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Difficulty:
45%
(medium)
Question Stats:
65% (01:47) correct
35%
(02:03)
wrong
based on 292
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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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(1) 3^y − 3^x is divisible by 10.
(2) y>x
Pure algebraic questions like this one are no longer part of the GMAT Data Sufficiency syllabus.
For relevant Data Sufficiency questions, please check the Data Sufficiency forum:
Data Sufficiency Forum
Data Sufficiency Forum
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Bunuel
(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
Posts: 118
Updated on: 11 Feb 2017, 02:37
Originally posted by Diwakar003 on 10 Feb 2017, 23:57.
Last edited by Diwakar003 on 11 Feb 2017, 02:37, edited 1 time in total.
Last edited by Diwakar003 on 11 Feb 2017, 02:37, edited 1 time in total.
Bunuel
(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!
Posts: 16
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
(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
ziyavutdinov
Hey.. this logic may not work with higher powers Eg: 3^8 - 3^0 = 6560.. giving y - x = 8
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
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
ziyavutdinov
From statement 1:- What if y=x then also divisible by 10 but then Y-X=0 so not sufficient
Hence ans is E
Sent from my iPad using GMAT Club Forum mobile app
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)..
Bunuel
I dont agree with the IMO.
For statement (1): 3^y-3^x, if y=0 and x=0, then it is divisible by 10 (same for y and x equal to 1).
After this an imminent pattern is followed. if y=5 then x=1 , if y=6 then x=2, if y=7 then x=3 and so on. Notice here the value of y-x is always =4.
But we can have two answers here so not sufficient.
For statement (2): Clearly not sufficient
If we combine the two statements, we can now rule out the possibility that x and y are 0 or 1. Hence the difference will always be 4.
Answer should be C.
Bunuel, KarishmaB, GMATNinja, please help, what am i missing
Jeeya
I
f y = 8 and x = 0, then y - x = 8
If y = 4 and x = 0, then y - x = 4.
Answer: E.
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Bunuel
Recall cyclicity of exponents of 3. Exponents of 3 end with 3, 9, 7 ,1
3^1 = 3
3^2 = 9
3^3 = 27
3^4 = 81
3^5 = 243
3^6 = 729
...
etc. So every time y and x have a difference of 4 or 8 or 12 etc, 3^y − 3^x will be divisible by 10.
There is no way to say what y - x is.
Answer (E)
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Posts: 91
Question Stem: We are asked to find the value of y − x.
This is a value question — we need one specific numerical value.
Statement 1: \(3^y\) − \(3^x\) is divisible by 10.
Statement 1 alone is not sufficient.
Statement 2: y > x
We know the difference is positive, but there is no way to narrow it to one value.
Statement 2 alone is not sufficient.
Statements 1 and 2 Together:
So, the two statements together are also not sufficient.
Correct Answer: (E)
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
This is a value question — we need one specific numerical value.
Statement 1: \(3^y\) − \(3^x\) is divisible by 10.
- If a number is divisible by 10, its units digit is 0.
- So, the units digit of \(3^y\) must be the same as that of \(3^x\), because only then will the subtraction \(3^y\) −\( 3^x\) end in 0.
- Now, looking at the units' digits of powers of 3, we know that the pattern repeats every 4 powers: 3, 9, 7, 1.
- So, x and y differ by a multiple of 4 (4, 8, 12, etc.)
- So, y − x could be 4, 8, 12, and so on or even -4, -8, -12, ...
- We cannot determine a single value for y − x.
Statement 1 alone is not sufficient.
Statement 2: y > x
We know the difference is positive, but there is no way to narrow it to one value.
Statement 2 alone is not sufficient.
Statements 1 and 2 Together:
- From Statement 1: y − x = multiple of 4.
- From Statement 2: y − x is positive.
- Combining them:
- y − x = positive multiple of 4, but we still don’t know exactly what value it has.
So, the two statements together are also not sufficient.
Correct Answer: (E)
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
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