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Number Properties

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Number Properties

by swerve » Sat Feb 08, 2020 11:05 am
Set \(P\) consists of the first \(n\) positive multiples of \(3\) and set \(Q\) consists of the first \(m\) positive multiples of \(5\). The sum of all the numbers in set \(P\) is equal to \(R\) and the sum of all the numbers of set \(Q\) is equal to \(S\). If \(n\) and \(m\) are positive integers, is the difference between \(R\) and \(S\) odd?

1) \(m\) is odd and \(n\) is even.
2) \(m\) can be expressed in the form of \(4x+3\) and \(n\) can be expressed in the form of \(2x\), where \(x\) is a positive integer.

The OA is E

Source: e-GMAT
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Source: — Data Sufficiency |
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Re: Number Properties

by deloitte247 » Sun Feb 09, 2020 12:15 pm
P = { 3, 6, 9, 12..........3n}
Q = { 5, 10, 15, 20......5m}
Sum of a series of elements in P = R=n/2 [a + l ] where a = first term and l = last term
Sum of series of elements in Q = S=m/2 [ a + l ]
R = n/2[ 3 + 3n ]; R is dependent on the value of n
Q = m/2[ 5 + 5m ]; S is dependent on the value of m
Question => is R - S = odd number?
Statement 1 => m is odd and n is even
If m = 3, then s = 3/2 [5+(5*3)] = 30 = even
But if m = 1 then s = 1/2[5 + 5] = 5 = odd
If n = 4 then R = 4/2 [3 +(3*4)] = 30 = even
If n = 2 then R = 2/2 [3 +(3*2)] = 9 = odd
Therefore, R - S results can either even or odd, statement 1 is NOT SUFFICIENT

Statement 2 => m = 4x + 3 and n = 2x this means m = (multiple of 4) + (odd number)
m = even + odd = odd number
n = multiple of 2 which will always be even
Therefore, m = odd and n = even; this is the same thing as information in statement 1. Hence statement 2 is NOT SUFFICIENT
Combining both statements together =>
Both statements contain the same information, m = odd and n = even, and from the test data in statement 1, it cannot be determined if R - S is even or odd. Hence, both statement together are NOT SUFFICIENT
Answer = C
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