Problem Solving (PS) | W, X, Y and Z are four different positive integers. When X

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Given that W, X, Y and Z are four different positive integers. When X is divided by Y, the quotient is Z and the remainder is W. If W = X – 7, what is the sum of all possible values ofW?

X is divided by Y, the quotient is Z and the remainder is W
=> X = Y*Z + W = YZ + W

W = X – 7
=> X = 7 + W = YZ + W
=> YZ = 7 = 1*7 = 7*1

=> We will have twocases

[table] Divisor (Y) = 1 or 7 and Quotient(Z) = 7 or1[tr]

- Case1: Y = 1 , Z =7

Divisor(Y) is 1
And we know that any positive integer divided by 1 will always give 0 as remainder

=> W = 0
=> X = 1*7+0 = 7
And Z = 7

=> X and Z become same, but they are different integers

Which is NOTPOSSIBLE[td]- Case2: Y = 7 , Z =1

Divisor(Y) is 7 => Reminders will be between 0 to 6
=> Following cases are possible
=> W = 0, same as Case 1, so we can ignore this => NOTPOSSIBLE
=> W = 1, Both W and
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Statistics : Posted by BrushMyQuant • on 08 Mar 2019, 12:27 • Replies 4 • Views 8753

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