What is the value of y−x?

Question

(1) 3^y − 3^x is divisible by 10.

(2) y>x

rohit8865 · Answer

(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

Diwakar003 · Answer

(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!

ziyavutdinov · Answer

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

shouri · Answer

Hey.. this logic may not work with higher powers Eg: 3^8 - 3^0 = 6560.. giving y - x = 8

mohshu · Answer

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

awdxzs · Answer

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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iliavko · Answer

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)..

Jeeya · Answer

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

Bunuel · Answer

I
f y = 8 and x = 0, then y - x = 8
If y = 4 and x = 0, then y - x = 4.

Answer: E.

KarishmaB · Answer

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)

shwetakoshija · Answer

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.
 
 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

What is the value of y−x?

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