data sufficiency

[romitvsingh]

What is the average (arithmetic mean ) of j and k?

1) the average of j+k and k+4 is 11

2) the average of j,k and 14 is 10

[shankar.ashwin]

(j+k)/2 is the average, so if we can find (j+k) we can find the average.

Statement 1:

[(j+k) + (k+4)]/2 = 11

j+2k+4 = 22

j+2k = 18 - we cannot find j+k from this - Insufficient

Statement 2:

j+k+14/3 = 10

j+k+14 = 30

J+k = 16 - sufficient - B IMO

[GMATGuruNY]

What is the average (arithmetic mean ) of j and k?

1) the average of j+k and k+4 is 11

2) the average of j,k and 14 is 10

For those who would struggle with the algebra, an alternate approach is to plug in values.
Try two cases.
If the average of j+k is the same in each case, the statement is SUFFICIENT.
If the average of j+k changes, the statement is INSUFFICIENT.

Statement 1: The average of j+k and k+4 is 11.
Let k=0.
Since the average of j+k and k+4 is 11, we get:
((j+0) + (0+4))/2 = 11
j = 18.
Average of j+k = (18+0)/2 = 9.

Let k=1.
Since the average of j+k and k+4 is 11, we get:
((j+1) + (1+4))/2 = 11
j = 16.
Average of j+k = (16+1)/2 = 8.5.
Since the average of j+k changes, INSUFFICIENT.

Statement 2: The average of j,k and 14 is 10.
Let k=0.
Since the average of j,k and 14 is 10, we get:
(j+0+14)/3 = 10.
j+14 = 30.
j = 16.
Average of j+k = (16+0)/2 = 8.

Let k=1.
Since the average of j,k and 14 is 10, we get:
(j+1+14)/3 = 10.
j+15 = 30.
j = 15.
Average of j+k = (15+1)/2 = 8.
Since the average of j+k stays the same, SUFFICIENT.

The correct answer is B.

[romitvsingh]

But the ans to the problem is D IN GMAT OG 11th edition pg no 308 que no 68

What is the average (arithmetic mean ) of j and k?

1) the average of j+k and k+4 is 11

2) the average of j,k and 14 is 10

For those who would struggle with the algebra, an alternate approach is to plug in values.
Try two cases.
If the average of j+k is the same in each case, the statement is SUFFICIENT.
If the average of j+k changes, the statement is INSUFFICIENT.

Statement 1: The average of j+k and k+4 is 11.
Let k=0.
Since the average of j+k and k+4 is 11, we get:
((j+0) + (0+4))/2 = 11
j = 18.
Average of j+k = (18+0)/2 = 9.

Let k=1.
Since the average of j+k and k+4 is 11, we get:
((j+1) + (1+4))/2 = 11
j = 16.
Average of j+k = (16+1)/2 = 8.5.
Since the average of j+k changes, INSUFFICIENT.

Statement 2: The average of j,k and 14 is 10.
Let k=0.
Since the average of j,k and 14 is 10, we get:
(j+0+14)/3 = 10.
j+14 = 30.
j = 16.
Average of j+k = (16+0)/2 = 8.

Let k=1.
Since the average of j,k and 14 is 10, we get:
(j+1+14)/3 = 10.
j+15 = 30.
j = 15.
Average of j+k = (15+1)/2 = 8.
Since the average of j+k stays the same, SUFFICIENT.

The correct answer is B.