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01 Feb 2020, 19:40
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GMATBusters’ Quant Quiz Question -7
For questions from previous quizzes click here
What is the remainder when 3^48 is divisible by 19?
A. 8
B. 9
C. 10
D. 11
E. 12
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01 Feb 2020, 23:57
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Solution:
3^1 = 3,
3^2 = 9,
3^3 = 27,
3^4= 81,
so since units digit of 3^4 is 1, so following the similar pattern, units digit of 3^48 = (3^4)^12 = 1, so the the remainder will be the digit the ending with 1 = 11.
Answer D.
3^1 = 3,
3^2 = 9,
3^3 = 27,
3^4= 81,
so since units digit of 3^4 is 1, so following the similar pattern, units digit of 3^48 = (3^4)^12 = 1, so the the remainder will be the digit the ending with 1 = 11.
Answer D.
General Discussion
01 Feb 2020, 19:42
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Remainder questions are based on a pattern. Let us check the Pattern
When 3 is divided by 19, remainder = 3
When 3^2 is divided by 19, remainder = 9
When 3^4 is divided by 19, remainder = 5
When 3^8 is divided by 19, remainder = 5*5= 25 = remainder of 6
When 3^16 is divided by 19, remainder = 6*6= 36 = remainder of 17 or -2
When 3^48 is divided by 19, remainder = -2*-2*-2 = -8 , converting to Positive remainder= -8+19 = 11
The remainder = 11
Answer D
When 3 is divided by 19, remainder = 3
When 3^2 is divided by 19, remainder = 9
When 3^4 is divided by 19, remainder = 5
When 3^8 is divided by 19, remainder = 5*5= 25 = remainder of 6
When 3^16 is divided by 19, remainder = 6*6= 36 = remainder of 17 or -2
When 3^48 is divided by 19, remainder = -2*-2*-2 = -8 , converting to Positive remainder= -8+19 = 11
The remainder = 11
Answer D
Concept of Negative Remainder:
By definition, the remainder cannot be negative. But in certain cases, you can assume that for your convenience/ease the calculation.
But a negative remainder in real sense means that you need to add the divisor in the negative remainder to find the real remainder. Always convert the final remainder in POSITIVE.
By definition, the remainder cannot be negative. But in certain cases, you can assume that for your convenience/ease the calculation.
But a negative remainder in real sense means that you need to add the divisor in the negative remainder to find the real remainder. Always convert the final remainder in POSITIVE.
