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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 – 4, which of the following is a possible value of X?

I. 6
II. 7
III. 8
  • a)
    I only
  • b)
    II only
  • c)
    I and II only
  • d)
    II and III only
  • e)
    I, II, and III
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
W, X, Y and Z are four different positive integers. When X is divided ...
When X is divided by Y, the quotient is Z and the remainder is W. This can be expressed as X = Y * Z + W.
We are also given that W = X - 4.
Substituting the value of W in the equation X = Y * Z + W, we get: X = Y * Z + (X - 4)
Rearranging the equation, we have: 4 = Y * Z - 4
Simplifying further, we get: Y * Z = 8
Now, let's consider the possible values of X and check if they satisfy the equation:
I. If X = 6, then W = X - 4 = 6 - 4 = 2. Since W is the remainder when X is divided by Y, and Y and Z are different positive integers, the only possible combination is Y = 2 and Z = 4. Therefore, X = Y * Z + W = 2 * 4 + 2 = 10.
II. If X = 7, then W = X - 4 = 7 - 4 = 3. The possible combination for Y and Z is Y = 3 and Z = 2. Therefore, X = Y * Z + W = 3 * 2 + 3 = 9.
III. If X = 8, then W = X - 4 = 8 - 4 = 4. The possible combination for Y and Z is Y = 4 and Z = 2. Therefore, X = Y * Z + W = 4 * 2 + 4 = 12.
Among the given options, X can take the values 10, 9, and 12, which correspond to options I, II, and III. Therefore, the possible value of X is I, II, and III.
Hence, the correct answer is option C, I and II only.
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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 – 4, which of the following is a possible value of X?I. 6II. 7III. 8a)I onlyb)II onlyc)I and II onlyd)II and III onlye)I, II, and IIICorrect answer is option 'C'. Can you explain this answer?
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