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A telephone number has the form ABC-DEF-GHIJ, where each letter repres

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A telephone number has the form ABC-DEF-GHIJ, where each letter repres  [#permalink]

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18 Mar 2019, 02:31
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Difficulty:

35% (medium)

Question Stats:

64% (03:30) correct 36% (03:03) wrong based on 27 sessions

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A telephone number has the form ABC-DEF-GHIJ, where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, A > B > C, D > E > F, and G > H > I > J. Furthermore, D, E, and F are consecutive even digits; G, H, I, and J are consecutive odd digits; and A + B + C = 9. Find A.

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

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Re: A telephone number has the form ABC-DEF-GHIJ, where each letter repres  [#permalink]

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18 Mar 2019, 05:24
Bunuel wrote:
A telephone number has the form ABC-DEF-GHIJ, where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, A > B > C, D > E > F, and G > H > I > J. Furthermore, D, E, and F are consecutive even digits; G, H, I, and J are consecutive odd digits; and A + B + C = 9. Find A.

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

GHIJ ; 9,7,5,3,1
DEF; 6,4,2
ABC: 8,1,0
IMO E
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Re: A telephone number has the form ABC-DEF-GHIJ, where each letter repres  [#permalink]

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18 Mar 2019, 06:03
Bunuel wrote:
A telephone number has the form ABC-DEF-GHIJ, where each letter represents a different digit. The digits in each part of the number are in decreasing order; that is, A > B > C, D > E > F, and G > H > I > J. Furthermore, D, E, and F are consecutive even digits; G, H, I, and J are consecutive odd digits; and A + B + C = 9. Find A.

(A) 4
(B) 5
(C) 6
(D) 7
(E) 8

D,E,F are consecutive even integers - three options possible are (8,6,4),(6,4,2), or (4,2,0)

G,H,I,J are consecutive odd integers - two possible options are (9,7,5,3) or (7,5,3,1)

Let's start trying combinations

Option 1
G = 9, H = 7, I = 5, J = 3 (we are left with 1)
D = 8, E = 6, F = 4(left with 2 and 0) - does not add up to 9
D = 6, E = 4, F = 2(left with 8 and 0) - we have a match for A + B + C = 9

Therefore, the value of A is 8(Option E) as A > B > C
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Re: A telephone number has the form ABC-DEF-GHIJ, where each letter repres   [#permalink] 18 Mar 2019, 06:03
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