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# PS : Digits

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CEO
Joined: 15 Aug 2003
Posts: 3467
Followers: 61

Kudos [?]: 718 [0], given: 781

PS : Digits [#permalink]  13 Sep 2003, 05:00
00:00

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
Joined: 22 May 2003
Posts: 334
Location: Uruguay
Followers: 1

Kudos [?]: 41 [0], given: 0

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
SVP
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
Followers: 5

Kudos [?]: 43 [0], given: 0

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
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 11 [0], given: 0

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
Joined: 30 Oct 2003
Posts: 1794
Location: NewJersey USA
Followers: 5

Kudos [?]: 43 [0], given: 0

Yeah u got me there. The problem stem should be changed to distinct different digits.
Intern
Joined: 20 Jan 2004
Posts: 3
Location: Dallas, TX
Followers: 0

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

a<>0 [#permalink]  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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