It is currently Wed Nov 21, 2018 4:55 am

 All times are UTC - 5 hours [ DST ]

 Page 1 of 1 [ 5 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: GMAT AlgebraPosted: Thu Aug 05, 2010 6:00 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Let d > c > b > a. If c is twice as far from a as it is from d, and b is twice as far from c as it is from a, then
(db) / (da) =
A. 2/9
B. 1/3
C. 2/3
D. 7/9
E. 3/2

Geometrical and algebraic solutions are below.

Top

 Post subject: Re: math: algebra, number linePosted: Thu Aug 05, 2010 6:20 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Since the exercise mentions a number line, draw one. Since d > a, label the left end of the number line with d and the right end with a. The values of b and c will be between a and d:

Start with the relationship between c, a, and d. Since c is twice as far from a as it is from d,
the segment between a and d is divided into 3 pieces – two pieces between c and a and one piece between d and c. Each piece is 1/3 of d to a.

The relationship between b, c, and a says that b is twice as far from c as it is from a. This
means the segment between a and c is divided into 3 pieces.

The segment between c and a was 2/3 of the segment between d and a. Dividing 2/3 into 3 pieces makes each piece (2/3) / 3 = 2/9.

So db (the length of the segment between d and b) makes 7/9 of da (the length of the segment between d and a).

Top

 Post subject: Re: math: algebra, number linePosted: Thu Aug 05, 2010 6:34 am

Joined: Sun May 30, 2010 2:23 am
Posts: 498
This question can also be solved algebraically. It might seem more difficult but it can be fast if you are good at fractions and simplifying expressions.

"c is twice as far from a as it is from d" means that
|ca| = 2|cd|
but since we know that d > c > b > a we can avoid using absolute values:
ca = 2(dc)

In much the same way we transform "b is twice as far from c as it is from a" into algebra:
cb = 2(ba)

Remember, that the question asks us to find: (db) / (da).

From formula ca = 2(dc) we can find that
d = (3ca) / 2

From formula cb = 2(ba) we can find that
b = (c + 2a) / 3

Let us plug both formulas into expression we need to calculate:
(db) / (da) = [(3ca)/2 – (c + 2a)/3] / [(3ca)/2 – a] =
= [(7/6) × (ca)] / [(3/2) × (ca)]] =
= (7/6) / (3/2) = 7/9

Top

 Post subject: Re: math: algebra, number linePosted: Sun Oct 02, 2011 4:53 pm

Joined: Sun May 30, 2010 3:15 am
Posts: 424
I don't quite understand the problem. I don't understand why 6 is twice as far from 0 as it is from 9. How is "if c is twice as far from a as it is from d, and b is twice as far from c as it is from a" interpret in the equation?

Top

 Post subject: Re: math: algebra, number linePosted: Sun Oct 02, 2011 5:11 pm

Joined: Sun May 30, 2010 2:23 am
Posts: 498
Quote:
I don't quite understand the problem. I don't understand why 6 is twice as far from 0 as it is from 9.
All real numbers form a number line. Each number corresponds to a point. The distance between such points is the same as the distance between the numbers.
Looking at the number line you can see that the distance between some real numbers a and b equals |ab|.

Quote:
I don't understand why 6 is twice as far from 0 as it is from 9.
The distance between 6 and 0 is |6 – 0| = 6. The distance between 6 and 9 is |6 – 9| = 3. Therefore the distance between 6 and 0 is twice larger than the distance between 6 and 9.

Quote:
How is "if c is twice as far from a as it is from d, and b is twice as far from c as it is from a" interpret in the equation?
|ca| = 2|cd|
|cb| = 2|ba|

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 5 posts ]

 All times are UTC - 5 hours [ DST ]

#### Who is online

Users browsing this forum: No registered users and 5 guests

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forumYou cannot post attachments in this forum

Search for:
 Jump to:  Select a forum ------------------ GMAT    GMAT: Quantitative Section (Math)    GMAT: Verbal Section    GMAT: Integrated Reasoning    GMAT: General Questions GRE    GRE: Quantitative Reasoning (Math)    GRE: Verbal Reasoning    GRE: General Questions General questions    Other questions