Seed X costs $5 per pound and Seed Y costs $7 per pound. Seed Z is a

Question

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

14101992 · Accepted Answer

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.

KM2018AA · Answer

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

mohshu · Answer

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

sasyaharry · Answer

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 A D   B CE

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

Answer is  A

rohithtv89 · Answer

...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.

HimanshuW11 · Answer

prvarm24 · Answer

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

exc4libur · Answer

20=a+b
z=5a+7b

(1) sufi

z=5a+7b<120, 5(20-b)+7b<120,
2b<20, b<10;
a+b=20, b<10, a>10.

(2) insufic

Ans (A)

CEdward · Answer

I take way too long per question, but to be honest I am glad that I get to the answer. So again a lot of these mixture problems are all about setting up the equations.

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

We know from the stem that X + Y = 20.
This statement tells us that 5X + 7Y < 120
Substitute the first equation into the inequality and we get x >10.
Sufficient.

(2) Y < 12
X + Y = 20
Y = 20 - X
Plug that in to the inequality
X > 8
Insufficient.

AnkithaSrinivas · Answer

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

if both the seeds were mixed of same quantity: 20

it will be 100 and 140 
average: 120

but because it is given in a that it is less than 120, it is clear one has to be more

djangobackend · Answer

St.1 - can do mentally as well using weighted avgs. 
5 and 7 are the price values, now if avg. was right in middle i.e., 6 then it means ratio of a/b = 1:1 i.e., both contributed equally i.e. A=10 and B=10, but st.1 says that avg is less than 6 so means the value is drifting more towards 5 OR in other words, the weights of 5 is more than weights of 7 OR simply A >10 and B<10 hence sufficient.

St.2 - clearly not suff

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

Seed X costs $5 per pound and Seed Y costs $7 per pound. Seed Z is a

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

Seed X costs $5 per pound and Seed Y costs $7 per pound. Seed Z is a

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards