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C
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Difficulty:
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Question Stats:
79% (00:59) correct
21%
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wrong
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Is the product of a positive and a negative integer less than -10?
(1) The positive integer is greater than 3
(2) The negative integer is less than -2
(1) The positive integer is greater than 3
(2) The negative integer is less than -2
What is wrong with this solution -
Let x and y be the positive and negative integer,
Now a) x>3
b) y<-2 also means that -y>2
Since I can multiply inequalities if both sides are positive then -xy>6 which means that xy< -6 so I cannot conclusively determine if xy is less than -10 and I get answer E
With number testing maximum product is -12 Hence answer is C which is the correct answer. What did I do wrong with the above method?
Let x and y be the positive and negative integer,
Now a) x>3
b) y<-2 also means that -y>2
Since I can multiply inequalities if both sides are positive then -xy>6 which means that xy< -6 so I cannot conclusively determine if xy is less than -10 and I get answer E
With number testing maximum product is -12 Hence answer is C which is the correct answer. What did I do wrong with the above method?
24 Aug 2012, 04:40
Kudos
Bookmarks
teal
You forgot that your numbers are integers. Therefore, \(x\geq{4}\) and \(y\leq-3\). From here, continue as you did above.
18 Jan 2018, 08:35
Kudos
Bookmarks
teal
So lets say the positive integer is 'x' and the negative integer is 'y'. We have to determine if x*y < -10
(1) x > 3. So the minimum value of x is 4 (has to be an integer). But nothing about y, so insufficient.
(2) y < -2. So maximum value of y is -3 (has to be an integer). But nothing about x, so insufficient.
Combining the two statements, if we take x = 4 and y = -3, then their product = 4*-3 = -12. For any other values of x & y satisfying the two statements, product will be less than -12 only. (eg, x=5, y=-3 gives us -15 and x=4, y=-4 gives us -16 and so on...)
So if product is less than -12, it will obviously be less than -10 also. (any number to the left of -12 will also be to the left of -10 on the number line). Sufficient.
Hence C answer
