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# PS : Digits

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CEO
Joined: 15 Aug 2003
Posts: 3452

Kudos [?]: 925 [0], given: 781

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13 Sep 2003, 06:00
00:00

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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

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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

Kudos [?]: 925 [0], given: 781

Senior Manager
Joined: 22 May 2003
Posts: 328

Kudos [?]: 175 [0], given: 0

Location: Uruguay

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13 Sep 2003, 21:33
Anser is A. Took me like 4 min

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

Kudos [?]: 175 [0], given: 0

SVP
Joined: 30 Oct 2003
Posts: 1788

Kudos [?]: 114 [0], given: 0

Location: NewJersey USA

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18 Jan 2004, 23:22
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

Kudos [?]: 114 [0], given: 0

Director
Joined: 28 Oct 2003
Posts: 501

Kudos [?]: 34 [0], given: 0

Location: 55405

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19 Jan 2004, 00:52
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.

Kudos [?]: 34 [0], given: 0

SVP
Joined: 30 Oct 2003
Posts: 1788

Kudos [?]: 114 [0], given: 0

Location: NewJersey USA

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19 Jan 2004, 06:20
Yeah u got me there. The problem stem should be changed to distinct different digits.

Kudos [?]: 114 [0], given: 0

Intern
Joined: 20 Jan 2004
Posts: 3

Kudos [?]: [0], given: 0

Location: Dallas, TX

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20 Jan 2004, 15:40
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

Kudos [?]: [0], given: 0

a<>0   [#permalink] 20 Jan 2004, 15:40
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