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26 Mar 2018, 00:41
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C
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Difficulty:
75%
(hard)
Question Stats:
53% (02:43) correct
47%
(02:29)
wrong
based on 116
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In a Physics class of a science course, there are N students present on a particular day. If N is an odd number, is N less than 50?
(1) If 2 more students had been present in the class, they could have been evenly divided in groups of 5 each.
(2) If 3 more students had been present in the class, they could have been evenly divided in groups of 7 each.
(1) If 2 more students had been present in the class, they could have been evenly divided in groups of 5 each.
(2) If 3 more students had been present in the class, they could have been evenly divided in groups of 7 each.
26 Mar 2018, 01:47
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amanvermagmat
As we're asked about the max value of N (less than 50?), we'll look at the edge of the range.
This is a Logical appraoch.
(1) So N+2 is divisible by 5, that is, its unit digit is a 0 or a 5. Since N is odd, its unit digit must be a 3.
So any two digit number ending in 3 works. Insufficient.
(2) So N+3 is divisible by 7. Once again, for every even multiple of 7 we can find a value of N. For example, 7*8 - 3 = 53 works as does 7*2 - 3 = 11.
Insufficient.
Combined:
We need to find a number whose unit's digit is 3 and that is 3 less than a multiple of 7. That is, we need to find a multiple of 7 whose units digit is 6. Since the first such multiple of 7 is 56, giving N=56-3=53, then N must be larger than 50. So the answer to our question is NO.
(C) is our answer.
26 Mar 2018, 04:38
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amanvermagmat
considering statement 1
N can be 3, 13, 23, 33, 43 >> not sufficient
considering statement 2
N can be 11, 25, 39 >> not sufficient
now considering 1 & 2 together :
there is no such number less than 50 which can satisfy condition 1 & 2.
Now going back to question :
If N is an odd number, is N less than 50? : NO
answer is C: Both together sufficient .
Kudos if it helps.!!
