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The GMAT is scored on a scale of 200 to 800 in 10 point incr
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Updated on: 27 Aug 2014, 06:30
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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 firstyear class at a certain business school consists of 478 students. Did any students of the same gender in the firstyear class who were born in the samenamed month have the same GMAT score? (1) The range of GMAT scores in the firstyear class is 600 to 780. (2) 60% of the students in the firstyear 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.
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MGMAT 1 > 530 MGMAT 2> 640 MGMAT 3 > 610 GMAT ==> 730
Originally posted by enigma123 on 22 Nov 2011, 16:40.
Last edited by Bunuel on 27 Aug 2014, 06:30, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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23 Nov 2011, 08:28
enigma123 wrote: 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 firstyear class at a certain business school consists of 478 students. Did any students of the same gender in the firstyear class who were born in the samenamed month have the same GMAT score? (1) The range of GMAT scores in the firstyear class is 600 to 780. (2) 60% of the students in the firstyear class are male. 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.
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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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24 Oct 2015, 06:23
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
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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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23 Nov 2011, 08:15
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.
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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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20 Oct 2015, 06:36
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
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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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20 Dec 2016, 12:41
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



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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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20 Dec 2016, 15:02
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
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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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10 Jul 2017, 04:03
IanStewart wrote: enigma123 wrote: 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 firstyear class at a certain business school consists of 478 students. Did any students of the same gender in the firstyear class who were born in the samenamed month have the same GMAT score? (1) The range of GMAT scores in the firstyear class is 600 to 780. (2) 60% of the students in the firstyear class are male. 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. How do we know the no.of men or women? The question doesn't give us any info about the number.



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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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25 Jun 2018, 10:19
That is such a good question. Could anyone please share the link to more questions using the same logic? Thanks!
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The GMAT is scored on a scale of 200 to 800 in 10 point incr
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25 Jun 2018, 11:46
2 Possible Genders 12 Possible Birth Months 19 Possible Scores
Max 2 * 12 * 19 = 456 unique genderbirth monthscore Combinations Since 478 students, some must have same genderbirth monthscore At least 22 students have same genderbirth monthscore
A is sufficient



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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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05 Aug 2018, 10:12
What if the whole class consists of only males?



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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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05 Aug 2018, 10:27
enigma123 wrote: 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 firstyear class at a certain business school consists of 478 students. Did any students of the same gender in the firstyear class who were born in the samenamed month have the same GMAT score? (1) The range of GMAT scores in the firstyear class is 600 to 780. (2) 60% of the students in the firstyear 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. this is an interesting question. did you make this question yourself, or was it made by a nonGMAC related provider? I've never seen a question which is self referencing
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The GMAT is scored on a scale of 200 to 800 in 10 point incr
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27 Aug 2018, 19:27
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. : SUFFICIENTConsider 2): 60% male Total possible outcome = 2*61*12 remains the same, hence it does nothing to reduce outcomes : Not SUFFICIENTHence, answer is A
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The GMAT is scored on a scale of 200 to 800 in 10 point incr
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18 Sep 2018, 08:56
Nishika wrote: What if the whole class consists of only males? 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)



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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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27 Sep 2018, 13:26
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.
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Re: The GMAT is scored on a scale of 200 to 800 in 10 point incr
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10 Aug 2019, 10:34
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




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