Data Sufficiency

BTGmoderatorDC wrote: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.




OA A

Source: Official Guide

Let the 6 digit password be written as _ _ _ _ 1 6 (Given that Initial password ends in 16)

From (1) The above 6 digit password is written as 2 1 X 1 1 6 (password begins with 21 and 4 digit is 1). Let 3rd digit be X

Also given that 5th digit of password is units digits when 7 *(Sum of 1st digit and 3rd digit)

5th Digit is 1

1st digit is 2, 3rd digit is X When 2 +X is multiplied by 7 we should get units digit of 1 in resultant product.

X can take value from 0 to 1 only ( Given 3rd and 4th digit are month 01 to 12)

So if product of 7* (2+X) has to be 1 then X has to be 1. i.e 7 *(2+1) = 21 .

Password ca be written as 2 1 1 1 1 6. Birthday is 21/11
Hence The Information in (1) is Sufficient.

From (2) The above 6 digit password is X 1 Y Z 1 6 and X+Y = 3 So X+Y can be 1+2 or 2+1 but Y has to be 0 or 1 because it given that 3rd and 4th digit of password correspond to the month. Month can only be (01, 02,.....10, 11 to 12) so 3rd digit (Y) can only be 0 or 1.

Hence if X+Y = 3 then Y =1 and x =2.

So password can be written as 2 1 1 Z 1 6

Also given 6th digits is Unites digits of 3 *(2nd digit + 4th Digit) 3*(1+Z)

6th Digit is given as 6. So 3 *(1+Z) = X6 Z can take values from 0 to 9 . Its last digit of a month. 01, 02, .....10, 11, 12
for 3*(1+Z) = X6, then Z has to be 1 . For no other value from 0 to 9 except 1 multiple of 3 has units digit of 6

So the password can be written as 2 1 1 1 1 6 birthday 21/11

Hence Answer is D. Each statement alone is Sufficient to Answer the Question