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25. x and h are both positive integers. When x is divided by 7, the quotient is h with a remainder of 3. Which of the following could be the value of x? (A) 7 (B) 21 (C) 50 (D) 52 (E) 57
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.
GIVEN: When x is divided by 7, the quotient is h with a remainder of 3 So, the possible values of x are: 3, 10, 17, 24, 31, etc
Notice that each possible value of x is THREE MORE than some multiple of 7.
Now check the answer choices.... (A) 7 This is a multiple of 7. ELIMINATE (B) 21 This is a multiple of 7. ELIMINATE (C) 50 This is ONE MORE than a multiple of 7 (49). ELIMINATE (D) 52 This is THREE MORE than a multiple of 7 (49). PERFECT!!!