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If w, x, y, z are integers and w + x = y, is y divisible by z?
1) w and x each have a remainder of 1 when divided by z
2) z = 2
2) z = 2
- a)Exactly one of the statements can answer the question
- b)Both statements are required to answer the question
- c)Each statement can answer the question individually
- d)More information is required as the information provided is insufficient to answer the question
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
If w, x, y, z are integers and w + x = y, is y divisible by z?1) w and...
Given: wx=integerwx=integer and yz=integeryz=integer. Hence, wx+yz=wz+yxxz=integerwx+yz=wz+yxxz=integer and the question is whether this integer is odd.
(1) wx + yz is odd --> if w=x=1w=x=1 and y=z=2y=z=2 then wx+yz=2=evenwx+yz=2=even but if w=x=1w=x=1 and y=2y=2, z=1z=1 then wx+yz=3=oddwx+yz=3=odd. Not sufficient.
(2) wz + yx is odd --> wz+yxxz=oddxz=integerwz+yxxz=oddxz=integer --> odd=(xz)∗integerodd=(xz)∗integer --> all multiple must be odd in order the product to be odd, hence integer=oddinteger=odd. Sufficient.
Answer: B.
Most Upvoted Answer
If w, x, y, z are integers and w + x = y, is y divisible by z?1) w and...
W= zk +1 x=zl+1 zk+zl+2 =w
if z=positive then w =z(k+l)+2
if z=other than positive we are not sure
hence when z=2 it's evident
hence both the statement are required
if z=positive then w =z(k+l)+2
if z=other than positive we are not sure
hence when z=2 it's evident
hence both the statement are required
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If w, x, y, z are integers and w + x = y, is y divisible by z?1) w and...
Understanding the Problem
We need to determine if y, defined as w + x, is divisible by z given the equation w + x = y.
Statement Analysis
Statement 1: w and x each have a remainder of 1 when divided by z
- This implies:
- w = kz + 1 for some integer k
- x = mz + 1 for some integer m
- Therefore, y = w + x = (k + m)z + 2.
- Since y is expressed as (k + m)z + 2, y will have a remainder of 2 when divided by z.
- Thus, y is not divisible by z.
- Conclusion: Statement 1 alone is sufficient to answer the question.
Statement 2: z = 2
- We rewrite y:
- y = w + x.
- The divisibility of y by 2 depends on whether w and x are even or odd.
- If both w and x are even, y is even and divisible by 2.
- If both are odd, y is even and divisible by 2.
- If one is even and the other is odd, y is odd and not divisible by 2.
- Conclusion: Statement 2 alone is not sufficient to answer the question.
Combining Both Statements
- From Statement 1, we know y is not divisible by z.
- From Statement 2, we know z = 2.
- Thus, y is confirmed to be not divisible by z = 2.
Final Conclusion
Both statements together give a definitive answer that y is not divisible by z, making both required to answer the question accurately.
Thus, the correct option is b: Both statements are required to answer the question.
We need to determine if y, defined as w + x, is divisible by z given the equation w + x = y.
Statement Analysis
Statement 1: w and x each have a remainder of 1 when divided by z
- This implies:
- w = kz + 1 for some integer k
- x = mz + 1 for some integer m
- Therefore, y = w + x = (k + m)z + 2.
- Since y is expressed as (k + m)z + 2, y will have a remainder of 2 when divided by z.
- Thus, y is not divisible by z.
- Conclusion: Statement 1 alone is sufficient to answer the question.
Statement 2: z = 2
- We rewrite y:
- y = w + x.
- The divisibility of y by 2 depends on whether w and x are even or odd.
- If both w and x are even, y is even and divisible by 2.
- If both are odd, y is even and divisible by 2.
- If one is even and the other is odd, y is odd and not divisible by 2.
- Conclusion: Statement 2 alone is not sufficient to answer the question.
Combining Both Statements
- From Statement 1, we know y is not divisible by z.
- From Statement 2, we know z = 2.
- Thus, y is confirmed to be not divisible by z = 2.
Final Conclusion
Both statements together give a definitive answer that y is not divisible by z, making both required to answer the question accurately.
Thus, the correct option is b: Both statements are required to answer the question.
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If w, x, y, z are integers and w + x = y, is y divisible by z?1) w and x each have a remainder of 1 when divided by z2) z = 2a)Exactly one of the statements can answer the questionb)Both statements are required to answer the questionc)Each statement can answer the question individuallyd)More information is required as the information provided is insufficient to answer the questionCorrect answer is option 'B'. Can you explain this answer?
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