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Wednesday, April 18, 2007
"ALGEBRA QUESTION OF THE DAY"
A number, when divided by 12, gives a remainder of 7. If the same number is divided by 6, then the remainder must be (A) 1 (B) 2 (C) 3 (D) 4 (E) 5
CORRECT ANS IS We are told that the remainder is 7 when the number is divided by 12. Hence, we can represent the number as 12x + 7. Now, 7 can be written as 6 + 1. Plugging this into the expression yields 12x + (6 + 1) = (12x + 6) + 1 = by regrouping 6(2x + 1) + 1 by factoring 6 out of the first two terms This shows that the remainder is 1 when the expression 12x + 7 is divided by 6. The answer is (A). Method II (Substitution): Choose the number 19, which gives a remainder of 7 when divided by 12. Now, divide 19 by 6: 19 6 = 3 1 6 This shows that 6 divides into 19 with a remainder of 1. The answer is (A).
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ReplyDeleteCORRECT ANS IS
ReplyDeleteWe are told that the remainder is 7 when the number is divided by 12. Hence, we can represent the
number as 12x + 7. Now, 7 can be written as 6 + 1. Plugging this into the expression yields
12x + (6 + 1) =
(12x + 6) + 1 = by regrouping
6(2x + 1) + 1 by factoring 6 out of the first two terms
This shows that the remainder is 1 when the expression 12x + 7 is divided by 6. The answer is (A).
Method II (Substitution):
Choose the number 19, which gives a remainder of 7 when divided by 12. Now, divide 19 by 6:
19
6
=
3
1
6
This shows that 6 divides into 19 with a remainder of 1. The answer is (A).