EgmatQuantExpert wrote:
e-GMAT Question of the Week #2 If all the N students of a class are classified into groups of either n, or (n+1), or (n+2) students, every time 3 students are left out and cannot be included in any of those groups formed. What is the value of N?
1. N is between 7 and 70
2. n is the smallest number with exactly 3 distinct factors
Given N = nk + 3
N = (n+1)p + 3
N = (n+2)q + 3
Hence N = LCM of (n, (n+1), (n+2)) * x + 3
Also n>3, lets say n =4, then LCM of (4,5,6) is 60, hence N = 60x + 3 = 63, 123, 183,...etc.
lets say n = 5, then LCM of (5,6,7) = 210, hence N = 210x +3 = 213, 423,...etc,
similarly for other consecutive numbers.
Statement 1: 7<N<70
From our upfront work, we can see that N = 60(1) + 3 = 63, is the only # that satisfies constraint of statement 1.
Hence Statement 1 alone is Sufficient.
Statement 2:
n is the smallest number with three distinct factors.
Hence n is a square of a prime number & since it needs to be the smallest, \(n = 2^2 = 4\)
So from our upfront work, we can say N = 60x + 3 = 63, 123, 183,...etc.
Statement 2 gives multiple values of N.
Hence Statement 2 alone is Insufficient.
Answer A.
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