Though seems like CAT qustion here we are

ans is 13,
batsman scored 145 runs which means 145-54 = 91 runs extra
so these extra 91 runs must be divided by one of the following options equally
bingo 13, In order to check our ans
91/13 = 7 in every innings including the new one 7 more runs will be added
now 54+7 must be prime as given in statement

Algebraically
T/n = 54
T=54n
t+145/n+1 = P
54n+145/n+1 = p
now p could be 57,59,61,67,71
put one be one
find ,if we get ony one int value for n out of 5 values , here we'll get it for 61
hence ans 13

I had a different approach by plugging in the answer choices!

1. 7

The total innings before the innings in which he scored 145 was 6, hence 6*54=324+145=469.this when divided by 7 gives 67, which is a prime number lesser than 72.

3. 13

Following the same methodology
13-1=12*54=648+145=793/13=61, which again is a prime number lesser than 72.

Where am I wrong?

abhasjha wrote:The average runs scored by a batsman in a certain number of innings is 54.After he plays one more innings, in which he scores 145 runs his average runs in all the innings played becomes a prime number less than 72.Find the total number of innings he played?

(a)7
(b)12
(c)13
(d)can not be determined .

A = 54
Prime numbers greater than 54 and less than 72 : 59,61,67,71

54n + 145 = (one of the above numbers, say, p) * (n+1)
54n + 145 = Pn + P
n = (145-P)/(P-54)
Value of P that results in n being an integer = 61 and 67
n = 12 or 6

Choose D

Cheers

The extra runs (145-54= 91) gets distributed among n matches . we are further given that the innings played by batsmen is a prime number less than 72 - indicating that the new average is a integer.

Now 91 = 13x7 . product of two prime numbers .So there can be two cases ..

Case 1 . he plays 13 innings and the avg increases by 91/13 = 7 and the new avg is 54+7 = 61.

OR

Case 2 . He plays 7 innings and the avg increases by 91/7= 13 . and the new avg is 54+13= 67.

61 and 67 are both prime numbers less than 72 . we do not know what case it is ? hence it can not be determined

So ans (d)

yes i found the flaw ans is indeed D, thanks all