A certain bakery sells rye bread in 16-ounce loaves and

Question

A certain bakery sells rye bread in 16-ounce loaves and 24-ounce loaves, and all loaves of the same size sell for the same price per loaf regardless of the number of loaves purchased. What is the price of a 24-ounce loaf of rye bread in this bakery?

(1) The total price of a 16-ounce loaf and a 24-ounce loaf of this bread is $2.40.
(2) The total price of two 16-ounce loaves and one 24-ounce loaf of this bread is $3.40.

Bunuel · Answer

A certain bakery sells rye bread in 16-ounce loaves and 24-ounce loaves, and all loaves of the same size sell for the same price per loaf regardless of the number of loaves purchased. What is the price of a 24-ounce loaf of rye bread in this bakery?

Let x be the price of 16-ounce loaves and y the price of 24-ounce loaves. Question: y=?

(1) The total price of a 16-ounce loaf and a 24-ounce loaf of this bread is $2.40 --> x+y=$2.4. Not sufficient.
(2) The total price of two 16-ounce loaves and one 24-ounce loaf of this bread is $3.40 --> 2x+y=$3.4. . Not sufficient.

(1)+(2) We have 2 distinct linear equations with 2 unknowns, hence we can solve for x and y. Sufficient.

Answer: C.

krrish · Answer

stmt1: 2 unknowns and one equation can't be solved. A, D ruled out. 
stmt2: 2 unknows one equation can't be solved B, ruled out

now left with c and E. combine both equations we can solve. so E ruled out 
hence C

gaurav5691 · Answer

2x+y=$3.40
By hit and trial method -> x=$1; y=$1.40
and the other value obtained by hit and trial is x=$2;y=-$0.6
 Since negative value isnt possible for price, we reject the second outcome. 
Hence we are able to deduce the price of 24ounce Rye Bread. 
Answer should be  B

CrackverbalGMAT · Answer

Let the price of ONE 16-ounce loaf of rye bread be S and that of ONE 24-ounce loaf of rye bread be T.
We need to ascertain the value of $ T.

From statement I alone, S + T = 2.40
Two unknowns but only one independent equation. We cannot find a unique value for T.
Statement I alone is insufficient. Answer options A and D can be eliminated.

From statement II alone, 2S + T = 3.40
Similar situation as with statement I alone. No unique value for T.
Statement II alone is insufficient. Answer option B can be eliminated.

Combining statements I and II, we have

S + T = 2.40 
2S + T = 3.40

Multiplying the first equation by 2 and subtracting the second equation from the resultant equation, we have, 
T = 1.40 and therefore, S = 1.
The combination of statements is sufficient to find the value of T. Answer option E can be eliminated.

The correct answer option is C.

Hope that helps!
Aravind B T

gaurav5691 · Answer

CrackVerbalGMAT

From statement II alone, 2S + T = 3.40

By hit and trial can we not find out the solution, which is S=1, T=1.4

Second value being S=2, T=-0.6. 
Since T cant be negative, hence we reject the other value. 
We also arent able to determine any other possible positive value for this equation.

We explicitly did not require the usage of Statement 1

Hence B should be the answer

CrackverbalGMAT · Answer

Hello Gaurav 5691,

Using the same technique of Hit & Trial, why is not possible that S = 1.5 and T = 0.4? 
Why are 1 and 1.4 so special?

The term 'Hit & Trial' is usually used with a negative connotation by most test takers I have interacted with (almost with a condescending tone). Trial & Error (or what is called Hit & Trial) is a very important method for deriving empirical results and should be employed while solving questions in standardized tests.

However, employing it recklessly like you are doing here is not a good idea. There is absolutely no premise to your argument, where in you say that there are only two sets of values that will satisfy a Linear equation in two variables.

The equation 2S + T = 3.40 can be satisfied by infinite combinations of S and T. 
A very basic concept in Algebra – if you have 2 unknowns, you need 2 independent equations to solve for unique values of both unknowns.

That’s why the equation given in statement 2 needs to be combined with statement 1 to get a unique answer.
The correct answer is C.

Hope that helps!

bumpbot · Answer

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A certain bakery sells rye bread in 16-ounce loaves and

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