R is a list of 15 consecutive integers, and T is a list of 21

Question

R is a list of 15 consecutive integers, and T is a list of 21 consecutive integers. The median of the integers in list R is equal to the least integer in list T. If the two lists are combined into one list of 36 integers, how many different integers are on the combined list?

A. 25
B. 27
C. 28
D. 32
E. 36

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Dereno · Answer

List R contains 15 items which are consecutive. Let them be x1, x2, x3, and so on till x15. The median is x8.

There is another list T with 21 consecutive integers, where the starting value is x8.

So the number of items of list R which is repeating in List T are from x8 to x15. That’s is 8 items in total.

Non repeating or different items in the combined list = (15+21)-8 = 36 - 8 =  28

Option C

GraemeGmatPanda · Answer

Another way of doing this one:

Let's just take the numbers 1 to 15 for R (1, 2, 3, 4, ... 13, 14, 15)
The median of that list is 8 (the median of a list of consecutive numbers is the average of the first and last, which is (1 + 15)/2)

So that means T goes from 8 to 8 + 21 - 1 = 28(since there are 21 numbers inclusive)
The combined list is therefore 1, 2, 3, ... 26, 27, 28
So 28 numbers in total

Hope this hels!

Ayeka · Answer

R= a, a+1, a+2, a+3,.......a+14
Median in R= a+7 
In T, starting value is a+7 
T= a+7, a+8, a+9,.......a+27

Combined list is a, a+1, a+2,.......a+27 
That is 28 numbers in total

C

findingmyself · Answer

R can be written as x, x+1....x+7........x+14 
 T can be written as x+7.......x+27 (Since T starts from the median of S)

Overalap between two sets, consider a simple example to make it simple. Let x be 1. 
 Set R=1,2,3....15 (Median is 8)--->15 elements 
 Ser T=8,9,10,11....28--->21 elements 
 Common is from 8 to 15 (inclusive)--->8 elements 
 Unique is from 1 to 28

Souradeep17 · Answer

R={15 elements}
T={21 elements}
all are consecutive elements

median of R is starting of T
median is 8 th term , so basically we will have 8 to 15 (8 terms common in both set)

Now then total different integers = 15+21-8=28 Option C

R is a list of 15 consecutive integers, and T is a list of 21

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R is a list of 15 consecutive integers, and T is a list of 21

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards