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The GMAT is scored on a scale of 200 to 800

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The GMAT is scored on a scale of 200 to 800

by abhi332 » Thu Feb 25, 2010 12:46 pm
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.

[spoiler]OA:A[/spoiler]
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by KapTeacherEli » Thu Feb 25, 2010 5:13 pm
We're looking for repeats of months, genders and scores among the 478 students in a class. Now, without any further information, there are 2 possible genders, 61 possible score increments (200-290, 300-390, etc., +800), and 12 months of the year. That leaves us over two thousand combinations (no need to calculate an exact number, just eyeball it). We know we'll defnitely have a repeat if the number of combinations is smaller than the number of students; so we'll be looking for answers that narrow down the possibilities.

We should start with 2) here, since it's much easier to evaluate. 60% male does nothing for us; there are still 5 times as many combinations as there are students, so while it's entirely possible that some students repeat, it's equally possible that none do. We eliminate choices (B) and (D), and move on.

1) is more useful. With scores from 600 to 780, that leaves 19 possible scores (remember to count 600 as a possible score! Don't make a fencepost error.) So, we've got 19 scores times 2 genders times 12 months, or 456 combinations. With 456 combinations, and 478 students, we are guaranteed to see at least one repeat. (1) is sufficient, and (A) is our answer.
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www.kaptest.com/gmat

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by harsh.champ » Sun Feb 28, 2010 11:25 am
abhi332 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 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.

[spoiler]OA:A[/spoiler]
Statement 1:- we find that 600,610,620....770,780. - 19 scores are possible.
Now at the first look ,this question seems impossible using statement 1,but if we consider all the combinations as shown by
Eli,we find that the answer is possible using A.
On the 1st attempt I would have gone with E.

Hey abhi,
I wanted to ask the source of the question and what score category (700-800) would this question fall in??
Thanks.
It takes time and effort to explain, so if my comment helped you please press Thanks button :)



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by abhi332 » Sun Feb 28, 2010 12:02 pm
source: Manhattan

This question is pretty difficult and will be very difficult in exam time. My guess this question is well above 700
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by nitesh50 » Thu Dec 13, 2018 2:58 am
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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