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Re: When x is divided by 10, the quotient is y with a remainder
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17 Aug 2018, 16:03
Expert Reply
Explanation
This is a bit of a trick question—any number that yields remainder 4 when divided by 10 will also yield remainder 4 when divided by 5. This is because the remainder 4 is less than both divisors, and all multiples of 10 are also multiples of 5.
For example, 14 yields remainder 4 when divided either by 10 or by 5. This also works for 24, 34, 44, 54, etc.
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Re: When x is divided by 10, the quotient is y with a remainder
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07 Jun 2020, 08:05
1
Expert Reply
sandy wrote:
When x is divided by 10, the quotient is y with a remainder of 4. If x and y are both positive integers, what is the remainder when x is divided by 5?
(A) 0 (B) 1 (C) 2 (D) 3 (E) 4
APPROACH #1: Test a possible value of x 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.
So, from the given information, the possible values of x are: 4, 14, 24, 34, 44, 54,.... If you divide any of these possible x-values by 5, you'll always get a remainder of 4.
Answer: E
APPROACH #2: Use algebra
There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3
From the given information we can write: x = 10y + 4 We can rewrite this as: x = (5)(2x) + 4 We know that (5)(2x) is a multiple of 5, which means (5)(2x) + 4 is 4 MORE THAN a multiple of 5 So, when we divide (5)(2x) + 4 by 5, the remainder will be 4
Answer: E
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