Given that x and y are positive integers, what is the units digit of

Question

Given that x and y are positive integers, what is the units digit of (5*x*y)^(289)?

(1) x is odd.
(2) y is even.

Skywalker18 · Accepted Answer

We need to find units digit of (5*x*y)^(289)
(1) x is odd.
if x is odd the term (5*x*y) can have units digit of 5 or 0 depending on y .
x=3 (Odd) , y = 3 then (5*x*y)= 45
x=3(Odd) , y=2 then (5*x*y)= 30
Not sufficient

(2) y is even
if y =2 (even) , then the term (5*x*y) = 10*x
the units digit of (5*x*y) will be zero irrespective of x being odd or even .
Sufficient

Answer B

chetan2u · Answer

Hi,
It is very important we understand the Q, take out the required INFO from the Q and work for a solution...

INFO 
1)x and y are positive integers

requirement 
 units digit of (5*x*y)^(289)

INFERENCE 
1) the units digit will depend on the base, as the base is a multiple of 5..
2) if 5xy is ODD, the units digit will be 5, and
3) If 5xy is even, teh units digit will be 0..

lets see the statements 
 (1) x is odd. 
since x is odd, 5x is ODD..
But now 5xy will depend on y..
if y is odd, units digit is 5, otherwise 0
Insuff

(2) y is even 
since y is even, 5xy will be EVEN, irrespective of x..
so units digit will be 0
Suff

B

MathRevolution · Answer

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

Given that x and y are positive integers, what is the units digit of (5*x*y)^(289)?

(1) x is odd.
(2) y is even.

When you modify the original condition and the question, if x or y is even from 5xy, once place of 5xy is always 0. Then, you need to figure out if x or y is odd. In 1), x is odd, which is unique and sufficient.
Thus, the answer is A. 
This is one of the mistake type questions. Getting this kind of question right leads you to the score range of 50-51.

 Once we modify the original condition and the question according to the variable approach method 1, we can solve approximately 30% of DS questions.

 For cases where we need 2 more equations, such as original conditions with “2 variables”, or “3 variables and 1 equation”, or “4 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 70% chance that C is the answer, while E has 25% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since C is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, D or E.

stonecold · Answer

Here is what i think
We only need to know if any one of x and y is even or not as if so the case then the UD will be 0
hence B is sufficient.

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Given that x and y are positive integers, what is the units digit of

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Given that x and y are positive integers, what is the units digit of

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