(1) The price of the mix was $135 per pound.
Mixing 10 portions of the first variety(costing 120$), 2 portions of second variety(costing 135$),
and 6 portions of third variety(costing 160$), will yield a mix priced at 135$ - The ratio is 10:2:6(5:1:3)
Mixing 10 portions of the first variety(costing 120$), 4 portions of second variety(costing 135$),
and 6 portions of third variety(costing 160$), will yield a mix priced at 135$ - The ratio is 10:4:6(5:2:3) - Insufficient

(2) Only 3 pounds of the variety priced at $135 per pound was used.
How many pounds of variety priced at $135 was used does not give the ratio in which the three varieties were mixed Insufficient

On combining the information from both the statements, we still cannot find out a unique ratio
Mixing 10 portions of the first variety(costing 120$), 3 portions of second variety(costing 135$),
and 6 portions of third variety(costing 160$), will yield a mix priced at 135$ - The ratio is 10:3:6
Mixing 20 portions of the first variety(costing 120$), 3 portions of second variety(costing 135$),
and 12 portions of third variety(costing 160$), will yield a mix priced at 135$ - The ratio is 20:3:12 (Insufficient - Option E)
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(1) New, but insufficient information
(2) New, but insufficient information

(1) and (2)
2 new information, left with 2 unrelated variables and a constant. Hence insufficient and E.

Tea A = x pounds
Tea B = y pounds
Tea C = z pounds

We need to find x:y:z

(1) ((120*x + 135*y + 160*z) / (x+y+z) ) = 135
Insufficient

(2) z=3
Insufficient

(1) + (2)
Put z=3 in the weighted average formula above.
Insufficient

Ans. E

From (1) is follows that the mix was selling at $135 per pound.
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Responding to a pm:

3 varieties - $120 (tea1), $135(tea2), $160(tea3)

Stmnt 1: The price of the mix was $135 per pound.
Note that one of the tea was priced at $135 per pound. So the other two teas would be mixed in a ratio to give an average of 135 too.

w1/w2 = (160 - 135) / (135 - 120) = 5/3

So you need to mix $120 and $160 teas in the ratio 5:3. The tea costing $135 can be added in any quantity, the average will stay the same. We don't know the ratio of the quantity of the three teas so not sufficient.

Stmnt 2: Only 3 pounds of the variety priced at $135 per pound was used.
No ratio of the three. Not sufficient.

Using both together, note that we know that tea1 and tea3 were mixed in the ratio 5:3 but we do not know how much exactly of each was used. Did we use 5 pounds and 3 pounds? Or 10 pounds and 6 pounds? Or 15 pounds and 9 pounds? We don't know. We know that 3 pounds of tea2 was used. Depending on how much of tea1 and tea3 were used, the ratio would be different.
If we used 5 pounds and 3 pounds of tea1 and tea3, ratio tea1:tea2:tea3 would be 5:3:3
If we used 10 pounds and 6 pounds of tea1 and tea3, ratio tea1:tea2:tea3 would be 10:3:6
If we used 15 pounds and 9 pounds of tea1 and tea3, ratio tea1:tea2:tea3 would be 15:3:9 = 5:1:3
and so on...
Not sufficient
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