If x is a positive integer, what is the units digit of 567^24*x^y

Question

If x is a positive integer, what is the units digit of  567^{24}*x^y ?

(1)  x^2+x-6<0  and y is an integer less than 5.
(2) y=0

Self made

deepthit · Answer

I go with B

Statement 1: -3<x<2 so x is 1 
statement 2 : y=0, what ever the value of x, if y = 0 , the value of the term will be 1 so only term to consider to determine the value of entire expression is 7^(24)

Hence D

NEELAGIRI · Answer

If x is a positive integer, what is the units digit of  567^{24}*x^y ?

(1)  x^2+x-6<0  and y is an integer less than 5.
(2) y=0

statement1: x^2+x-6<0 so -3<x<2. given x is positive integer. so the  value of x will be 1 
the value of y is independent.  SUFFICIENT

statement2: y=0. so what ever is the positive value of x, anything power 0 will be 1.
 SUFFICIENT

SO  D

#NEELAGIRI

Akuthiala · Answer

Statement 1: X^2 - X < 6 for it to be true. Since x is a positive integer the only value for x is 1. Sufficient since the value or sign of y doesn't matter
Statement 2: states than x^y is 1 so sufficient.

Ans D

Balajikarthick1990 · Answer

My take is D.

Before approaching, 567^24 follows a unit digit cycle of 3 : 567^1 = 7, 567^2 = 9, 567^3 = 3, and rem(24/3) = 0. That means the question gets reduced to 3*(x)^y.

Statement 1: X is a positive integer x=1 alone satisfies the equation and y can take any value less than 5

3(1)^y...since irrespective of value of y , the result is going to be 3 ---Sufficient

Statement 2:

Y=0....we know that 3(x)^0 = 3 as anything to the power of zero is 1 ---Sufficient

RatneshS · Answer

Guys is not 0 a positive integer?
Answer may be 0 or 1. why are you all not including the value x=0??
Ans is not D

abhimahna · Answer

0 is a non negative non positive integer.  So, x cannot be 0.

Balajikarthick1990 · Answer

Hi 
0 is considered as a neutral number. That's the reason it separates positive and negative in a graph.

So positive integer starts from 1

Hope this helps

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SanjayaGupta · Answer

The answer would be D.

As the statement for 1 is enough to get the unique ans.

The unit digit of 567^24 comes for 4 cycles of the unit digit 7 and which will result as 1.
x lies between -3 and 2 and its mentioned that the x is positive number hence we can take x as 1 . And 1^y will result as 1

And the statement 2 also satisfies the ans .as the y=0.

Hence option D

stonecold · Answer

One of the Best Questions on Units digit concept.
Here we need the units digit of n=> (567)^24 * x^y
Applying the concept of unit digit ->
Units digit of (567)^24 is always 1
So we need the unit digit of x^y to be able to tell the unit digit of n.

Statement 1
Here x=> (-3,2) is the range of x
x>0 so x must be 1
and y is a integer <5

Basically y can be anything
as (one)^any integer = one
hence the unit digit of n will be 1*1 => 1

Statement 2
y=0
So in this case x can be any integer >0
Because x^0 will be 1 
hence the unit digit of n will be 1*1 => 1

Hence D

exc4libur · Answer

x = positive integer

units.digit:567^{24}*x^y=units(7^{24}*x^y) 
 cycles(7)= =4…units:7^{24}=24/4=integer=4th.cycle=  
 find:units(1*x^y)=units(x^y)

(1)  x^2+x-6<0  and y is an integer less than 5.   sufic.

x^2+x-6<0…(x+3)(x-2)<0…(less.than=inside.rng)…-3<x=positive.integer<2…x=1 
 units(x^y)=(1^y)=1

(2) y=0   sufic.

units(x^y)=(x^0)=1

Ans. (D)

dyogendrarao · Answer

Hi, just to correct the cyclicity piece. The unit digit cyclicity for 7 is 4 ( 7,9,3,1) and not 3. In this case it worked as 24 is divisible by both 3 and 4 but just something to keep in mind.

Thanks

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If x is a positive integer, what is the units digit of 567^24*x^y

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If x is a positive integer, what is the units digit of 567^24*x^y

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