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# If m and k are non-zero integers and if y^(m+k) = y^m, what is the

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Director
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If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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24 Mar 2011, 06:54
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23% (01:58) correct 77% (01:51) wrong based on 302 sessions

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If m and k are non-zero integers and if y^(m+k) = y^m, what is the value of y?

(1) k is odd.
(2) y is odd.

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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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27 Mar 2011, 03:31
7
2
rxs0005 wrote:
If m and k are non-zero integers and

If y^(m+k) = y^m

what is the value of y?

(1) k is odd.
(2) y is odd.

The solutions above are not quite right. Before looking at the statements, If y^(m+k) = y^m, then we know that (y^m)(y^k) = y^m. There are now two possibilities: either y^k = 1, in which case y = 1 or y = -1, since k is nonzero, or y = 0.

From Statement 1, we can be sure that y is not -1, but y can still be 0 or 1. From Statement 2, we can be sure that y is not 0, but y can still be 1 or -1 (if k is even). Using both Statements, we can be sure that y = 1 and the answer is C.
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##### General Discussion
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Joined: 20 Dec 2010
Posts: 1820
Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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24 Mar 2011, 07:41
1
rxs0005 wrote:
If m and k are non-zero integers and

If y^(m+k) = y^m

what is the value of y?

(1) k is odd.
(2) y is odd.

y^m*y^k = y^m
y^k=1

(1) k=odd
k can be 1,3,5,-1.

Means; y must be 1.
Sufficient.

(2)y=odd

(1)^1=1
(-1)^2=1

Not Sufficient.

Ans: "A"
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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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24 Mar 2011, 07:44
y^(m+k) = y^m

=> y^m x y^k = y^m

=> y^k = 1

Statement 1:

If k is odd,

then y = 1

Sufficient

Statement 2:

y is odd

y can be +1 or -1 if the value of k is even

and y can be +1 if the value of k is odd

Not sufficient!

Ans - A
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Retired Moderator
Joined: 20 Dec 2010
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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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27 Mar 2011, 03:52
IanStewart wrote:
rxs0005 wrote:
If m and k are non-zero integers and

If y^(m+k) = y^m

what is the value of y?

(1) k is odd.
(2) y is odd.

The solutions above are not quite right. Before looking at the statements, If y^(m+k) = y^m, then we know that (y^m)(y^k) = y^m. There are now two possibilities: either y^k = 1, in which case y = 1 or y = -1, since k is nonzero, or y = 0.

From Statement 1, we can be sure that y is not -1, but y can still be 0 or 1. From Statement 2, we can be sure that y is not 0, but y can still be 1 or -1 (if k is even). Using both Statements, we can be sure that y = 1 and the answer is C.

Thanks IanStewart. Wonder why rxs0005 kept mum!!!
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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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27 Mar 2011, 16:41
Ian GMAT does not recognize 0^( anything) so with that in mind A should be the answer otherwise C would be correct and based on deductive reasons this kind of problem would not show up in GMAT where we need to exclude 0^
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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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28 Mar 2011, 07:00
rxs0005 wrote:
Ian GMAT does not recognize 0^( anything) so with that in mind A should be the answer otherwise C would be correct and based on deductive reasons this kind of problem would not show up in GMAT where we need to exclude 0^

The GMAT certainly does recognize 0^x, at least when x is a positive integer; that's always equal to zero. I'm not sure why you think that is undefined; 0^2, for example, is just equal to the product of two zeros, which is certainly zero. You may be thinking of the specific exception 0^0, which is not defined. In any case, the question probably should specify that m and k are positive integers to avoid exceptional cases.
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Joined: 08 Nov 2010
Posts: 338
Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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28 Mar 2011, 09:24
1
It must be C.

y^m*y^k = y^m

y^m(y^k-1)=0

so we know y=0/y=1/y=-1 (when k is even)

I - k is odd so y can still be 0 or 1 ---- Insufficient.
II - y is odd (so 1 or -1) --- still insufficient.

I+II - y is not 0 --- means y^k-1=0 ----- y^k=1
if K is odd - Y must be 1.

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Senior Manager
Joined: 08 Nov 2010
Posts: 338
Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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28 Mar 2011, 09:24
1
It must be C.

y^m*y^k = y^m

y^m(y^k-1)=0

so we know y=0/y=1/y=-1 (when k is even)

I - k is odd so y can still be 0 or 1 ---- Insufficient.
II - y is odd (so 1 or -1) --- still insufficient.

I+II - y is not 0 --- means y^k-1=0 ----- y^k=1
if K is odd - Y must be 1.

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01 Aug 2018, 11:10
Can someone please explain me this :

If m and k are non-zero integers and if y^(m+k) = y^m, what is the value of y?

(1) k is odd.
(2) y is odd
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01 Aug 2018, 18:23
1
To find the value of y

$$y^{m+k} = y^m$$

=> $$y^m * y^k = y^m$$

=> $$y^k = 1$$

=> k = 0 and y is any integer other than zero OR

=> k = 1 and y is either 0 or 1

Statement 1

k is odd.

If k is odd => k = 1 and y is either 0 or 1

No unique value for y

Statement 1 is not sufficient

Statement 2

y is odd

y can be 1 and k can be 1 satisfying $$y^k = 1$$

y can be 5(or any integer other than 0) and k can be 0 satisfying $$y^k = 1$$

No unique value for y

Statement 2 is not sufficient

Combining statements 1 and 2

k is odd and y is odd

=> only k = 1 and y = 1 satisfy the given equations.

