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# In a Physics class of a science course, there are N students

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In a Physics class of a science course, there are N students  [#permalink]

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26 Mar 2018, 00:41
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Difficulty:

75% (hard)

Question Stats:

64% (02:50) correct 36% (02:10) wrong based on 52 sessions

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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.
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In a Physics class of a science course, there are N students  [#permalink]

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26 Mar 2018, 01:47
amanvermagmat wrote:
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.

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.

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Re: In a Physics class of a science course, there are N students  [#permalink]

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26 Mar 2018, 04:38
amanvermagmat wrote:
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.

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.!!
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Re: In a Physics class of a science course, there are N students  [#permalink]

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27 Mar 2018, 03:07
Oops, think N = 18 and N = 53, the answer is E
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Re: In a Physics class of a science course, there are N students  [#permalink]

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27 Mar 2018, 03:24
colinlin1 wrote:
Oops, think N = 18 and N = 53, the answer is E

Hello

But the question stem says, "..if N is an odd number.." so we will have to discard the value of 18 for N.
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Re: In a Physics class of a science course, there are N students  [#permalink]

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27 Mar 2018, 17:44
amanvermagmat wrote:
colinlin1 wrote:
Oops, think N = 18 and N = 53, the answer is E

Hello

But the question stem says, "..if N is an odd number.." so we will have to discard the value of 18 for N.

Thank you, you are right.
Re: In a Physics class of a science course, there are N students   [#permalink] 27 Mar 2018, 17:44
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