A code consisting of 10 digits/alphabets is generated whenever you buy an online gift card. The codes generated can have repetition of both digits and aphabets. In one such code generated, the probability of choosing two digits from the digits/alphabets used in the code is between 10% and 33%, both inclusive, while the probability of choosing two vowels from the digits/alphabets used in the code is at least 1% but less than 10%. Alphabets consist of five vowels and 21 consonants. Based on the information provided, select for Maximum Consonants an option that gives the maximum number of consonants possible in the code, and select for Minimum Consonants an option that gives the minimum number of consonants possible in the code.

The code has digit and alphabets, which are total 10 in number. We are looking at probability of selecting 2 elements in 10 items, so let us find the different probabilities. Remeber we do not have to calculate the decimal part as that is not important here, so just mark tha xy or the values if you can recollect. If element is just 1: \frac{1}{10} * \frac{0}{9} = 0 % If there are two elements : \frac{2}{10} * \frac{1}{9} = \frac{1}{45} \ \ or \ \ \frac{100}{45} % = 2.xy % If there are three elements : \frac{3}{10} * \frac{2}{9} = \frac{1}{15} \ \ or \ \ \frac{100}{15} % = 6.xy % If there are four elements : \frac{4}{10} * \frac{3}{9} = \frac{2}{15} \ \ or \ \ \frac{200}{15} % = 12.xy % If there are five elements : \frac{5}{10} * \frac{4}{9} = \frac{2}{9} \ \ or \ \ \frac{200}{9} % = 22.22 % If there are six elements : \frac{6}{10} * \frac{5}{9} = \frac{1}{3} \ \ or \ \ \frac{100}{3} % = 33.33 % Now, let us find the number of digits and vowels Digit: The probability of choosing two digits from the digits/alphabets used in the code is between 10% and 33%, both inclusive. So, there could be 4 or 5 digits in the code. Vowel: The probability of choosing two vowels from the digits/alphabets used in the code is at least 1% but less than 10%. So, there could be 2 or 3 vowels in the code. Max number of consonants = 10 - Min number of digits - Min number of vowels = 10 - 4 - 2 = 4 Min number of consonants = 10 - Max number of digits - Max number of vowels = 10 - 5 - 3 = 2

Bunuel , KarishmaB , ScottTargetTestPrep Please help with this question. I am not able to figure it out.

no of digits=D no of vowels=v no of consonants=c => d(d-1)/9.10=0.1 -0.33 => v(v-1)/9.10=0.01-0.1 => d=4,5 => v=2,3 => (d+v)_min=6, (d+v)_max=8 => c_max=4, c_min=2 Posted from my mobile device

For first condition (to choose two digits ) there are only 2 possible scenarios 5C2/10C2 or 4C2/10C2 which gives us probability b/w 10 & 33% .... the no of possible digits are 4 or 5 this implies that no of alphabets are either 5 or 6 Using second condition to choose vowels there are again only 2 possible scenarios 2C2/10C2 or 3C2/10C2 which gives us probability between 1 & 10% Now if there are (2,3) vowels out of (5,6) alphabets then max consonents: 6-2 =4 & min consonents: 5-3 = 2

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