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The first four digits of the six-digit initial password for a shopper'

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The first four digits of the six-digit initial password for a shopper'  [#permalink]

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New post 21 Sep 2019, 19:22
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A
B
C
D
E

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  85% (hard)

Question Stats:

32% (03:20) correct 68% (03:14) wrong based on 25 sessions

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The first four digits of the six-digit initial password for a shopper's card at a certain grocery store is the customer's birthday in day-month digit form. For example, 15 August corresponds to 1508 and 5 March corresponds to 0503. The 5th digit of the initial password is the units digit of seven times the sum of the first and third digits, and the 6th digit of the initial password is the units digit of three times the sum of the second and fourth digits. What month, and what day of that month, was a customer born whose initial password ends in 16 ?

(1) The customer's initial password begins with 21, and its fourth digit is 1.
(2) The sum of the first and third digits of the customer's initial password is 3, and its second digit is 1.


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Re: The first four digits of the six-digit initial password for a shopper'  [#permalink]

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New post 22 Sep 2019, 01:47
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let the -digit be ABCD16

if (A+C)*7 produce a number with a unit digit of 1, then A+C = 3,
and the possible pairs of (A,C) are (3,0) and (2,1) because C can only be 0 or 1 (CD is the month which range between 01 and 12)

if (B+D)*3 produce a number with a unit digit of 6, then B+D can be equal to 2 or 8 , which produce too many possibilities.

from statement (1), the number is 21C116
as we deduced, if A = 2, then C = 1 , and the month is 11 (November) --> sufficient

from statement (2), the number is A1CD16 , and we already know that A+C = 3 --> insufficient
if B = 1, then D can be 1 or 7, and C can be 1 or 0 respectively
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Re: The first four digits of the six-digit initial password for a shopper'  [#permalink]

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New post 22 Sep 2019, 08:00
Can anyone please help with statement B

The sum of 1st and 3rd digit is 3, third digit can't be more than 1
All digits needs to be positive integers so the only possible value seems 2,1 so 1st Digit would be 2 and 3rd would be 1
And 4th Digit is easily figurable


Please help what am I missing

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Re: The first four digits of the six-digit initial password for a shopper'  [#permalink]

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New post 22 Sep 2019, 08:44
itoyj wrote:
Can anyone please help with statement B

The sum of 1st and 3rd digit is 3, third digit can't be more than 1
All digits needs to be positive integers so the only possible value seems 2,1 so 1st Digit would be 2 and 3rd would be 1
And 4th Digit is easily figurable


Please help what am I missing

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the red part is not correct. C can be 0 or 1
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Re: The first four digits of the six-digit initial password for a shopper'  [#permalink]

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New post 22 Sep 2019, 09:17
[quote="Mahmoudfawzy83"][quote="itoyj"]Can anyone please help with statement B

The sum of 1st and 3rd digit is 3, third digit can't be more than 1
[color=#ff0000]All digits needs to be positive integers[/color] so the only possible value seems 2,1 so 1st Digit would be 2 and 3rd would be 1
And 4th Digit is easily figurable


Please help what am I missing

[size=80][b][i]Posted from my mobile device[/i][/b][/size][/quote]

the red part is not correct. C can be 0 or 1[/quote]


Isn't it obvious, that dates needs to be positive, I thought that it is not even assumption, it is universal truth
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Re: The first four digits of the six-digit initial password for a shopper'  [#permalink]

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New post 22 Sep 2019, 11:36
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Dear itoyj
dates needs to be positive, but the tens digit of it can be zero.
if CD is the two-digit representing the month,
then January is 01 (where C = 0 and D = 1)
and December is 12 (where C = 1 and D = 2)
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Re: The first four digits of the six-digit initial password for a shopper'   [#permalink] 22 Sep 2019, 11:36
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