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last digit of integer x^2 - y^2 a zero

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last digit of integer x^2 - y^2 a zero

by Uva@90 » Fri Oct 25, 2013 10:13 pm
Is the last digit of integer x^2 - y^2 a zero?
(1) x - y is an integer divisible by 30
(2) x + y is an integer divisible by 70


OA C

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Source: — Data Sufficiency |
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by riz_gmat » Fri Oct 25, 2013 10:47 pm
As we know , x^2 - y^2 = (x + y) (x - y)
from 1) we know (x - y) = 30(K) (some factor of 30)
but we dont know abt (x + y) , if (x + y) is zero , then x^2 -y^2 = 0,
here question is Is the last digit of integer x^2 - y^2 a zero.
hence Statement 1 alone insufficient,
similarly statement 2 alone too insufficient.
both statements together sufficient to answer.
Hence, C
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by theCodeToGMAT » Sat Oct 26, 2013 1:53 am
We are given that x^2 - y^2 is an integer.. and not x & y are integers.. So, we cannot necessarily assume they are integers

To find: (x+y)(x-Y) has unit digit 0

Statement 1:
(X-Y) has Unit digit "0" .. maybe numbers are 30.2 & 0.2 or 31 & 1
INSUFFICIENT

Statement 2:
(X+Y) has unit digit "0".. maybe numbers are 70.2 & 0.2 or 71 & 1.
INSUFFICIENT

Combining..
Both (x+y) & (X-Y) has "0" as Unit Digit.
SUFFICIENT

Answer [spoiler]{C}[/spoiler]
R A H U L
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