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# Q26: K is a set of integers such that if the integer r is in

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Q26: K is a set of integers such that if the integer r is in [#permalink]  01 May 2007, 00:49
Q26:
K is a set of integers such that if the integer r is in K, then r + 1 is also in K. Is 100 in K?
(1) 50 is in K.
(2) 150 is in K.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
9
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.
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Re: set [#permalink]  01 May 2007, 01:13
Balvinder wrote:
Q26:
K is a set of integers such that if the integer r is in K, then r + 1 is also in K. Is 100 in K?
(1) 50 is in K.
(2) 150 is in K.
A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
9
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

From question stem we have k{r,r+1,(r+1)+1,((r+1)+1)+1,....,infinity}

There fore statement 1 is sufficient.

But statement 2 says that 150 is in k that means 150,151,152,153,...infinity are in k but we cannot say that 100 is also in k hence insufficent.

Javed.

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This is an infinte series.

If 50 is in K, then the series includes integers from 50 to infinity plus some unkown integers less than 50, but we're not sure what they are.
However, we know 100 is in the series.

If 150 is in K, then the series includes integers from 150 to infinity plus some unkown integers less than 150, but we're not sure what they are and thus we don't know if 100 is part of the series.

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The set k is {r,r+1,r+2,r+3,r+4.... }

St1:
If 50 is in k, then 100 must be in k and 101 must be in k. Sufficient.

St2:
Insufficient. 150 and up are in k, but we do not know what's below. Insufficient.

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--------------------------------------------------------------------------------
Q26:
K is a set of integers such that if the integer r is in K, then r + 1 is also in K. Is 100 in K?
(1) 50 is in K.
(2) 150 is in K.
--------------------------------------------------------------------------------

r belongs to K, r+1 belongs to K, (r+1)+1 belongs to K, ...

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