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10 May 2022, 02:00
Kudos
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A
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Difficulty:
5%
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Question Stats:
91% (01:16) correct
9%
(01:29)
wrong
based on 79
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A positive integer when divided by 357 gives a remainder 37. By dividing the same number by 17, the remainder would be:
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
(A) 3
(B) 4
(C) 5
(D) 6
(E) 7
10 May 2022, 05:47
Kudos
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Bunuel
--------------------------ASIDE----------------------
When it comes to remainders, we have a nice property 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.
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Given: A positive integer when divided by 357 gives a remainder 37
So, some possible values are: 37, 37+357, 37+2(357), 37+3(357), etc
There are infinitely-many values that satisfy the given information.
So, let's test the easiest/smallest one.
If the number is 37, then we get a remainder of 3 when 37 is divided by 17 (i.e., 37 ÷ 17 = 2 with remainder 3)
Answer: A
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19 May 2022, 10:06
Kudos
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Bunuel
357=17*21
n=357K+37
n=(17*21)K+37
(17*21)K is divisible by 17, and 37 when divide by 17 leaves reminder 3 ((17*2)+3)
n=17P+3, Reminder =3
Answer A
