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If knz≠0, what is the ratio of k to n? 1) The ratio of k

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by Max@Math Revolution » Mon Mar 28, 2016 4:00 am
If knz≠0, what is the ratio of k to n?

1) The ratio of k to z is 2 to 3
2) The ratio of z to n is 4 to 5


* A solution will be posted in two days.
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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Mar 28, 2016 10:43 am
If knz ≠ 0, what is the ratio of k to n?

1) The ratio of k to z is 2 to 3
2) The ratio of z to n is 4 to 5
Target question: What is the ratio of k to n?

Given: knz ≠ 0
This tells us that none of the variables equals zero.

Statement 1: The ratio of k to z is 2 to 3
There's no info about the value of n, so there's no way to find the ratio of k to n.
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The ratio of z to n is 4 to 5
There's no info about the value of k, so there's no way to find the ratio of k to n.
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1 tells us that k : z = 2 : 3
Statement 2 tells us that z : n is 4 : 5

We can create equivalent ratios so that the z-value is the same for each ratio.

Rewrite statement 1 to get: k : z = 8 : 12
Rewrite statement 2 to get: z : n is 12 : 15

Combine to get: k : z : n = 8 : 12 : 15
So, the ratio k : n = 8 : 15

Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

For more on COMBINING RATIOS, see this free video: https://www.gmatprepnow.com/module/gmat ... video/1083

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
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by Max@Math Revolution » Tue Mar 29, 2016 11:19 pm
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.


If knz≠0, what is the ratio of k to n?

1) The ratio of k to z is 2 to 3
2) The ratio of z to n is 4 to 5


In the original condition, there are 3 variables(k,z,n), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), multiply 4 to k:z=2:3 and 3 to z:n=4:5, which makes k:z=8:12 and z:n=12:15 respectively. Then, k:z:n=8:12:15 is derived and k:n=8:15, which is unique and sufficient.
Therefore, the answer is C.
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by Max@Math Revolution » Tue Mar 29, 2016 11:22 pm
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.


If knz≠0, what is the ratio of k to n?

1) The ratio of k to z is 2 to 3
2) The ratio of z to n is 4 to 5


In the original condition, there are 3 variables(k,z,n), which should match with the number of equations. So you need 3 equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer.
When 1) & 2), multiply 4 to k:z=2:3 and 3 to z:n=4:5, which makes k:z=8:12 and z:n=12:15 respectively. Then, k:z:n=8:12:15 is derived and k:n=8:15, which is unique and sufficient.
Therefore, the answer is C.
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