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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: 52431
A person mixed three varieties of tea priced at $120 per pound,$135  [#permalink]

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03 Jul 2017, 11:05
4
10
00:00

Difficulty:

75% (hard)

Question Stats:

55% (01:59) correct 45% (01:58) wrong based on 353 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. _________________ Senior PS Moderator Joined: 26 Feb 2016 Posts: 3334 Location: India GPA: 3.12 A person mixed three varieties of tea priced at$120 per pound, $135 [#permalink] ### Show Tags 03 Jul 2017, 11:32 2 1 (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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Manager
Joined: 23 May 2017
Posts: 241
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, 11:35
3
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: 93 Re: A person mixed three varieties of tea priced at$120 per pound, $135 [#permalink] ### Show Tags 03 Jul 2017, 11:51 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: 367
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, 12:02
1
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: 84 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, 08:22 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: 474
GMAT 1: 700 Q50 V34
Re: A person mixed three varieties of tea priced at $120 per pound,$135  [#permalink]

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04 Jan 2018, 12:11
Hi Bunuel,

Thanks

From (1) is follows that the mix was selling at $135 per pound. _________________ Manager Joined: 16 Jan 2018 Posts: 62 Concentration: Finance, Technology GMAT 1: 600 Q40 V33 Re: A person mixed three varieties of tea priced at$120 per pound, $135 [#permalink] ### Show Tags 05 Jun 2018, 16:54 Got it wrong.. but only cz it was from bunuel and i thought 1+2 would be sme kind of uniq although the equation (straight forward as it was) said otherwise Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8810 Location: Pune, India Re: A person mixed three varieties of tea priced at$120 per pound, $135 [#permalink] ### Show Tags 28 Jun 2018, 03:05 1 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.

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.