Vincen wrote: ↑

Sun May 09, 2021 2:07 pm

What is the tens digit of positive integer \(x?\)

(1) \(x\) divided by 100 has a remainder of 30.
(2) \(x\) divided by 110 has a remainder of 30.

Answer:A

Source:Official Guide

Target question: What is the tens digit of positive integer x ?

Statement 1: x divided by 100 has a remainder of 30
ASIDE: When it comes to remainders, we have a nice rule that says:
If N divided by D leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc.
For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc.
In other words, the possible values of k are: 1, 6, 11, 16, 21, 26, 31, . . . etc.

So, from statement 1, we can conclude that the possible values of x are: 30, 130, 230, 330, 430, 530,. . .
In ALL possible values of x, the tens digit is always 3
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x divided by 110 has a remainder of 30
From statement 2, we can conclude that the possible values of x are: 30, 140, 250, 360, 470, 580,. . .
Notice that the the tens digit can have many different values
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

Cheers,
Brent