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amanvermagmat
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A lock can be opened by a specific 3-digit code, where each digit can 08 Apr 2018, 05:38
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E
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65% (hard)

Question Stats:

54% (01:59) correct 46% (01:56) wrong based on 108 sessions

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A lock can be opened only by a single specific 3-digit code, where each digit can be one out of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. If the middle digit is the average of the other two digits, then what is the 3-digit code of this lock?

(1) Rightmost digit is 9.

(2) Leftmost digit is not a prime number.
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E
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twister68
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A lock can be opened by a specific 3-digit code, where each digit can 08 Apr 2018, 12:23
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Ans: E combining the two, we still have two codes possible 999 and 159. Therefore insufficient


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A lock can be opened by a specific 3-digit code, where each digit can 24 Sep 2019, 06:16
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amanvermagmat
A lock can be opened only by a single specific 3-digit code, where each digit can be one out of 0, 1, 2, 3, 4, 5, 6, 7, 8, 9. If the middle digit is the average of the other two digits, then what is the 3-digit code of this lock?

(1) Rightmost digit is 9.
(2) Leftmost digit is not a prime number.

[L,M,R]… M=R+L/2… R+L/2=integer so R+L must be both EVEN or both ODD; also R+L≤18;

(1) R=9=ODD: R+L≤18…9+L≤18…L≤9=ODD={1,3,5,7,9}; M=(9+{1,3,5,7,9})/2, insufic.
(2) L≠Prime: L≠{2,3,5,7}={0,1,4,6,8,9}, insufic.
(1&2) L={1,9}, R=9, M=9+1/2=5 or M=9+9/2=9, insufic.

Answer (E)
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