Posting two similar questions together to clarify a doubt

[vinni.k]

Posting two similar questions together. The first one is simple, and another is also same but i am not able to understand the last calculation part.

Q1. What is the maximum number of 1 1/4 =5/4 foot pieces of wire that can be cut from a wire that is 24 feet long?
(A) 11
(B) 18
(C) 19
(D) 20
(E) 30

OA is C

dividing 24 by 5/4 = 19.2. So here i know answer is C

Now Q2.
What is the maximum number of 1 3/4 = 7/4 foot pieces of wood that can be cut from 4 pieces of wood that are 12 feet in length ?
(A) 6
(B) 14
(C) 21
(D) 24
(E) 27

OA is E

Here, i am doing exactly the same thing and getting 27.2 i.e E, but answer is D.

I have explanations of both the questions, but i am a little confused. Please clarify.

Thanks

[EconomistGMATTutor]

Posting two similar questions together. The first one is simple, and another is also same but i am not able to understand the last calculation part.

Q1. What is the maximum number of 1 1/4 =5/4 foot pieces of wire that can be cut from a wire that is 24 feet long?
(A) 11
(B) 18
(C) 19
(D) 20
(E) 30

OA is C

dividing 24 by 5/4 = 19.2. So here i know answer is C

Now Q2.
What is the maximum number of 1 3/4 = 7/4 foot pieces of wood that can be cut from 4 pieces of wood that are 12 feet in length ?
(A) 6
(B) 14
(C) 21
(D) 24
(E) 27

OA is E

Here, i am doing exactly the same thing and getting 27.2 i.e E, but answer is D.

Hi vinni.k,
Let's take a look at question 1.

In the first question, we are given a wire of 24 ft long and we are asked to cut 5/4 foot pieces of wire.
We just need to divide 24 by 5/4 to find the maximum number of 5/4 foot pieces. So it will be
$$24\div\frac{5}{4}$$
$$=24\times\frac{4}{5}$$
$$=\frac{96}{5}$$
$$=19.2$$
Hence, there will be 19 pieces of 5/4 foot length.
You did it correctly.

Now let's move on to Question 2.
Question 2 states:
What is the maximum number of 1 3/4 = 7/4 foot pieces of wood that can be cut from 4 pieces of wood that are 12 feet in length ?
In this question, we are told that we have 4 pieces of wood each of length 12 feet.
And we need to cut 7/4 foot pieces.

Let's find out how many 7/4 foot pieces can we cut from the first piece of 12 ft.
Same logic: Divide 12 by 7/4
$$12\div\frac{7}{4}$$
$$=12\times\frac{4}{7}$$
$$=\frac{48}{7}$$
$$=6.8$$

It means the we can cut 6 full pieces of length 7/4 but the rest of the piece will be of less length.
I think, at this point you made a mistake of rounding off 6.8 to 7. But we can not do it. Because we only need to count those pieces of wood that have a length of 7/4 ft.

It means from a 12 ft piece of wood we can only cut 6 pieces of length 7/4 ft.
So from 4 pieces of wood that are 12 feet in length, we will be able to cut 6 x 4 = 24 pieces each of length 7/4 ft.

Therefore, Option D is correct.

Hope it makes sense.
I am available if you'd like any follow up.

[vinni.k]

Thanks

Now, It is clear to me. I can visualise the 6 pieces of wood of length 7/4.

Regards