

Hector1S · Answer

How do we know the no.of men or women? The question doesn't give us any info about the number.

Juliaz · Answer

That is such a good question. Could anyone please share the link to more questions using the same logic?
Thanks!

Posted from my mobile device

gmatzpractice · Answer

2 Possible Genders
12 Possible Birth Months
19 Possible Scores

Max 2 * 12 * 19 = 456 unique gender-birth month-score Combinations 
Since 478 students, some must have same gender-birth month-score 
At least 22 students have same gender-birth month-score

A is sufficient

Nishika · Answer

What if the whole class consists of only males?

yamato · Answer

this is an interesting question. did you make this question yourself, or was it made by a non-GMAC related provider? I've never seen a question which is self referencing

Blackishmamba · Answer

Total possible outcomes = 2*61*12 (2 possible genders, 61 possible score increments (from 200 to 800), and 12 months).
We need to reduce this number of possible outcomes to less than the number of students because then we'll definitely have a repeat.

Consider 1): between 600 and 780, there are 19 possible scores. 
Total possible outcomes=2*19*12=456 which is less than 478, the number of students,hence we are sure to see at least one repeat. : SUFFICIENT

Consider 2): 60% male
Total possible outcome = 2*61*12 remains the same, hence it does nothing to reduce outcomes :  Not SUFFICIENT

Hence, answer is  A

Hero8888 · Answer

Then you can spread max 12 people for one score. In range 600 to 780 you have total 19 scores (600, 610,620...,770,780)
So you are able to uniquely distribute only 12*19=228 students of 478. Any 229th student and so on will take one of already taken possitions. Your constraints even limit possible options (worsen the case)

Arro44 · Answer

Really intersting type of question.

At first it appeared like we were missing several important bits of information to solve the question, but the more time one spend reasoning, the more the picture cleared up.

The seemed almost like a small riddle.

anud33p · Answer

This question uses the pigeonhole principle - one rendition (probably the most literal) of which states that if there are n number of pigeons and m number of nests, such that m < n (i.e. number of nests is less than the number of pigeons), then there will be at least two pigeons in at least one of the nests.

Here, the question replaces pigeons with people and adds two more criteria (Gender & Month). Assume the score, the month and the gender together make one nest. How many different nests are possible? Using the fundamental principle of counting we get: Number of Scores * month * gender

Case I: There are 19 different scores possible, 2 different genders (unless stated in the question) and 12 different months.
So, the number of nests = 19 * 2 * 12 = 456.
Number of people in the class = 478.
Therefore, there will be some overlap. Sufficient.

Case II: All it states is that 60% of the students are male ~ (3/5)*478 which is not even a whole number. That itself should make it look suspicious. But even otherwise, we can probe it further:
Number of nests = 61 (200 to 800 scores) * 2 * 12 = 1464. Number of students = 478.
So, there may be or may not be any overlap. Hence, insufficient.

Hope this made sense

Cheers
AA

Cheers AA

omsworlds · Answer

Still, that no. (478) will be of same gender.. If this is the case then its easier.. all male, so same gender will have more than one score and born in same month..
12*19= 228, while students of same gender are 478... 478 > 228 ...

omsworlds · Answer

half of 478= 239.

Say no. of male =1, then no. of female= 478-1=477, so more than half of 478 are of same gender (477 females)

if no. of male = 200, no. of females= 278, still more than half are of same gender.. (278 females)

if no. of males = 300, no. of females= 178, again, more than half are of same gender.. (300 males)

if no. of males= 239, no. of female= 239, same no. of male and female.. again exactly half are of same gender.. (239 males, 239 females)

so if no. of males is greater than no. of females , then more than half will be male (of same gender)
and if no. of males is fewer than no. of females, then more than half will be female (again of same gender)

so in any case, exactly half or more than half will be of same gender..

Hope its clear...

IanStewart · Answer

This is very definitely not a GMATPrep question, so the "Source: GMATPrep" tag should be fixed.

Harsh2111s · Answer

Let's start with statement 1- 
Range 600-780, thus we have 19 individual scores to be distributed in 478 students.
same score-same gender-same month born
total score -total gender-total months
19----------2------------12
Thus there will be at least 1 candidate with same gender in the first-year class who were born in the same-named month have the same GMAT score.
You have only 12 months and 2 gender thus 24 possible variations.
Jan - Male - 600
Feb-Male-610
Mar-Male-620
---------
---------
Dec-Male-720

Anyway with 478 students repeat cases will definitely occur.

Hope it helps

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