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Is the product of a positive and a negative integer less than -10?

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Manager
Joined: 13 May 2010
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Is the product of a positive and a negative integer less than -10? [#permalink]

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Updated on: 19 May 2018, 04:57
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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?

Originally posted by teal on 24 Aug 2012, 01:14.
Last edited by Bunuel on 19 May 2018, 04:57, edited 2 times in total.
Edited the question.
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Joined: 22 Mar 2011
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Re: Is the product of a positive and a negative integer less than -10? [#permalink]

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24 Aug 2012, 04:40
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 than -10? [#permalink]

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18 Jan 2018, 08:35
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.

Manager
Joined: 13 Sep 2016
Posts: 124
Re: Is the product of a positive and a negative integer less than -10? [#permalink]

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19 May 2018, 04:30
Is the product of a positive integer and a negative integer less than -10?

(1) The positive integer is greater than 3.

(2) The negative integer is less than -2.
Intern
Joined: 19 May 2018
Posts: 5
Re: Is the product of a positive and a negative integer less than -10? [#permalink]

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19 May 2018, 04:38
Yes consider +ve no 4 and -ve no -3 multiplication gives -12 which is less than -10.

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Joined: 02 Sep 2009
Posts: 46146
Re: Is the product of a positive and a negative integer less than -10? [#permalink]

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19 May 2018, 04:58
alanforde800Maximus wrote:
Is the product of a positive integer and a negative integer less than -10?

(1) The positive integer is greater than 3.

(2) The negative integer is less than -2.

Merging topics. Please check the discussion above.
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Re: Is the product of a positive and a negative integer less than -10?   [#permalink] 19 May 2018, 04:58
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