CAT Quant questions

[shahlageoffrey]

If the box pictured to the right is a cube, then the difference in length between line segment BC and line segment AB is approximately what fraction of the distance from A to C?

10%
20%
30%
40%
50%


Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar. If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?

15/29
5/8
5/16
1/2
13/27

Dear,

I need help with the above problems. Would you please tell me how can I solve for them?

Many thanks

[jnelson0612]

For the first one, will you please post an image? I've provided instructions for how to do that in response to your question in the General Math forum.

For the second one, you only have fractions in the problem and answers. You have no real numbers. Given that, let's plug in real numbers. I want to come up with a total amount that he is making and then take the relevant fractions from there. Let's see:

"Miguel is mixing up a salad dressing. Regardless of the number of servings, the recipe requires that 5/8 of the finished dressing mix be olive oil, 1/4 vinegar, and the remainder an even mixture of salt, pepper and sugar."

I should plug a number that is divisible by all denominators. Hmm, I have an 8 and a 4. I also have equal parts of three seasonings, salt, pepper, and sugar. So let's use a base number divisible by 8, 4, and 3. 24 fits the bill. I'm going to say that he makes 24 cups of dressing.

If properly made, that is 15 cups olive oil (5/8), 6 cups vinegar (1/4), and 1 cup salt, 1 cup pepper, and 1 cup sugar (3 cups remaining, and all are equal). That matches 24 total cups.

"If Miguel accidentally doubles the vinegar and forgets the sugar altogether, what proportion of the botched dressing will be olive oil?"

Okay, if he does that he would have:
15 cups olive oil
12 cups vinegar
1 cup salt
1 cup pepper

So 29 total cups of dressing. What proportion will be olive oil? 15/29

Please let us know if you need further help with this one.

[amar.kher]

Hi, I'm trying to solve this algebraically but am having a tough time doing so. How would you approach it without using smart numbers?

thanks!

[RonPurewal]

Hello,
One of the core rules of the forum is "one problem per post".

To the most recent poster -- If you have questions about either of these problems, please do the following, in sequence:
1/ Search the forum for that problem. If you find a thread on the problem, post on it.
2/ If you don't find any threads, post a new thread. If you are asking about both problems, please post two threads.

Thanks.