Hello! I’m Deedee a new member of the Gregmat prep program. I’m following the 2 month plan and watching the fractions, decimals practice questions video but I don’t understand how greg is solving these questions. I don’t understand the rationale of the answers. Please I’m confused and need help.

What’s the question?

Fractions, decimals, percents and ratios

I meant the question that you don’t understand how to solve.

How would **you** approach these problems?

This is so that I can point out any gaps in your understanding.

For the first question, I don’t know how to approach the question because it doesn’t make sense to me but I know it’s a ratio question.

For the second one, I chose option D because digit b can be any number so I think there are multiple answers to this question thus there’s no clear answer.

For the last one, I listed out the reciprocals from 43 to 48 then tried to add them up but I gave up because the number I got was too large.

Think algebraically. Let AB = x. How would you define the remaining distances in terms of x?

That’s not Quantity A though. Notice that 0.\overline{3} = 0.33333... and 0.\overline{7} = 0.777777...... What do you think they sum up to?

Approach that differently. What do you think these numbers are *roughly* equal to? It may help to write them out as a decimal (to two decimal places for instance).

Okay, CD= x and BC = x/3.

The sum will be 1.1 which is greater than 1.0 so should I ignore digit b?

The numbers are roughly equal to 0.12 so that means 1/8 is the closest answer since 1/8 is 0.125

There is no “digit b”. Quantity A ~ 1.1, which is greater than Quantity B. That’s all you need.

Can you use that to find x and hence point C?

Indeed.

Okay, thanks for breaking those questions down! Yes, I tried to use x to find point C but I still don’t know what to do with the x because AD = x+x+x/3= 7x/3

So we have

AB = x

CD = x

BC = ~~1/3 x~~ 3x

So, AD = AB + BC + CD. Also notice that the length of AD is (1/2 - 1/3).

Can you use that to find x? Once you find x, can you use that to find point C?

Yes, so AD= 1/6 therefore x = 14, CD= 14, CD= 1/2 - C= 14. My answer is C= -13.5 which I know is wrong. I’m definitely missing something here.

I don’t understand how x = 14. If AD = 1/6, we have

x is not 14.

So I did it again and x is 1/14. So CD= 1/14, D= 1/2, C=?. So D-C= 1/14. C= 1/2-1/14 then C= 3/7. Please is this the correct answer?

x = 1/14 indeed.

Yes, it’s not part of the options but that’s the answer I got. 1/2 -1/14= 6/14 which reduces to 3/7. Could you please solve the question and explain your steps?

Sorry, I made a mistake. Indeed, 1/2 - 1/14 = 3/7.

And I made another mistake as well. The reason is that if AB = x, AB = 1/3 BC, which means that BC = 3x (**not 1/3 x**)

With that, we find x:

AB + BC + CD = 1/6

x + x + 3x = 1/6

5x = 1/6

x = 1/30

Now find C:

C = 1/3 + AB + BC

C = 1/3 + 1/30 + 1/10

C = 11/30 + 1/10

C = 14/30

C = 7/15

This is option D. Apologies again for the mistakes.

I understand now. Thank you!