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03 Jul 2017, 12:05
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E
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Difficulty:
75%
(hard)
Question Stats:
54% (02:01) correct
46%
(01:58)
wrong
based on 795
sessions
History
Date
Time
Result
Not Attempted Yet
A person mixed three varieties of tea priced at $120 per pound, $135 per pound and $160 per pound. In what ratio did he mix the three varieties of tea?
(1) The price of the mix was $135 per pound.
(2) Only 3 pounds of the variety priced at $135 per pound was used.
(1) The price of the mix was $135 per pound.
(2) Only 3 pounds of the variety priced at $135 per pound was used.
28 Jun 2018, 04:05
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Bookmarks
Bunuel
A person mixed three varieties of tea priced at $120 per pound, $135 per pound and $160 per pound. In what ratio did he mix the three varieties of tea?
(1) The price of the mix was $135 per pound.
(2) Only 3 pounds of the variety priced at $135 per pound was used.
(1) The price of the mix was $135 per pound.
(2) Only 3 pounds of the variety priced at $135 per pound was used.
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
03 Jul 2017, 12:35
Kudos
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1st Tea = $ 120 = a pounds mixed
2nd Tea = $ 135 = b pounds mixed
3rd Tea = $ 160 = c pounds mixed
(1) The price of the mix was $135 per pound.
= \(\frac{120a + 135b + 160c}{(a + b + c)}\) = $135 : Not sufficient
(2) Only 3 pounds of the variety priced at $135 per pound was used.
b = 3 ; = \(\frac{120a + 135 * 3 + 160c}{(a + b + c)}\) : Not sufficient
[1] + [2]
=> \(\frac{120a + 135 * 3 + 160c}{(a + b + c)}\) = $135 :
=>120 a + 135 * 3 + 160c = 135a + 135 * 3 + 135c
=> 25 c = 15 a
=> 5c = 3a
still we do not know the relatioship between a & b or b & c
hence E
2nd Tea = $ 135 = b pounds mixed
3rd Tea = $ 160 = c pounds mixed
(1) The price of the mix was $135 per pound.
= \(\frac{120a + 135b + 160c}{(a + b + c)}\) = $135 : Not sufficient
(2) Only 3 pounds of the variety priced at $135 per pound was used.
b = 3 ; = \(\frac{120a + 135 * 3 + 160c}{(a + b + c)}\) : Not sufficient
[1] + [2]
=> \(\frac{120a + 135 * 3 + 160c}{(a + b + c)}\) = $135 :
=>120 a + 135 * 3 + 160c = 135a + 135 * 3 + 135c
=> 25 c = 15 a
=> 5c = 3a
still we do not know the relatioship between a & b or b & c
hence E
