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29 Jul 2012, 06:27
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Q4. Is y – x positive?
(1) y > 0
(2) x = 1 – y
The question we are asked is in fact is y>x?
(1) Not sufficient, as we don't know anything about x.
(2) We have x+y=1, again not sufficient. We can have x=y=0.5, or x=0.25 < y=0.75, or x=0.75 > y=0.25
(1) and (2) not sufficient, we can use the examples from the analysis for (2) above.
Answer E
(1) y > 0
(2) x = 1 – y
The question we are asked is in fact is y>x?
(1) Not sufficient, as we don't know anything about x.
(2) We have x+y=1, again not sufficient. We can have x=y=0.5, or x=0.25 < y=0.75, or x=0.75 > y=0.25
(1) and (2) not sufficient, we can use the examples from the analysis for (2) above.
Answer E
29 Jul 2012, 06:46
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Q5. If a and b are integers, and a not= b, is |a|b > 0?
(1) |a^b| > 0
(2) |a|^b is a non-zero integer
The question can be rephrased as are a and b distinct non-zero integers and is b positive?
(1) We can deduce that \(a\neq0\), but b can be 0.
Take a=1, b=0, then \(|a^0|=1>0\) and |a|b=0.
But if we take a=2 and b=1, then \(|a^b|=2>0\) and |a|b=2>0.
Not sufficient.
(2) Again \(a\neq0\). But a can be 1, in which case b can be negative or 0.
Not sufficient.
(1) and (2) Since we cannot guarantee that \(b\neq0\), again not sufficient.
Answer E
(1) |a^b| > 0
(2) |a|^b is a non-zero integer
The question can be rephrased as are a and b distinct non-zero integers and is b positive?
(1) We can deduce that \(a\neq0\), but b can be 0.
Take a=1, b=0, then \(|a^0|=1>0\) and |a|b=0.
But if we take a=2 and b=1, then \(|a^b|=2>0\) and |a|b=2>0.
Not sufficient.
(2) Again \(a\neq0\). But a can be 1, in which case b can be negative or 0.
Not sufficient.
(1) and (2) Since we cannot guarantee that \(b\neq0\), again not sufficient.
Answer E
29 Jul 2012, 06:56
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Q6. If M and N are integers, is (10^M + N)/3 an integer?
1. N = 5
2. MN is even
(1) M can be negative, in which case \((10^M + N)/3\) is not an integer.
But for example, if M=0, N=5, \((10^M + N)/3=6/3=2\) is an integer.
Not sufficicent.
(2) MN even means at least one of the two numbers must be even.
We can take M=0 and N=3, then \((10^M + N)/3=4/3\) it's not an integer.
But for M=1 and N=2, \((10^M + N)/3=12/3=4\) it is an integer.
Not sufficient.
(1) and (2): N=5, but since MN is even, it means that M must be even.
Still, we cannot exclude the case M negative, for which the given expression is not an integer.
Therefore, not sufficient.
Answer E
1. N = 5
2. MN is even
(1) M can be negative, in which case \((10^M + N)/3\) is not an integer.
But for example, if M=0, N=5, \((10^M + N)/3=6/3=2\) is an integer.
Not sufficicent.
(2) MN even means at least one of the two numbers must be even.
We can take M=0 and N=3, then \((10^M + N)/3=4/3\) it's not an integer.
But for M=1 and N=2, \((10^M + N)/3=12/3=4\) it is an integer.
Not sufficient.
(1) and (2): N=5, but since MN is even, it means that M must be even.
Still, we cannot exclude the case M negative, for which the given expression is not an integer.
Therefore, not sufficient.
Answer E
