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ANS :=> C. 11/16

Prepare the equations like 1) For set S (b-a)/2 = (3/4)b i.e. a = -1/2 b 2) For set Q ( c-b ) / 2 = (7/8) c i.e. b = -6/8 c

Now for set R , c-a/2 = ? put value of a in the form of b , then put value of b in the form of c , Solve it ( ans : 11/16 c )

I have a small concern with this question- a median of a set of all integers in an interval can’t be 3/4. If you’re talking about midpoint and real numbers or rational numbers, then this would make more sense. And in that case I would agree with rneve above me, looking at the midpoint of sets S and Q as (b – a)/2 = 3b/4 etc. should work.

Here’s one approach: Set S: We know that the largest number is b and the median is 3b/4. Since the median is in the middle of the numbers of set S, we know that the smallest number in set S is 2b/4 You can see that 3b/4 (the median) lies directly in the middle 2b/4 and b (i.e., 2b/4, 3b/4, 4b/4) So, set S ranges from b/2 to b

Set Q: Here the largest number is c and the median is 7c/8. Using similar logic from above, we can conclude that set Q ranges from 6c/8 to 8c/8, with 7c/8 squarely in the middle.

Here’s the important step. 6c/8 is the smallest number in set Q. This value is equivalent to b (the largest value in set S)

So, now we have a relationship between c and b. We know that 6c/8 = b From here, we can find two integer values for b and c that satisfy this equation amd determine how sets S and Q might look.

One solution is b=6 and c=8 For set S, we know that the largest value is 6, so keep adding numbers until we meet the criterion that the median is 3/4 b. We do the same with set S, beginning with c=8. From here we can conclude that set S={3,4,5,6} and set Q={6,7,8} The median of {3,4,5,6,7,8} is 5.5, which means the median is 11/16 of c

We could have chosen other numbers for b and c but the fraction remains 11/16 For example, b=12 and c=16 gives us S={6,7,8,9,10,11,12} and Q={12,13,14,15,16} The median of {6, 7, . . . 15, 16} is 11, making it 11/16 of c

This question can be answered quickly by supposing numbers.

Given that median of set S = 3/4b and median of Q = 7/8c

In choosing number try to choose comfortable numbers.

If we assume c = 8, the median of Q will be 7,

So set Q = {6,7,8} thus making b =6. But we want b to be divisible by 4 since median of S = 3/4b

So assume c= 16, then median of Q will be 14.

So set Q = {12,13,14,15,16}

Hence b = 12

Now median of S = 3/4b = 9.

So set S = {6,7,8,9,10,11,12}

Hence the R ={6,7,8,9,10,11,12,13,14,15,16}

So median of R = 11.

Clearly this is 11/16c

Also, rneve has given a very good explanation for this question. Keep them coming dude….