GMAT question 80 help please

[ironsheep]

From the "GMAT Official Guide Quantitative Review 2019".

"Half of a large pizza is cut into 4 equal- sized pieces, and the other half is cut into 6 equal- sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?" The answer is 17/24

So first, I made it into (4/4) plus (6/6) and then those become (3/4) plus (4/6). You then get 17/12. That isn't the answer as 12 is the common denominator.

Then, I decided that since originally the pieces were (1/2)s I multiplied (3/4) by 2 and (4/6) by two and then add those up. The answer you get is 17/6.

I then tried (3/4) times 0.5 plus (4/6) times 0.5 and that answer is (7/12), which is also wrong.

What direction should I take and why?

 

[Otis]

… The answer is 17/24 … I [tried] 4/4 plus 6/6 and then … 3/4 plus 4/6 [getting] 17/12 …

They set up a problem in terms of half pizzas, and then they ask a question about a whole pizza. That's the catch.

So, your first approach is a good start (4/6 reduces to 2/3, by the way). You just didn't realize that the remaining portion of the whole pizza is 3/4ths of half the pizza plus 2/3rds of half the pizza. In other words:

\[\frac{3}{4} \times \frac{1}{2} + \frac{2}{3} \times \frac{1}{2}\]

?

 

[Deleted member 4993]

The pizza was cut into:

1/2 + 1/2

[1/8 + 1/8 + 1/8 + 1/8] + [1/12 + 1/12 + 1/12 + 1/12 + 1/12 + 1/12]

you ate:

1/8 + 1/12 + 1/12 = 7/24

Pizza left = 1 - 7/24 = ?

 

[ironsheep]

They set up a problem in terms of half pizzas, and then they ask a question about a whole pizza. That's the catch.

So, your first approach is a good start (4/6 reduces to 2/3, by the way). You just didn't realize that the remaining portion of the whole pizza is 3/4ths of half the pizza plus 2/3rds of half the pizza. In other words:

\[\frac{3}{4} \times \frac{1}{2} + \frac{2}{3} \times \frac{1}{2}\]

?

Thank you, I don't understand how in the word I did this wrong in the first place as this is the third path.

 

[pka]

From the "GMAT Official Guide Quantitative Review 2019".
"Half of a large pizza is cut into 4 equal- sized pieces, and the other half is cut into 6 equal- sized pieces. If a person were to eat 1 of the larger pieces and 2 of the smaller pieces, what fraction of the pizza would remain uneaten?" The answer is 17/24

\(\displaystyle \begin{align*}\frac{1}{2}\cdot\frac{1}{4}+\frac{1}{2}\cdot\frac{2}{6}&=\frac{1}{8}+\frac{2}{12}\\&=\frac{3}{24} +\frac{4}{24} \\&=\frac{7}{24} \end{align*}\)

So \(\displaystyle 1-\frac{7}{24}=\frac{17}{24} \).

 

[Otis]

… I don't understand how in the world I did this wrong in the first place …

These things happen (we all goof up). The bright side is that -- when faced with a contradiction and/or emotional content -- our brain reinforces the connections which encode correct information (that is, we learn from our mistakes), so you'll likely remember the next time. Cheers!