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# A person mixed three varieties of tea priced at $120 per pound,$135

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Math Expert
Joined: 02 Sep 2009
Posts: 44650
A person mixed three varieties of tea priced at $120 per pound,$135 [#permalink]

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03 Jul 2017, 12:05
1
KUDOS
Expert's post
4
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BOOKMARKED
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Difficulty:

75% (hard)

Question Stats:

54% (01:28) correct 46% (01:29) wrong based on 202 sessions

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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. [Reveal] Spoiler: OA _________________ BSchool Forum Moderator Joined: 26 Feb 2016 Posts: 2447 Location: India GPA: 3.12 A person mixed three varieties of tea priced at$120 per pound, $135 [#permalink] ### Show Tags 03 Jul 2017, 12:32 1 This post received KUDOS 1 This post was BOOKMARKED (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$
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$), will yield a mix priced at 135$
Ratio is 10 : 4 : 6(5:2:3)
Hence, 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, cannot give us the ratio in which the three varieties were mixed.(Insufficient)

On combining the information from both the statements,
we still cannot find out the ratio(unique in nature)
Mixing 10 portions of the first variety(costing 120$), 3 portions of second variety(costing 135$) and 6 portions of third variety(costing 160$), will yield a mix priced at 135$
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$), will yield a mix priced at 135$
Ratio is 20 : 3 : 12 (Insufficient) (Option E)
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Manager
Joined: 23 May 2017
Posts: 222
Concentration: Finance, Accounting
WE: Programming (Energy and Utilities)
Re: A person mixed three varieties of tea priced at $120 per pound,$135 [#permalink]

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03 Jul 2017, 12:35
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 _________________ If you like the post, please award me Kudos!! It motivates me Manager Joined: 03 May 2017 Posts: 109 Re: A person mixed three varieties of tea priced at$120 per pound, $135 [#permalink] ### Show Tags 03 Jul 2017, 12:51 Bunuel wrote: 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) 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.
Senior Manager
Joined: 06 Jul 2016
Posts: 425
Location: Singapore
Concentration: Strategy, Finance
Re: A person mixed three varieties of tea priced at $120 per pound,$135 [#permalink]

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03 Jul 2017, 13:02
1
KUDOS
Bunuel wrote:
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. Tea A =$120 per round
Tea B = $135 per round Tea C =$160 per round
Tea N = A + B + C
A:B:C = ?

1) Price of Tea N = $135 (120a+135b+160c)/(a+b+c)= 135 Insufficient. Multiple values possible. 2) B = 3 pounds No relation to A or C. Insufficient. (1+2) (120a+405+160c) / (a+3+c) = 135 a:c = 5:3 but we do not know the relationship with B. Insufficient. Hence should be E. _________________ Put in the work, and that dream score is yours! Manager Joined: 13 Apr 2017 Posts: 86 Location: India Concentration: General Management, International Business GMAT 1: 660 Q40 V41 GPA: 3.4 WE: Engineering (Energy and Utilities) Re: A person mixed three varieties of tea priced at$120 per pound, $135 [#permalink] ### Show Tags 21 Aug 2017, 09:22 Bunuel wrote: 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.

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
Senior Manager
Joined: 02 Apr 2014
Posts: 475
Re: A person mixed three varieties of tea priced at $120 per pound,$135 [#permalink]

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04 Jan 2018, 13:11
Hi Bunuel,

Thanks