gmatt1476 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.
DS21891.01
So basically the question says,
There's a six digit number. What are the first, second, third and fourth digits?
Let First digit = f
Second digit = s
Third digit..... = t
Fourth digit .. = x
Fifth digit...... = 1
Sixth digit ..... = 6
And given in the question stem also is that;
1 = 7(f + t) Note: 1 is the unit digit
6 = 3(s + x) Note: 6 is the unit digit
You're asked to find the values of each of f, s, t, x!
(1) Tells us that f, s, x are 2,1,1 respectively, leaving us with only t missing.
Using 1 = 7(f + t) ---->>>> 1 = 7(1 + t); so only one unknown in one equation tells you the equation is solvable. No need to solve! No time! (1) is SUFFICIENT.
(2) Tells us that f + t = 3 and s = 1. We are finding f, t, x!
So using... 6 = 3(s + x) and 1 = 7(f + t)
6 = 3(1+x) solvable! now let's see if we can find f, t
1 = 7(f + t)
3 = f + t
Looks like two equations with 2 variables but that's a decoy!
1 = 7f + 7t
3 = f + t
f = 3-t
1 = 7(3-t) + 7t ---->>> 1 = 14 - 7t +7t ------>>> the variable vanishes! Phew! we have a senseles math 1= 14!
Once your variable vanishes into a senseless math just know that mathematically that equation doesn't exist.
So u have two variables with one equations. We can't solve it!
NOT SUFFICIENT
Answer is definitely B
I call this method the *mathist* method. When u are trying to analyse the question into getting a straight out answer and you couldn't or your mind gets fuzzy, just get down and mathy with the your pen.
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Give kudos for gmatclub's sake!