integer problem

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divya23: Master | Next Rank: 500 Posts; Posts: 113; Joined: Mon Apr 26, 2010 8:58 am; Thanked: 2 times; Followed by:14 members

integer problem

by divya23 » Tue May 31, 2011 12:14 pm

Is x an integer?

(1) x + 5 is an integer.

(2) x / 1/4 is an integer.

Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.
EACH statement ALONE is sufficient.
Statements (1) and (2) TOGETHER are NOT SUFFICIENT
[spoiler]
OA = A
my doubt here is 1.5 + 5 = 2 integer but here x is not integer den how ???[/spoiler]

Quote

Source: Beat The GMAT — Data Sufficiency | Tue May 31, 2011 12:14 pm

Stuart@KaplanGMAT: GMAT Instructor; Posts: 3225; Joined: Tue Jan 08, 2008 2:40 pm; Location: Toronto; Thanked: 1710 times; Followed by:614 members; GMAT Score:800

by Stuart@KaplanGMAT » Tue May 31, 2011 12:54 pm

divya23 wrote: OA = A
my doubt here is 1.5 + 5 = 2 integer but here x is not integer den how ???

Hi,

1.5 + 5 = 6.5, not 2. Since 6.5 isn't an integer, x=1.5 is not permitted for statement one.

Here's a good rule to remember regarding integers:

whenever you add, multiply or subtract two integers, the result will always be an integer.

Looking at (1):

x + 5 = int

x = int - 5

Since x is one integer minus another integer, x MUST be an integer.

On the other hand, looking at (2):

x / (1/4) = int
x * 4 = int
x = int/4

Since the rule cited above doesn't apply to division, we have no way of knowing whether x is an integer.