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If x is a positive integer, what is the units digit of 567^24*x^y
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Updated on: 22 Sep 2016, 23:56
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If x is a positive integer, what is the units digit of \(567^{24}*x^y\)? (1) \(x^2+x6<0\) and y is an integer less than 5. (2) y=0 Self made
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Originally posted by chetan2u on 22 Sep 2016, 23:16.
Last edited by Bunuel on 22 Sep 2016, 23:56, edited 1 time in total.
RENAMED THE TOPIC.



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If x is a positive integer, what is the units digit of 567^24*x^y
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Updated on: 23 Sep 2016, 00:26
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
Originally posted by deepthit on 22 Sep 2016, 23:20.
Last edited by deepthit on 23 Sep 2016, 00:26, edited 1 time in total.



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If x is a positive integer, what is the units digit of 567^24*x^y
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23 Sep 2016, 00:21
If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?
(1) \(x^2+x6<0\) and y is an integer less than 5. (2) y=0
statement1: x^2+x6<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
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Re: If x is a positive integer, what is the units digit of 567^24*x^y
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23 Sep 2016, 11:07
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



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Re: If x is a positive integer, what is the units digit of 567^24*x^y
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23 Sep 2016, 22:50
chetan2u wrote: If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?
(1) \(x^2+x6<0\) and y is an integer less than 5. (2) y=0
Self made 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
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Re: If x is a positive integer, what is the units digit of 567^24*x^y
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24 Sep 2016, 11:23
chetan2u wrote: If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?
(1) \(x^2+x6<0\) and y is an integer less than 5. (2) y=0
Self made 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



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Re: If x is a positive integer, what is the units digit of 567^24*x^y
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24 Sep 2016, 11:34
RatneshS wrote: chetan2u wrote: If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?
(1) \(x^2+x6<0\) and y is an integer less than 5. (2) y=0
Self made 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 0 is a non negative non positive integer. So, x cannot be 0.
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Re: If x is a positive integer, what is the units digit of 567^24*x^y
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24 Sep 2016, 11:40
RatneshS wrote: chetan2u wrote: If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?
(1) \(x^2+x6<0\) and y is an integer less than 5. (2) y=0
Self made 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 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 Posted from my mobile device
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Re: If x is a positive integer, what is the units digit of 567^24*x^y
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24 Sep 2016, 23:52
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



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Re: If x is a positive integer, what is the units digit of 567^24*x^y
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24 Nov 2016, 04:52
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
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Re: If x is a positive integer, what is the units digit of 567^24*x^y
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07 Nov 2019, 12:24
chetan2u wrote: If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?
(1) \(x^2+x6<0\) and y is an integer less than 5. (2) y=0 x = positive integer \(units.digit:567^{24}*x^y=units(7^{24}*x^y)\) \(cycles(7)=[7,9,3,1]=4…units:7^{24}=24/4=integer=4th.cycle=[1]\) \(find:units(1*x^y)=units(x^y)\) (1) \(x^2+x6<0\) and y is an integer less than 5. sufic.\(x^2+x6<0…(x+3)(x2)<0…(less.than=inside.rng)…3<x=positive.integer<2…x=1\) \(units(x^y)=(1^y)=1\) (2) y=0 sufic.\(units(x^y)=(x^0)=1\) Ans. (D)



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Re: If x is a positive integer, what is the units digit of 567^24*x^y
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29 Nov 2019, 02:33
Balajikarthick1990 wrote: chetan2u wrote: If x is a positive integer, what is the units digit of \(567^{24}*x^y\)?
(1) \(x^2+x6<0\) and y is an integer less than 5. (2) y=0
Self made 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 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




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