Problem Solving

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?

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

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.