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# Is the product of a positive and a negative integer less

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Manager
Joined: 13 May 2010
Posts: 122
Is the product of a positive and a negative integer less [#permalink]

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24 Aug 2012, 00:14
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Difficulty:

5% (low)

Question Stats:

84% (00:43) correct 16% (00:48) wrong based on 92 sessions

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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

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?
[Reveal] Spoiler: OA

Last edited by Bunuel on 24 Aug 2012, 00:21, edited 1 time in total.
RENAMED THE TOPIC.
Director
Joined: 22 Mar 2011
Posts: 608
WE: Science (Education)
Re: Is the product of a positive and a negative integer less [#permalink]

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24 Aug 2012, 03:40
teal wrote:
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

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?

You forgot that your numbers are integers. Therefore, $$x\geq{4}$$ and $$y\leq-3$$. From here, continue as you did above.
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Re: Is the product of a positive and a negative integer less [#permalink]

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18 Jan 2018, 07:35
teal wrote:
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

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?

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.

Re: Is the product of a positive and a negative integer less   [#permalink] 18 Jan 2018, 07:35
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