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Number properties ! this is killing me !!

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Number properties ! this is killing me !!

by vishubn » Thu Oct 02, 2008 9:33 pm
If x + y is an integer, is y an integer?
(1) x – y is an integer.
(2) x + 2y is an integer.
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.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

vishu
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by stop@800 » Thu Oct 02, 2008 9:41 pm
x+y is integer

A
x – y is an integer

so add both
2x integer
but no info about x

so no infor about y


other sub
x+y
x-y subtract
2y integer
but no info for y




B
x + 2y is an integer
and
x + y is an integer

so y has to be integer

ans IMO is B
whats the OA?
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by Gmatterz » Thu Oct 02, 2008 10:05 pm
Hi Vishu,
The approach to thsi DS question would be as i believe


here the given data is

x + y = int

here in y may or may not be int

for eg

3 + 3 = 6-- here y is int(3)
5.2 + 0.8 = 6 --here y is not int(0.8)

now consider the statement 1

x - y = int

here again y may or may not be int henec i guess thsi sis insufficient

consider statement 2

x + 2y = int

for eg x = 2 and y = 3
the x + 2y = 8 (here y is 6 int)

now suppose x = 3 and y = 0.2

then x + 2y = 3.4(this cannot be true as the answer has to be int,henec the value of y in this case can never be non int,it has to be always int

hence teh statement 2 seem sto be sufficient

So the answer would be B
Whatz the OA? is there any other approach anyone can put light on ?

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by vishubn » Thu Oct 02, 2008 10:21 pm
It is B indeed jsut wandering why i went wrong !

thanbks u guys

Vishu
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by gmat08orbust » Thu Oct 02, 2008 10:34 pm
An easier way to solve this one without any substitution:

Given: X+Y=int_0
Prove: Y=int?

1) X-Y=int_1

Subtract prompt equation from eq in 1:
X-Y=int_1
-(X+Y)=int_0
-2Y=int_1+int_0

This tells you that Y is the sum of two integers. Because we don't know if int_1 and int_0 are even or odd we cannot say if (int_1+int_0)/2 is a integer.

INSUFFICIENT

2) X+2Y = int_2

Notice you can write this as:
X+Y+Y = int_2
[subbing in the given equation]
int_1+Y=int_2
Y=int_1-int2 -> Y is the sum of two integers and is therefore sufficient.

SUFFICIENT

Answer is B.
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