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When positive integer x is divided successively by 3, 4, and 7, the
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28 Aug 2022, 04:18
28 Aug 2022, 04:18
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When positive integer x is divided successively by 3, 4, and 7, the remainders are 2, 1, and 4, respectively. What is the remainder when x is divided by 84 ?
A. 83
B. 80
C. 75
D. 53
E. 42
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A. 83
B. 80
C. 75
D. 53
E. 42
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GMAT 1: 760 Q51 V40 
Re: When positive integer x is divided successively by 3, 4, and 7, the
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28 Aug 2022, 04:49
28 Aug 2022, 04:49
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It is given that, x is divided successively by 3, 4, and 7, and the remainders are 2, 1, and 4.
We need to start from the end here.
Thus combining (1) and (2) we have, Q = 4(7Q'' + 4) + 1 ... (3)
Substitution value of Q from (3) to (4) we have,
x = 3[4(7Q'' + 4) + 1] + 2 = 3 [28Q'' + 16 + 1] + 2 = 84Q'' + 53
So when we divide this number by 84 the remainder is 53.
Answer: D
- We need to understand what is the meaning of successive division. Here, x is divided by 3 and we get a quotient (say Q) and a remainder of 2. We pick the quotient (Q) and then again divide Q by 4 to get another quotient (Q') and a remainder of 1. When we divide this quotient (Q') by 7, we get a quotient of Q'' and a remainder of 4.
We need to start from the end here.
- When we divide this quotient (Q') by 7, we get a quotient of Q'' and a remainder of 4.
- Q' = 7Q'' + 4 ... (1)
- When we divide this quotient (Q) by 4, we get a quotient of Q' and a remainder of 1.
- Q = 4Q' + 1 ... (2)
Thus combining (1) and (2) we have, Q = 4(7Q'' + 4) + 1 ... (3)
- x is divided by 3 and we get a quotient (say Q) and a remainder of 2.
- x = 3Q + 2 .... (4)
Substitution value of Q from (3) to (4) we have,
x = 3[4(7Q'' + 4) + 1] + 2 = 3 [28Q'' + 16 + 1] + 2 = 84Q'' + 53
So when we divide this number by 84 the remainder is 53.
Answer: D
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Re: When positive integer x is divided successively by 3, 4, and 7, the
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06 Nov 2022, 03:46
06 Nov 2022, 03:46
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Given that When positive integer x is divided successively by 3, 4, and 7, the remainders are 2, 1, and 4, respectively and we need to find the remainder when x is divided by 84 ?
We need to solve this problem backwards
When an integer (lets say A) is divided by 7, the remainder is 4
Theory: Dividend = Divisor*Quotient + Remainder
A -> Dividend
7 -> Divisor
t -> Quotient (Assume)
4 -> Remainder
=> A = 7*t + 4 = 7t + 4
When an integer (Lets say "B") is divided by 4, gives A as quotient and 1 as remainder
=> B = 4A + 1 = 4*(7t + 4) + 1 = 28t + 16 + 1 = 28t + 17
When x is divided by 3, gives B as quotient and 2 as remainder
=> x = 3B + 2 = 3*(28t + 17) + 2 = 84t + 51 + 2 = 84t + 53
=> x when divided by 84 gives 53 remainder
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Remainders
We need to solve this problem backwards
- - Something divided by 7 and gives 1 as remainder.
- Take that number as quotient for division by 4 and remainder as 1.
- Take the new number formed as the quotient for division by 3 and remainder as 2 to get the value of x.
- Then divide x by 84 to check the remainder.
When an integer (lets say A) is divided by 7, the remainder is 4
Theory: Dividend = Divisor*Quotient + Remainder
A -> Dividend
7 -> Divisor
t -> Quotient (Assume)
4 -> Remainder
=> A = 7*t + 4 = 7t + 4
When an integer (Lets say "B") is divided by 4, gives A as quotient and 1 as remainder
=> B = 4A + 1 = 4*(7t + 4) + 1 = 28t + 16 + 1 = 28t + 17
When x is divided by 3, gives B as quotient and 2 as remainder
=> x = 3B + 2 = 3*(28t + 17) + 2 = 84t + 51 + 2 = 84t + 53
=> x when divided by 84 gives 53 remainder
So, Answer will be D
Hope it helps!
Watch the following video to learn the Basics of Remainders
