Question on averages

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 amFollowed by: 11 members; Location: NY; Thanked: 28 times

by abhasjha » Mon Aug 26, 2013 3:23 am

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 .

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon Aug 26, 2013 4:38 am

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

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon Aug 26, 2013 4:46 am

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

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vinay1983: Legendary Member; Posts: 643; Joined: Wed Aug 14, 2013 4:27 amFollowed by: 7 members; Thanked: 48 times

by vinay1983 » Mon Aug 26, 2013 4:50 am

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?

You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to!

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ganeshrkamath: Master | Next Rank: 500 Posts; Posts: 283; Joined: Sun Jun 23, 2013 11:56 pmFollowed by: 26 members; Location: Bangalore, India; Thanked: 97 times; GMAT Score:750

by ganeshrkamath » Mon Aug 26, 2013 5:54 am

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

Last edited by ganeshrkamath on Mon Aug 26, 2013 6:13 am, edited 1 time in total.

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abhasjha: Master | Next Rank: 500 Posts; Posts: 379; Joined: Tue Sep 30, 2008 7:17 amFollowed by: 11 members; Location: NY; Thanked: 28 times

by abhasjha » Mon Aug 26, 2013 6:10 am

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)

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GMAT/MBA Expert

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by [email protected] » Mon Aug 26, 2013 11:40 am

Hi All,

I think that this probably goes without saying, but this is NOT a GMAT question. It does test some GMAT Quant concepts (averages, prime numbers), but is not in the format that the test will present.

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

Contact Rich at [email protected]

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vipulgoyal: Master | Next Rank: 500 Posts; Posts: 468; Joined: Mon Jul 25, 2011 10:20 pmFollowed by: 4 members; Thanked: 29 times

by vipulgoyal » Mon Aug 26, 2013 8:25 pm

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

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