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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Set X consists of all two-digit primes and set Y tagged by: Vincen ##### This topic has 3 expert replies and 0 member replies ## Set X consists of all two-digit primes and set Y 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? ### GMAT/MBA Expert Legendary Member Joined 14 Jan 2015 Posted: 2667 messages Followed by: 122 members Upvotes: 1153 GMAT Score: 770 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 _________________ Veritas Prep | GMAT Instructor Veritas Prep Reviews Save$100 off any live Veritas Prep GMAT Course

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### GMAT/MBA Expert

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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

GMAT assassins aren't born, they're made,
Rich

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### GMAT/MBA Expert

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Quote:
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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