If both j and k are nonzero numbers, what is the value of j ?

Question

If both j and k are nonzero numbers, what is the value of  \frac{j}{k} ?

(1)  j^2 = k^3 
(2)  j^3 = k^2

Explanation: 
Statement (1) is insufficient: there are several possible values of j and k. For instance,if j=1 and k=1,  \frac{j}{k}  =1. However, if j=8 and k=4,  \frac{j}{k}=2 . 
Statement (2) is also insufficient: in this case, j and k could k each equal 1, or the reverse of the statement (1) scenario: j = 4 and k = 8, in which case  \frac{j}{k}=1/2 .

Taken together, the statements are sufficient. There is only one set of values for j and k that satisfy both: j = 1 and k = 1. Choice (C) is correct.

gmatser1 · Answer

I got this wrong. I thought the answer was E.

Couldn't it be possible that in the first scenario j=-1 and k=1?
Likewise, couldn't it be possible that in the second scenario j=1 and k=-1?

camlan1990 · Answer

k, j must be positive so there is the only value of j=k=1, satisfying both 1 and 2

Ans: C

AdlaT · Answer

Solution:

Statement: 1)  j^2 = k^3

From this we know k must be positive but we don't know sign of j

Hence Insufficient.

Statement: 2)  j^3 = k^2

From this we know j must be positive but we don't know sign of k.

Hence Insufficient.

Statement 1 and statement 2 together:

j^3 = k^2 ----> k^3*j=k^2 ---> j*k=1 .

If j and k are integers then Ans is 1.

if j and k are not integers--> j=1/2  and  k=2 , then Ans  1/4 .

Two different Ans. Hence Insufficient.

Ans Should be E.

please some one help us.

TheKingInTheNorth · Answer

If both j and k are nonzero numbers, what is the value of j/k?

(1) j^2=k^3
(2) j^3=k^2

St 1 -> As j^2 the value is always positive 
As , j^2=k^3 is given in the statement .

Note that j can both positive and negative .
And k is always positive .

As there is two different value of j . Hence not sufficient .

St -> 2 .

As K^2 the value is always positive 
As ,` is given in the statement .

Note that k can both positive and negative .
And j is always positive .

As there is two different value of k . Hence not sufficient .
But together we get that k and j positive .

AND THE ONLY VALUE THAT SATISFY THE ABOVE CONDITION IS 1 .

HENCE THE ANS IS C .

Regards,

kudos appreciated .

hotshot02 · Answer

Hi  Bunuel

Please can you explain this

Thanks!

Bunuel · Answer

If both j and k are nonzero numbers, what is the value of  \frac{j}{k} ?

(1)  j^2 = k^3 . If j = 1 and k = 1, then j/k = 1 but if j = -1 and k = 1, then j/k = -1. Not sufficient.
 
(2)  j^3 = k^2 . If j = 1 and k = 1, then j/k = 1 but if j = 1 and k = -1, then j/k = -1. Not sufficient.

(1)+(2) Multiply equations: j^5 = k^5 --> j = k --> j/k = 1. Sufficient.

Answer: C.

Hope it's clear.

hotshot02 · Answer

Thanks for the crisp explanation Bunuel
I got it now.

JeffTargetTestPrep · Answer

We need to determine the value of j/k.

Statement One Alone:

j^2 = k^3

Statement one alone is not sufficient to answer the question. For example, if j = 1 and k = 1, then j/k = 1; however, if j = -1 and k = 1, then j/k = -1.

Statement Two Alone:

j^3 = k^2

Statement two alone is not sufficient to answer the question. For example, if j = 1 and k = 1, then j/k = 1; however, if j = 1 and k = -1, then j/k = -1.

Statements One and Two Together:

If we square each side of j^2 = k^3, we get j^4 = k^6. Since k^6 = (k^2)^3, we have:

j^4 = (k^2)^3 = (j^3)^3 = j^9

Since we know j is non-zero, we can divide each side of this equality to get j^5 = 1. Thus, j = 1 and it follows that k = 1.

Using the information above, we know that in order for j^2 = k^3 and j^3 = k^2, j must be 1 and k must be 1, and therefore j/k = 1.

Answer: C

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If both j and k are nonzero numbers, what is the value of j ?

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