Brent@GMATPrepNow wrote: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.
What is the value of Z?
1) W = X - 4
2) W + Z = 4
Difficulty level: 650 - 700
Source:
www.gmatprepnow.com
Target question: What is the value of Z?
Given: When X is divided by Y, the quotient is Z and the remainder is W.
------ASIDE-------
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
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So, from the given information, we can write:
X = YZ + W
Statement 1: W = X - 4
Take
X = YZ + W and replace X with X - 4 to get: X = YZ + X - 4
Subtract X from both sides: 0 = YZ - 4
Rewrite as: 4 = YZ
We're told that Y and Z are DIFFERENT positive INTEGERS. So, there are only 2 possible cases:
case i: Y = 1 and Z = 4
case ii: Y = 4 and Z = 1
case i yields a CONTRADICTION.
If Y = 1, then we are dividing X by 1, and if we divide by 1, the remainder will always be ZERO.
In other words, if Y = 1, then W = 0
However, we are told that W is a POSITIVE integer.
So, we can definitely rule out case i, which means it MUST be the case that Y = 4 and Z = 1 (case ii)
So, the answer to the target question is
Z = 1
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: W + Z = 4
Since W and Z are DIFFERENT positive INTEGERS. So, there are only 2 possible cases:
case i: W = 1 and Z = 3
case ii: W = 3 and Z = 1
Let's check each case to see whether each case yields a contradiction.
case i: W = 1 and Z = 3
We get: "When X is divided by Y, the quotient is 3 and the remainder is 1"
So, for example, it could be the case that X = 7 and Y = 2
We get: When 7 is divided by 2, the quotient is 3 and the remainder is 1
So, case i is possible. (In this case, the answer to the target question is
Z = 3
case ii: W = 3 and Z = 1
We get: "When X is divided by Y, the quotient is 1 and the remainder is 3"
So, for example, it could be the case that X = 7 and Y = 4
We get: When 7 is divided by 4, the quotient is 1 and the remainder is 3
So, case ii is also possible. (In this case, the answer to the target question is
Z = 1
Since we cannot answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent
