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What is the value of y−x?

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Bunuel
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What is the value of y−x? [#permalink] New post   10 Feb 2017, 09:41
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A
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E

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45% (medium)

Question Stats:

64% (01:49) correct 36% (02:02) wrong based on 176 sessions
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What is the value of y−x?

(1) 3^y − 3^x is divisible by 10.

(2) y>x
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E
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Diwakar003
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What is the value of y−x? [#permalink] New post   Updated on: 11 Feb 2017, 03:37
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Bunuel wrote:
What is the value of y−x?

(1) 3^y − 3^x is divisible by 10.

(2) y>x


(1) 3^y − 3^x is divisible by 10

3^y − 3^x = 10k.
3^x(3^(y-x) -1 )=10x.

3^x will not be divisible by 10. So (3^(y-x) -1 ) has to be divisible by 10.

a.One of the cases is x=y, so y-x=o.

b. Other case is when 3^(y-x) has its last digit as 1, so 3^(y-x)-1 will end in 0 thus divisible by 10. For this y-x should be a multiple of 4(Cyclicity of powers of 3). So y-x can be 4,8,12, and so on.

Not sufficient.

(2) y>x - Not sufficient.

(1)+(2) - We can eliminate only case (a) mentioned above as y>x, yet case (b) itself has many values. - Not sufficient.

Answer - E

Cheers!

Originally posted by Diwakar003 on 11 Feb 2017, 00:57.
Last edited by Diwakar003 on 11 Feb 2017, 03:37, edited 1 time in total.
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rohit8865
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What is the value of y−x? [#permalink] New post   10 Feb 2017, 10:44
Bunuel wrote:
What is the value of y−x?

(1) 3^y − 3^x is divisible by 10.

(2) y>x


(1) if y= 4 , x =0 then y-x=4
if y=1 , x=1 then y-x = 0
insuff..

(2) clearly insuff

combining we know y is not equal to x thus

if y= 8 , x= 0 then y-x=8
or
if y= 4 , x =0 then y-x=4
insuff

Ans E
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ziyavutdinov
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Re: What is the value of y−x? [#permalink] New post   11 Feb 2017, 02:14
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What is the value of y−x?

(1) 3^y − 3^x is divisible by 10.

(2) y>x

A is an answer

3^1=3
3^2=9
3^3=27
3^4=81
3^5=243
3^6=729
etc.

(1) If 3^y − 3^x is divisible by 10 the result of 3^y − 3^x must end with zero.

From above we can see that 3^5-3^1=243-3=240 is divisible by 10. The same can be said about 3^6-3^2=729-9=720 divisible by 10

If y=5 x=1 y-x=5-1=4; if y=6 x=2 y-x=6-2=4 etc. So, y-x is allways 4. Sufficient

(2) is clearly insufficient

So straight A
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Re: What is the value of y−x? [#permalink] New post   11 Feb 2017, 02:32
ziyavutdinov wrote:
What is the value of y−x?

(1) 3^y − 3^x is divisible by 10.

(2) y>x

A is an answer

3^1=3
3^2=9
3^3=27
3^4=81
3^5=243
3^6=729
etc.

(1) If 3^y − 3^x is divisible by 10 the result of 3^y − 3^x must end with zero.

From above we can see that 3^5-3^1=243-3=240 is divisible by 10. The same can be said about 3^6-3^2=729-9=720 divisible by 10

If y=5 x=1 y-x=5-1=4; if y=6 x=2 y-x=6-2=4 etc. So, y-x is allways 4. Sufficient

(2) is clearly insufficient

So straight A


Hey.. this logic may not work with higher powers Eg: 3^8 - 3^0 = 6560.. giving y - x = 8
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Re: What is the value of y−x? [#permalink] New post   11 Feb 2017, 11:29
stat 2 : not suff,

stat 1 : conisder x= 1 and y = 1,, then y-x = 0 and zero is divisible 10.
y-x has other other values , when 3^y - 3^x is divisible by 10..

combining the tow stats,, no new info,,hence ans E
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Re: What is the value of y−x? [#permalink] New post   11 Feb 2017, 13:16
ziyavutdinov wrote:
What is the value of y−x?

(1) 3^y − 3^x is divisible by 10.

(2) y>x

A is an answer

3^1=3
3^2=9
3^3=27
3^4=81
3^5=243
3^6=729
etc.

(1) If 3^y − 3^x is divisible by 10 the result of 3^y − 3^x must end with zero.

From above we can see that 3^5-3^1=243-3=240 is divisible by 10. The same can be said about 3^6-3^2=729-9=720 divisible by 10

If y=5 x=1 y-x=5-1=4; if y=6 x=2 y-x=6-2=4 etc. So, y-x is allways 4. Sufficient

(2) is clearly insufficient

So straight A

From statement 1:- What if y=x then also divisible by 10 but then Y-X=0 so not sufficient
Hence ans is E


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Re: What is the value of y−x? [#permalink] New post   24 Feb 2017, 06:33
So the only way to solve this is to run exponents in your head? Pff a harsh one!.. If you take into account the accumulated fatigue, etc Id say this is a 700 for many people (at least for me lol)..
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Re: What is the value of yx? [#permalink] New post   30 Mar 2022, 00:22
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Re: What is the value of yx? [#permalink]
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