This problem threw me off the first time around. Now I understand how to set up the equation but I'm having trouble with the algebra. First the problem: [Image of 4 integers A, B, C, and D on a number line] The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A? 1. 5^11 2. 5^10 3. -5^12 4. (-7)5^12 5. (-12)5^13 I can set up the equation: [spoiler]D minus three times the difference between C and D (or) 5^13 - 3(5^13-5^12) = A.[/spoiler] But after that, I'm lost with the algebra. Below is the algebra for the right answer: [spoiler]5^13 – 3(5^13 – 5^12) 5^13 – 3[5^12(5 – 1)] 5^13 – 3(5^12)(4) 5(5^12)– 12(5^12) (-7)5^12 The correct answer is D.[/spoiler] Can someone explain what operations are taking place in the first 2 lines? Thanks in advance.

Integers equally spaced on a line - help?

Expert replies

saritalr: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue Jul 27, 2010 12:26 pm; Location: Washington, DC; GMAT Score:700

by saritalr » Mon Aug 09, 2010 10:17 am

This problem threw me off the first time around. Now I understand how to set up the equation but I'm having trouble with the algebra. First the problem:

[Image of 4 integers A, B, C, and D on a number line]
The integers A, B, C, and D shown on the number line above are all equally spaced. If C and D are equal to 5^12 and 5^13, respectively, what is the value of A?

1. 5^11
2. 5^10
3. -5^12
4. (-7)5^12
5. (-12)5^13

I can set up the equation: [spoiler]D minus three times the difference between C and D (or) 5^13 - 3(5^13-5^12) = A.[/spoiler] But after that, I'm lost with the algebra.

Below is the algebra for the right answer:
[spoiler]5^13 – 3(5^13 – 5^12)
5^13 – 3[5^12(5 – 1)]
5^13 – 3(5^12)(4)
5(5^12)– 12(5^12)
(-7)5^12

The correct answer is D.[/spoiler]

Can someone explain what operations are taking place in the first 2 lines?

Thanks in advance.

Source: Beat The GMAT — Problem Solving | Mon Aug 09, 2010 10:17 am

selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Mon Aug 09, 2010 10:29 am

The integers are equally spaced.

A+x=B

B+x=C

C+x=D

x is an difference between 2 integers.

Now C=5^12 and D=5^13

5^12+X=5^13

x=5^13-5^12=5^12(5-1)=4.5^12

Since the integers are equally spaced.

A+3x=D

A+3(4.5^12)=5^13

A+12.5^12=5^13

A=5^13-12.5^12=5^12(5-12)

=-7.5^12

Hope this clarify.

--Anand--

nicolezl: Junior | Next Rank: 30 Posts; Posts: 29; Joined: Tue Jun 29, 2010 5:23 am; Thanked: 3 times

by nicolezl » Mon Aug 09, 2010 10:44 am

saritalr wrote:5^13 – 3(5^13 – 5^12)
5^13 – 3[5^12(5 – 1)]
5^13 – 3(5^12)(4)
5(5^12)– 12(5^12)
(-7)5^12

The correct answer is D.

Can someone explain what operations are taking place in the first 2 lines?

Thanks in advance.

In the second line, you factor out 5^12 from (5^13 - 5^12), which gives you 5^12*(5-1).

Does that help?

Nicole

https://interntoceo.wordpress.com

selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Mon Aug 09, 2010 10:45 am

saritalr,

Your approach is also same and correct..

[spoiler]5^13 - 3(5^13-5^12) = A

=5^13-3.5^12(5-1)

=5^13-12.5^12

=5^12(5-12)=-7.5^12[/spoiler]

--Anand--

saritalr: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue Jul 27, 2010 12:26 pm; Location: Washington, DC; GMAT Score:700

by saritalr » Mon Aug 09, 2010 10:55 am

selango wrote:
A=5^13-12.5^12=5^12(5-12)

=-7.5^12

Thanks Selango. Can you explain the above line - are you factoring something out?

saritalr: Junior | Next Rank: 30 Posts; Posts: 23; Joined: Tue Jul 27, 2010 12:26 pm; Location: Washington, DC; GMAT Score:700

by saritalr » Mon Aug 09, 2010 10:56 am

nicolezl wrote:
In the second line, you factor out 5^12 from (5^13 - 5^12), which gives you 5^12*(5-1).

Does that help?

Very helpful! Just what I needed - thank you!

selango: Legendary Member; Posts: 1460; Joined: Tue Dec 29, 2009 1:28 amFollowed by: 7 members; Thanked: 135 times

by selango » Mon Aug 09, 2010 4:33 pm

saritalr wrote:
selango wrote:
A=5^13-12.5^12=5^12(5-12)

=-7.5^12
Thanks Selango. Can you explain the above line - are you factoring something out?

A=5^13-12.5^12

Here I am taking 5^12 as common factor.

=5^12(5-12)

=5^12(-7)

Hope this clarify.

--Anand--

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