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PS : Digits

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CEO
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PS : Digits [#permalink] New post 13 Sep 2003, 05:00
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Do this in 1.5 mins and explain at leisure :)

In a 4-digit number, the sum of the first two digits is equal to that
of the last two digits. The sum of the first and last digits is equal to the third digit. Finally, the sum of the second and fourth digits is twice the sum of the other two digits. What is the third digit of the number?

a) 5
b) 8
c) 1
d) 4
Senior Manager
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GMAT Tests User
 [#permalink] New post 13 Sep 2003, 20:33
Anser is A. Took me like 4 min :x


If number is : ABCD

1)A+B=C+D
2)A+D=C
3)B+D=2A+2C

From 1 and 2: 2A+B=2C
Combine this with (3) and you get D=4A

So (using 2) C=5A

Since 1<=A<=9 and C=5A C could only be 1
SVP
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 [#permalink] New post 18 Jan 2004, 22:22
Answer is 4. It took me 2 mins
a,b,c,d are the digits
1. a + b = c + d
2. a + d = b
3. b + d = 2(a+c)

from 1 and 2 we have
2a = c

from 1 b = d+c/2 or b-d = c/2
from 3 we have 2b = 3c+c/2 so b = 7c/4

From this we know that c = 4 and b = 7
Director
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 [#permalink] New post 18 Jan 2004, 23:52
Though not a choice, zero also works.

I think setting up the equations was the easy part.

I wonder if there's a quick, methodical and easy way to solve the equations.
SVP
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 [#permalink] New post 19 Jan 2004, 05:20
Yeah u got me there. The problem stem should be changed to distinct different digits.
Intern
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a<>0 [#permalink] New post 20 Jan 2004, 14:40
Since a is the first digit of a 4 digit number, it is not zero.

Given the explanations above, the correct answer is A) C= 5
a<>0   [#permalink] 20 Jan 2004, 14:40
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