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# This one flummoxed me A, B, C, D, E, F, G, and H are

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Current Student
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This one flummoxed me A, B, C, D, E, F, G, and H are [#permalink]  15 Nov 2006, 06:27
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This one flummoxed me

A, B, C, D, E, F, G, and H are all integers, listed in order of increasing size. When these numbers are arranged on a number line, the distance between any two consecutive numbers is constant. If G and H are equal to 5^12 and 5^13, respectively, what is the value of A?
Senior Manager
Joined: 01 Oct 2006
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Distance betwen G and H is = 5^13 -5^12 =4*5^12
Distance between each pt is constant.
Value of A = 5^13 - 7*4*5^12 = -23 *5^12
Manager
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Can you explain how you came up with that? I am having a hard time figuring it out. Thanks
Senior Manager
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Let x be distance between 2 pts.
We have 8 pts from A to H

Value of A = Value of H -7x ( since numbers arranged as per their value on the number line)

Value of g and h are known so we can find out x.
x = value of H - value of G =5^13 -5^12 = 4*5^12
Value of A = 5^13 -7*4*5^12 = 5^12 (5 -28) = -23 *5^12
Manager
Joined: 29 Aug 2006
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Good one!...Tricked me!
Manager
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I do not understand:

x = value of H - value of G =5^13 -5^12 =

How do you get this ->4*5^12

Value of A = 5^13 -7*4*5^12 = 5^12 (5 -28) = -23 *5^12
Manager
Joined: 10 Jul 2006
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typicalgmatter
distance between 2 points = 5^13 - 5^12 = (5^12)*5 - 5^12 = 5^12 (5-1) = 4*5^12.

Since there are 7 distance like that between A and H.
Value of A = 5^13 - 7*4*5^12 = 5^13 - 28*5^12 = 5^12 (5 - 28) = 5^12 * (-23)
Manager
Joined: 12 Oct 2006
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I'm still somewhat lost. Is A a negative number?
Senior Manager
Joined: 20 Feb 2006
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This confused me initially because I in the stem it says the numbers are arranged according to SIZE, not value and so thought A could not be a negative number.
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