Ten musicians (A, B, C, D, E, F, G, H, I and J) are experts in at least one of the following three percussion instruments: tabla, mridangam, and ghatam. Among them, three are experts in tabla but not in mridangam or ghatam, another three are experts in mridangam but not in tabla or ghatam, and one is an expert in ghatam but not in tabla or mridangam. Further, two are experts in tabla and mridangam but not in ghatam, and one is an expert in tabla and ghatam but not in mridangam.
The following facts are known about these ten musicians.
Who among the following is DEFINITELY an expert in tabla but not in either mridangam or ghatam?
Who among the following is DEFINITELY an expert in mridangam but not in either tabla or ghatam?
Which of the following pairs CANNOT have any musician who is an expert in both tabla and mridangam but not in ghatam?
If C is an expert in mridangam and F is not, then which are the three musicians who are experts in tabla but not in either mridangam or ghatam?
Each of the ten musicians A, B, C, D, E, F, G, H, I & J is an expert in at least one of the percussion instruments.
3 are expert in only Tabla (T)
3 are expert in only Mridangam (M)
1 is expert in only Ghatam (G)
2 are expert in T & M but not G
1 is expert in T & G but Not on M
Total no of Musicians expert in T = 6
Total no of Musicians expert in M = 5
Total no of Musicians expert in G = 2
Since none of the musician who are expert in mridangam also expert in Ghatam. Hence A & B are not expert in Ghatam.
None of the musicians are expert in all 3 instruments, D is not expert in Mridangam. I has expertise in Ghatam because he is expert neither in Tabla n or Mridangam (From 4 and 5). Again since H is expert neither in Mridangam n or Ghatam, H is an expert in Tabla.
Total number of musicians who are expert in tabla is six. Besides D, F, G & H, either A or B (from 1) and either C or E are experts in tabla.
Total number of musicians who are expert in ghatam is two. Since D & I are experts in Ghatam, others are not experts in Ghatam.
Now, J is expert neither in Tabla nor in Ghatam. Hence J is an expert in Mridangam. Total number of musicians who have expertise in Mridangam is five.
Those a re A, B, J and F or G, Hence out of C & E one has expertise in Mridangam.
Out of A & B one of the musicians is an expert of only Mridangam the other has the expertise in both table & Mridangam.
Out of F & G one of the musicians is an expert of only table &the other has the expertise in both table & Mridangam.
Out of C & E one of the musicians is an expert of Tabla only and the other is an expert of Mridangam only
Alternate solutions:
The given information can be represented in the following Venn diagram
From (1), one of A and B will be in region c and the other one in region f.
From (2), D is in region d.
From (3), one of F and G will be in region a and the other one in f.
From (4), either both I and J will be in region c or one in region b and the other in region c.
From (5), one of H and I will be in region b and the other in region a.
By combining (4) and (5), I will be in region b, H in region a and J in region c.
Thus, we get the following.
Region a = 3 (F/G, H, C/E), Region b = 1 (I), Region c = 3 (A/B, J, C/E)
Region d = 1 (D), Region f = 2 (B/A, G/F)
Question 1:
H definitely is an expert only in Tabla
Option: 2
Question 2:
J definitely is an expert only in Mridangam
Option: 3
Question 3:
One of A and B, one of G and F are experts in both tabla and mridangam but not ghatam. Three of the choices has at least one of the above four musicians. But one (C and E) does not have any one of these four. Hence, that is the answer
Option: 3
Question 4:
Given, C is an expert in mridangam but not F. It means F and E are experts only in tabla. Thus, E, F and H will be the experts in tabla but not in mridangam or ghatam.
Option: 4
