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Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is
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12 Nov 2019, 05:51
\(\frac{j - 2}{4} \)= m (where m is an integer) and \(\frac{k - 5}{4}\) = n (where n is an integer) ==> \(\frac{j - 2}{4} \) - \(\frac{k - 5}{4}\) = p (where p is an integer) ==> j - k = 4p - 3 ==> check the answer choices, and the answer that cannot be expressed in this form is the correct answer
A. 43 B. 33 = 4(9) - 3 C. 21 = 4(6) - 3 D. 13 = 4(4) - 3 E. 5 = 4(2) - 3
Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is
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12 Nov 2019, 11:13
J=4p+2 K=4q+5 j-k = 4(p-q)-3 Insert values from options. Correct answer after adding 3 to it will be divisible by 4. 4(p-q)-3=43 ; 46 not divisible by 4 4(p-q)-3=33 ; 36 divisible by 4 4(p-q)-3=21 ; 24 divisible by 4 4(p-q)-3=13 ; 16 divisible by 4 4(p-q)-3=5 ; 8 divisible by 4
Since j - 2 and k - 5 are both divisible by 4, their difference is also divisible by 4; that is:
j - 2 - (k - 5) = j - k + 3 is divisible by 4.
Since j - k + 3 is divisible by 4, then when j - k is divided by 4, it should have a remainder of 1 (notice that if j - k is 1, then j - k + 3 = 4). Therefore, we are looking for the choice that doesn’t yield a remainder of 1 when it is divided by 4, and we see that is the number 43 (all the other choices do indeed yield a remainder of 1 when divided by 4).
Re: If j and k are positive integers, j - 2 is divisible by 4 and k - 5 is
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24 Nov 2019, 20:10
Solution
Given:
• j and k are positive integers • j – 2 is divisible by 4 • k – 5 is divisible by 4
To find:
• Which cannot be the value of j - k
Approach and Working Out:
• From the given information we can write,
o \(j – 2 = 4p_1\), where \(p_1\) is an integer
Implies, \(j = 4p_1 + 2\)
o Similarly, \(k – 5 = 4p_2\), where, \(p_2\) is an integer
\(k = 4p_2 + 5\)
• Thus, \(j – k = 4p_1 + 2 – 4p_2 – 5 = 4(p_1 – p_2) – 3 = 4(p_1 – p_2) – 4 + 1 = 4(p_1 – p_2 – 1) + 1= 4p + 1\) • The only option which is not in the form of 4p + 1 is option A, 43
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69% (02:01) correct 