Hence option C
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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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01 Aug 2018, 19:26
workout wrote:
To find the value of y

$$y^{m+k} = y^m$$

=> $$y^m * y^k = y^m$$

=> $$y^k = 1$$

=> k = 0 and y is any integer other than zero OR

=> k = 1 and y is either 0 or 1

Statement 1

k is odd.

If k is odd => k = 1 and y is either 0 or 1

No unique value for y

Statement 1 is not sufficient

Statement 2

y is odd

y can be 1 and k can be 1 satisfying $$y^k = 1$$

y can be 5(or any integer other than 0) and k can be 0 satisfying $$y^k = 1$$

No unique value for y

Statement 2 is not sufficient

Combining statements 1 and 2

k is odd and y is odd

=> only k = 1 and y = 1 satisfy the given equations.

Hence option C

K cannot be taken as zero. In statement 2 y can take 2 values 1 or -1 Therefore its insufficient.
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If you feel the post helped you then do send me the kudos (damn theya re more valuable than $) Manager Joined: 11 Mar 2018 Posts: 90 If m and k are non-zero integers and if y^(m+k) = y^m, what is the [#permalink] ### Show Tags 01 Aug 2018, 22:30 Koko11 wrote: Can someone please explain me this : If m and k are non-zero integers and if y^(m+k) = y^m, what is the value of y? (1) k is odd. (2) y is odd $$y^(m+k) = y^m$$ $$y^m * y^k = y^m$$ Therefore, $$y^k = 1$$ ------ (1) From this we concur, For k we can have only 0 or 1 or -1, but as per premise, K is not 0 Hence k=1 or -1 ------- (2) So if k = 1, From (1) we have y = 0 or 1 ---------- (3) and if k = -1, From (1) we have y = 1 -------- (4) (y cannot be 0 as 0 raised to negative number will always be not defined) Now, Statement 1 : k is odd From (2) we already know that k is odd Hence Statement 1 Insufficient as there is no new information Statement 2 : y is odd From (3), (4) and statement 2 we know, y = 1 Hence statement 2 alone is Sufficient. IMO it should be B. But OA says C. Does not seem to be correct _________________ Regards AD --------------------------------- A Kudos is one more question and its answer understood by somebody !!! Manager Joined: 20 Feb 2017 Posts: 165 Location: India Concentration: Operations, Strategy WE: Engineering (Other) Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the [#permalink] ### Show Tags 01 Aug 2018, 22:51 adstudy wrote: Koko11 wrote: Can someone please explain me this : If m and k are non-zero integers and if y^(m+k) = y^m, what is the value of y? (1) k is odd. (2) y is odd $$y^(m+k) = y^m$$ $$y^m * y^k = y^m$$ Therefore, $$y^k = 1$$ ------ (1) From this we concur, For k we can have only 0 or 1 or -1, but as per premise, K is not 0 Hence k=1 or -1 ------- (2) So if k = 1, From (1) we have y = 0 or 1 ---------- (3) and if k = -1, From (1) we have y = 1 -------- (4) (y cannot be 0 as 0 raised to negative number will always be not defined) Now, Statement 1 : k is odd From (2) we already know that k is odd Hence Statement 1 Insufficient as there is no new information Statement 2 : y is odd From (3), (4) and statement 2 we know, y = 1 Hence statement 2 alone is Sufficient. IMO it should be B. But OA says C. Does not seem to be correct In statement 2 Y could be -1, and therefore it is insufficient _________________ If you feel the post helped you then do send me the kudos (damn theya re more valuable than$)

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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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02 Aug 2018, 04:14
Raksat wrote:
Koko11 wrote:
Can someone please explain me this :

If m and k are non-zero integers and if y^(m+k) = y^m, what is the value of y?

(1) k is odd.
(2) y is odd

$$y^(m+k) = y^m$$
$$y^m * y^k = y^m$$

Therefore,

$$y^k = 1$$ ------ (1)

From this we concur,

For k we can have only 0 or 1 or -1,

but as per premise,

K is not 0

Hence k=1 or -1 ------- (2)

So if k = 1, From (1) we have

y = 0 or 1 ---------- (3)

and if k = -1, From (1) we have

y = 1 -------- (4) (y cannot be 0 as 0 raised to negative number will always be not defined)

Now,

Statement 1 : k is odd

From (2) we already know that k is odd

Hence Statement 1 Insufficient as there is no new information

Statement 2 : y is odd

From (3), (4) and statement 2 we know,

y = 1

Hence statement 2 alone is Sufficient.

IMO it should be B.

But OA says C.

Does not seem to be correct

In statement 2 Y could be -1, and therefore it is insufficient

With Y as -1 we can get $$y^k = 0$$ only if k = 0 and k cannot be zero as stated in the premise. Hence i considered it to be sufficient
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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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02 Aug 2018, 07:08
1
adstudy why can't K be 2? Then y could be -1.
Therefore we need statement 1 so that we could reach 1 unique solution. That is y=1
Therefore C is correct
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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the  [#permalink]

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02 Aug 2018, 23:50
Raksat wrote:
adstudy why can't K be 2? Then y could be -1.
Therefore we need statement 1 so that we could reach 1 unique solution. That is y=1
Therefore C is correct

thanks Raksat for pointing this out. I missed on that. Yes the answer now seems to be C
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Re: If m and k are non-zero integers and if y^(m+k) = y^m, what is the &nbs [#permalink] 02 Aug 2018, 23:50
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