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j, k, m, x, y and z are positive integers. When j is divided
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22 May 2019, 05:20
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j, k, m, x, y and z are positive integers. When j is divided by k, the remainder is m. When x is divided by y, the remainder is z. If ky = 75, which of the following CANNOT be the value of mz?
i) 49 ii) 50 iii) 56
A) iii only B) i and ii C) i and iii D) ii and iii E) i, ii and iii
j, k, m, x, y and z are positive integers. When j is divided
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22 May 2019, 08:54
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GreenlightTestPrep wrote:
j, k, m, x, y and z are positive integers. When j is divided by k, the remainder is m. When x is divided by y, the remainder is z. If ky = 75, which of the following CANNOT be the value of mz?
i) 49 ii) 50 iii) 56
A) iii only B) i and ii C) i and iii D) ii and iii E) i, ii and iii
Useful remainder property: When positive integer N is divided by positive integer D, the remainder R is such that 0 ≤ R < D For example, if we divide some positive integer by 7, the remainder will be 6, 5, 4, 3, 2, 1, or 0
When j is divided by k, the remainder is m The above property tells us that 0 ≤ m < k
When x is divided by y, the remainder is z The above property tells us that 0 ≤ z < y
If ky = 75, which of the following CANNOT be the value of mz? There are 3 ways in which ky = 75 1) k and y are 1 and 75 2) k and y are 3 and 25 3) k and y are 5 and 15
We can ELIMINATE case 1, because dividing by 1 will give us a remainder of 0, and we're told that all values are POSITIVE integers So, k and y are EITHER 3 & 25 OR 5 & 15 So, we have two possible cases: case a) m < 3 and k < 25 case b) m < 5 and k < 15
Now let's check the statements. iii) 56 Are there values of m and z such that mz = 56, AND one of the two cases (above) are met? YES! If m = 4 and k = 14, then mk = (4)(14) = 56 This meets the conditions in case b. That is, m < 5 and k < 15 Since mz CAN equal 56, we can ELIMINATE answer choices A, C, D and E (since they say that mz CANNOT equal 56)
By the process of elimination, the correct answer is B
j, k, m, x, y and z are positive integers. When j is divided
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26 Aug 2021, 11:57
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given ky=75, let k=5 and y=15 j,5,m,x,15,z j/5 with remainder m and m={1,2,3,4}, all numbers must be positive x/15 with remainder z and z={1,2,3...14} possible values of mz must be the product of two set numbers, set m and set z 49=7*7 not possible 50 not possible too 56=4*14 is possible
Answer is I & II, and it's B
GreenlightTestPrep wrote:
j, k, m, x, y and z are positive integers. When j is divided by k, the remainder is m. When x is divided by y, the remainder is z. If ky = 75, which of the following CANNOT be the value of mz?
i) 49 ii) 50 iii) 56
A) iii only B) i and ii C) i and iii D) ii and iii E) i, ii and iii
Re: j, k, m, x, y and z are positive integers. When j is divided
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15 Nov 2023, 21:32
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Re: j, k, m, x, y and z are positive integers. When j is divided [#permalink]