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

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

by Vincen » Mon Oct 16, 2017 6:41 am
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

The OA is D.

Do I have to make the list of elements in each set? I would like a shorter way to solve this PS question. Experts, may you help me?
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by DavidG@VeritasPrep » Mon Oct 16, 2017 7:32 am
Vincen 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

The OA is D.

Do I have to make the list of elements in each set? I would like a shorter way to solve this PS question. Experts, may you help me?
Smallest two-digit prime: 11
Largest two-digit prime: 97

Smallest positive ODD multiple of 5: 5
Largest ODD multiple of 5 (under 100): 95

In the combined set -
Largest value: 97
Smallest value: 5
Range: 97-5 = 92; The answer is D
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by [email protected] » Mon Oct 16, 2017 3:53 pm
Hi Vincen,

Notice that this question asks us for the RANGE of the group of values, so we don't have to find every number that exists in this group - we just need to find the largest and the smallest values.

Set X = two-digit primes
Smallest = 11
Largest = 97

Set Y consists of all positive odd multiples of 5 less than 100
Smallest = 5
Largest = 95

Thus, the range of this group of numbers is 97 - 5 = 92

Final Answer: D

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by EconomistGMATTutor » Tue Oct 17, 2017 12:27 pm
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

The OA is D.

Do I have to make the list of elements in each set? I would like a shorter way to solve this PS question. Experts, may you help me?
Hi Vincen,
Let's take a look at your question.

Set X consists of all two-digit primes.
$$X=\left\{11,\ 13,\ 17,\ ...,\ 97\right\}$$

Set Y consists of all positive odd multiples of 5 less than 100.
$$Y=\left\{5,\ 15,\ 25,\ ...,\ 95\right\}$$

Combine both the sets:
$$XUY=\left\{5,\ 11,\ 13,\ 15,\ ...,\ 95,\ 97\right\}$$

We know that range of a set is the difference between the largest value and the smallest value, therefore,
Range = 97 - 5 = 92

Option D is correct.

I am available, if you'd like any follow up.
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