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The number of employees in GMATClub is a prime number 03 Dec 2021, 10:47
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75% (hard)

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59% (02:35) correct 41% (02:16) wrong based on 169 sessions

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The number of employees in GMATClub is a prime number and is less than 300. The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:

A. 101 : 88
B. 87 : 100
C. 110 : 111
D. 85 : 98
E. 97 : 84

Source: CAT India 2006
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E
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The number of employees in GMATClub is a prime number 26 Dec 2021, 11:00
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Given: The number of employees in GMATClub is a prime number and is less than 300.
Asked: The ratio of the number of employees who are graduates and above, to that of employees who are not, can possibly be:


A. 101 : 88; Possible number of employees in GMATClub = 101 + 88 = 189 = 3*3*23; NOT a prime number; Incorrect
B. 87 : 100; Possible number of employees in GMATClub = 87 + 100 = 187 = 11*17; NOT a prime number; Incorrect
C. 110 : 111; Possible number of employees in GMATClub = 110 + 111 = 221 = 13*17; NOT a prime number; Incorrect
D. 85 : 98 ;Possible number of employees in GMATClub = 85 + 98 = 183 = 3*61; NOT a prime number; Incorrect
E. 97 : 84; Possible number of employees in GMATClub = 97 + 84 = 181 ; a prime number; Correct

IMO E
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The number of employees in GMATClub is a prime number 26 Dec 2021, 11:39
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We know that the number of graduates to those who aren't should sum to at most to 300 (of course, it would not be even be 300, as the total is a prime. However, I don't know what the nearest prime to 300 is :tongue_opt3 , so I will just assume that the sum cannot exceed 300.)

I started by looking at the options and soon realized that the ratio given is an actual number of graduated / non - graduates and is not a reduced form of data.

If you want to know how did I conclude this, read the details in the box, else feel free to skip.

Quote:
In the option choices we are give the ratio of \(\frac{Graduates }{ Non Graduates}\)

Now since this is an ratio, in most of the cases this is a reduced form. The actual number is a multiple of the numerator and denominator.

Ex. Assume, that the number of boys in a class is 4 and the number of girls in the class is 6.

The ratio of \(\frac{boys }{ girls }\) = \(\frac{ 4 }{ 6 }\) = \(\frac{ 2 }{ 3}\)

We get \(\frac{ 2 }{ 3}\) by cancelling the common factor '2' from the numerator and denominator.

Similarly, when we say that the ratio \(\frac{Graduates }{ Non Graduates}\) = \(\frac{ 101}{ 88}\), the ratio can represent either the actual number or can represent a reduced form where a common factor has been cancelled from both the numerator and the denominator.

The smallest factor that we can consider here is 2. However, if the numerator and denominator were a multiplied by the assumed factor '2' the total would exceed 300.

For ex. lets take option A

\(\frac{Graduates }{ Non Graduates}\) = \(\frac{101}{ 88}\)

Now, either the number of graduates and the number of non graduates is equal to 101 and 88 respectively or the ratio is \(\frac{101}{ 88}\) while the actual number is a multiple of a factor say x

\(\frac{Graduates }{ Non Graduates}\) = \(\frac{101 * x}{ 88 * x}\)

Even if we take 2 as the factor

Number of graduates = 101 * 2 = 202

Number of non - graduates = 88 * 2 = 176

The sum of this exceed 300, hence this is not possible.

Long story short - The options presented represent the actual number of graduates and non-graduates, not the reduced form.

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Option Analysis:

A

101 + 88 = 189

Divisible by 3; Not a prime.

B

87 + 100 = 187

Divisible by 11; Not a prime.

C

110 + 111 = 221

Divisible by 13; Not a prime.

D

85 + 98 = 183

Divisible by 3; Not a prime.

E

97 + 84 = 181

Prime; Also the only option left. :D
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The number of employees in GMATClub is a prime number 22 Oct 2024, 06:24
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