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Set X consists of all two-digit primes and set Y consists of all posit

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Set X consists of all two-digit primes and set Y consists of all posit [#permalink]
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Bunuel wrote:

Tough and Tricky questions: Statistics.

Set X consists of all two-digit primes and set Y consists of all positive odd multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set?

(A) 84
(B) 89
(C) 90
(D) 92
(E) 95

Set X = {11, 13, 17,............., 83, 89, 97}
Set Y = {5, 15, 25,..............., 75, 85, 95}

Combining two sets, say Set Z

Set Z = {5, 11, 13, 15, 17, 25,..................., 75, 83, 85, 89, 95, 97}

Range = Max Value - Min Value
Range (Z) = 97 - 5 = 92

OA D is the answer.

Solved the answer correct here and clicked the answer wrong.
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Re: Set X consists of all two-digit primes and set Y consists of all posit [#permalink]
skywalkerca84 wrote:
Bunuel wrote:

Tough and Tricky questions: Statistics.

Set X consists of all two-digit primes and set Y consists of all positive odd multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set?

(A) 84
(B) 89
(C) 90
(D) 92
(E) 95

If the question was rephrased to,

Set X consists of all two-digit primes and set Y consists of all multiples of 5 from 0 to 100, both inclusive. If the two sets are combined into one, what will be the range of the new set?

Would the answer be 100?

That's correct

Answer = 100 - 0 = 100
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Re: Set X consists of all two-digit primes and set Y consists of all posit [#permalink]
first odd multiply of 5 is 5
the last 2 digit prime is 97
97-5=92
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Re: Set X consists of all two-digit primes and set Y consists of all posit [#permalink]
We just want the first and the last integer in the set.
First set: 11,................,97
Second set: 5,............,95

Combining the two sets, we get:
5, 11,..........95, 97

Range= Last term-First term= 97-5= 92
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Re: Please suggest short-cut for this question [#permalink]
HannibalLecter wrote:
Set X consists of all two/digit primes and set Y consists of all positive odd multiples of 5 less than 100. If the two sets are combined into one, what will be the range of the new set?
(A) 84
(B) 89
(C) 90
(D) 92
(E) 95

Try this, it mostly relies on using the answers (an Alternative approach):

Set X has only two digit numbers and the smallest number in set Y is 5.
So, the smallest number in the union of X and Y is definitely 5.

Let's look at the answers, starting with the largest:
If (E) were true, then the largest number would be 100, impossible.
If (D) were true, the largest would be 97. 97 isn't a multilpe of 5, but is it prime?
There is no easy way to answer this unfortuantely, we'll need to check by dividing 97 by all odd integers smaller than the root of 97 which is a bit less than 10.
97/3 = not an integer (9+7 = 16 is not divisible by 3)
97/5 = not an integer
97/7 = (70 + 27) = not an integer (because 28 is divisible by 7)
97/9 = not an integer.
Therefore 97 must be prime so the range is at least 97 - 5 = 92. Since this is our largest option, we'll pick it!

(D) is our answer.
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Re: Set X consists of all two-digit primes and set Y consists of all posit [#permalink]
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A tip: If you have issues to remember all prime numbers, just remember the formula prime = 6n+1, and you will be able to pick a prime number. I didn't remeber 97 as prime, but I could recall the formula and get 6*16+1= 97 as a prime.
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Re: Set X consists of all two-digit primes and set Y consists of all posit [#permalink]
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Re: Set X consists of all two-digit primes and set Y consists of all posit [#permalink]
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