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01 Oct 2020, 02:30
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When the positive integer x is divided by 5, the remainder is 1. When x is divided by 8, the remainder is 4. What is the smallest positive integer y for which x + y is divisible by 40?
(A) 3
(B) 4
(C) 9
(D) 13
(E) 19
(A) 3
(B) 4
(C) 9
(D) 13
(E) 19
yashikaaggarwal
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01 Oct 2020, 02:48
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When positive integer X is divided by 5, the remainder is 1;
Here Value of X can be = 1,6,11,16,21,26,31,36....................................
when X is divided by 8, the remainder is 4.
Here Value of X can be = 4,12,20,28,36....................................
The first no. common to both constraint is 36
The least value of X = 36
the least value of Y such that X+Y is divisible by 40 is when X+Y/40 = 1
36+Y = 40
Y = 4
Answer is B
Here Value of X can be = 1,6,11,16,21,26,31,36....................................
when X is divided by 8, the remainder is 4.
Here Value of X can be = 4,12,20,28,36....................................
The first no. common to both constraint is 36
The least value of X = 36
the least value of Y such that X+Y is divisible by 40 is when X+Y/40 = 1
36+Y = 40
Y = 4
Answer is B
General Discussion
28 Dec 2023, 02:13
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When the positive integer x is divided by 5, the remainder is 1.
Dividend = Divisor * Quotient + Remainder
=> x = 5*a + 1 (where a is the quotient)
=> x = 5a + 1 ...(1)
When x is divided by 8, the remainder is 4.
=> x = 8*b + 4 (where b is the quotient)
=> x = 8b + 4 ...(2)
Only those values of x are possible which satisfy both the conditions (1) and (2)
=> x = 5a + 1 = 8b + 4
=> a = \(\frac{8b + 3}{5}\)
Possible values of b are b = 4, a = 7
=> x = 8*4 + 4 = 36
=> x + y will be divisible by 40 when y = 40 - 36 = 4
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Remainders
Dividend = Divisor * Quotient + Remainder
=> x = 5*a + 1 (where a is the quotient)
=> x = 5a + 1 ...(1)
When x is divided by 8, the remainder is 4.
=> x = 8*b + 4 (where b is the quotient)
=> x = 8b + 4 ...(2)
Only those values of x are possible which satisfy both the conditions (1) and (2)
=> x = 5a + 1 = 8b + 4
=> a = \(\frac{8b + 3}{5}\)
Possible values of b are b = 4, a = 7
=> x = 8*4 + 4 = 36
=> x + y will be divisible by 40 when y = 40 - 36 = 4
So, Answer will be B
Hope it helps!
Watch the following video to MASTER Remainders
