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Math Expert V
Joined: 02 Sep 2009
Posts: 58320
Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a  [#permalink]

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2
10 00:00

Difficulty:   65% (hard)

Question Stats: 63% (02:13) correct 37% (02:38) wrong based on 369 sessions

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Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a blend of the two seeds, and 20 pounds of Seed Z contains a pounds of Seed X and b pounds of Seed Y. Is a > 10?

(1) 20 pounds of Seed Z costs less than \$120

(2) b < 12

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Current Student G
Joined: 22 Jun 2016
Posts: 231
Re: Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a  [#permalink]

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9
2
Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a blend of the two seeds, and 20 pounds of Seed Z contains a pounds of Seed X and b pounds of Seed Y. Is a > 10?

5*a + 7*b = Total cost
a+b = total weight

S1. 20 pounds of Seed Z costs less than \$120

a+b= 20 --> b=20-a

5*a + 7*b < 120 ---> 5*a + 7*(20-a) < 120 ---> 140 - 2a < 120 ---> 2a > 20 ---> a>10

Sufficient!

S2. b < 12

b<12. Given that a+b=20

if b = 11, a<10
if b = 9, a>10

Insufficient!

Hence, answer should be A.
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Director  S
Joined: 21 Mar 2016
Posts: 513
Re: Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a  [#permalink]

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stat1: cost is not required,, not suff

stat2: if b = 11, a=9
b = 9 , a =11.
not suff

both combined not suff

ans E
Current Student B
Joined: 11 Sep 2016
Posts: 65
Location: India
Concentration: General Management, Leadership
GMAT 1: 710 Q47 V40 GPA: 3
WE: Sales (Manufacturing)
Re: Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a  [#permalink]

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5
This is a question of Weighted averages where X costs 5 \$/pound and Y costs 7 \$/pound

When a particular amount of X is added to a particular amount of Y, mixture Z results

The more the proportion of X or Y determines the inclination of average price of mixture towards per pound \$ price of X or Y

S1: it says that Mixture Z costs less than 6 \$ /pound (because 20 pounds of Z costs less than 120\$ => per pound cost less than 6\$) implying that the mixture Z should have more of X (which costs \$5 /pound) than Y (which costs \$7/pound) in order to make the weighted average price tilt towards the \$/pound price of X (being 5\$/pound) .

Hence a (proportion of X) has to have a higher number as compared to b (proportion of Y) in order to have the mixture Z cost less than \$ 6/pound . Now weight of mixture Z is 20 pounds. Hence a>10 . Sufficient

S2: b<12 . This statement only talks about proportion of X and Y in Z (without mentioning anything on price)
if b=3, a=17 , a>10- yes
if b=11, a=9 , a/\>10- no

Insufficient

Hence Answer is A
Manager  S
Joined: 22 Nov 2016
Posts: 202
Location: United States
GPA: 3.4
Re: Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a  [#permalink]

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1
Starting with the easier statement.

Statement 2: b<12 ; In the final mixture of 20 if b is 11, a =9 OR if b=9, a=11.
Clearly a can be more than 10 or less than 10..........Insufficient AD BCE

Statement 1: cost of final mixture is less than 120
We know that a+b=20
5a+7b<120
5a+7(20-a)<120
5a+140-7a<120
-2a<-20
a<10.............Sufficient

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Intern  B
Joined: 11 May 2018
Posts: 6
Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a  [#permalink]

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1
...and 20 pounds of Seed Z contains a pounds of Seed X and b pounds of Seed Y. Is a > 10?

If a = 10, then note that a = b. (to make up 20 pounds together)
So the question also translates to : Is a > b?

If we look at the prices now,
Seed X costs \$5 per pound and Seed Y costs \$7 per pound
If a = b, then Seed Z price per pound is simply the average of Seed X and Seed Y prices per pound, which is (\$5+\$7)/2 = \$6.

Now,
- If the price of Seed Z per pound is less than \$6, we know that there is more of Seed X in the mixture. So a > b.
- If the price of Seed Z per pound is more than \$6, we know that there is more of Seed Y in the mixture. So a < b.

Let's look at the 2 statements now..

(1) 20 pounds of Seed Z costs less than \$120
It's clear that the price of Seed Z per pound is less than \$6. So a > b. This statement in sufficient.

(2) b < 12
We have already established that the question translates to : Is a > b?
Since b < 12 :
- If I take b = 11, then a = 20 - b = 9. So a < b.
- If I take b = 9, then a = 20 - b = 11. So a > b.
This statement is insufficient as we can't establish a clear relationship between a and b.

So the answer is A.
Manager  S
Joined: 14 Jul 2014
Posts: 86
Location: India
Concentration: Social Entrepreneurship, Strategy
GMAT 1: 620 Q41 V34 WE: Information Technology (Computer Software)
Re: Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a  [#permalink]

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1
Bunuel wrote:
Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a blend of the two seeds, and 20 pounds of Seed Z contains a pounds of Seed X and b pounds of Seed Y. Is a > 10?

(1) 20 pounds of Seed Z costs less than \$120

(2) b < 12

Quote:
If Seed Z were made of exactly ½ Seed X and ½ Seed Y, then the cost of Seed Z would be \$6 per pound (exactly halfway between \$5 and \$7). So if 20 pounds of Seed Z costs \$120 (\$6 per pound) then a = 10 and b = 10. Statement 1 tells you that the total of 20 pounds of Seed Z is LESS than \$120 so there must be more pounds of Seed X than Seed Y. This means than a must be greater than 10 and statement 1 is sufficient.

Quote:
Statement 2 if b = 11 then a would be 9 and the answer is no to the question. However if b = 4 then a = 16 and the answer is yes. Statement 2 is not sufficient and the answer is A.
Intern  B
Joined: 29 Apr 2017
Posts: 28
Location: India
Concentration: Finance, Accounting
Re: Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a  [#permalink]

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X+Y=20
i.e. ab+b=20

Stmt 1
20 pounds cost less than 120
lets say a =b=10
cost =120
for the total to cost less than 120

logically a needs to be greater than b as a costs less than b

stmt 2 - b can be 11 or 9 so we cant comment on whether a>b or b>a Re: Seed X costs \$5 per pound and Seed Y costs \$7 per pound. Seed Z is a   [#permalink] 11 Nov 2018, 07:19
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