Target question: What is the value of x?AAPL wrote:If the remainder when positive integer x is divided by 7 is 4, what is the value of x?
1) x is less than 50
2) x is prime
Given: If the remainder when positive integer x is divided by 7 is 4
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.
From the given information, some possible values of x are: 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, . . . etc
Statement 1: x is less than 50
The possible values of x are: 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, . . . etc.
So, statement 1 tells us that x could equal 4, 11, 18, 25, 32, 39 or 46
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: x is prime
The possible values of x are: 4, 11, 18, 25, 32, 39, 46, 53, 60, 67, . . . etc.
From the list, we can already see two prime numbers.
x could equal 11 or 53
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT
Statements 1 and 2 combined
11 is the only possible value of x that satisfies BOTH statements.
So, the answer to the target question is x = 11
Since we can answer the target question with certainty, the combined statements are SUFFICIENT
Answer: C
Cheers,
Brent
