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Problem solving from GMAT PREP EXAM 1

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Problem solving from GMAT PREP EXAM 1

by beatgmatny1 » Sun Mar 16, 2014 9:18 am
Can someone please explain the appropriate method to solve the following question?

if -4<x<7 and -6<y<3, which of the following specifies all the possible values of xy?

a. -42<xy<21
b. -42<xy<24
c. -28<xy<18
d. -24<xy<21
e. -24<xy<24

Ans: B

Since the min xy value was -30, I eliminated c, d, and e. I was debating between a and b and I guessed B. Please explain on the appropriate method to solve this.

Thanks alot!
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by theCodeToGMAT » Sun Mar 16, 2014 12:34 pm
-4<x<7

-6<y<3

If we assume that x = -4 & y = -6 .. then xy = 24.. since, x>-4 & y>-6.. that means xy < 24

If we assume that x = 7 & y = -6.. then xy = -42. since, x < 7 & y > -6.. that means xy > -42

only, [spoiler]{B}[/spoiler] satisfies.[/spoiler]
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by [email protected] » Sun Mar 16, 2014 9:57 pm
Hi beatgmatny1,

This question is based on two Number Properties worth knowing:

(Negative)(Negative) = Positive
(Positive)(Negative) = Negative

We're asked to figure out the range of values for XY. The prompt does NOT state if X and Y have to be integers, so we can't assume that they are.

Since both X and Y can be positive or negative, we have to consider all of the possibilities.

The minimum value will be negative (when one value is positive and the other is negative). The minimum value occurs when X approaches 7 and Y approaches -6.

The maximum value will be positive (when either both values are negative or positive). The maximum value occurs when X approaches -4 and Y approaches -6

Final Answer: B

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by GMATGuruNY » Mon Mar 17, 2014 4:13 am
beatgmatny1 wrote:Can someone please explain the appropriate method to solve the following question?

if -4<x<7 and -6<y<3, which of the following specifies all the possible values of xy?

a. -42<xy<21
b. -42<xy<24
c. -28<xy<18
d. -24<xy<21
e. -24<xy<24

Ans: B
To combine ranges with respect to a given operation, perform the given operation using EVERY COMBINATION OF ENDPOINTS.

Here, the given operation is MULTIPLICATION.
Calculating the value of xy using every combination of endpoints, we get:
(-4)(-6) = 24.
(-4)(3) = -12.
(7)(-6) = -42.
(7)(3) = 21.
The SMALLEST result gives us the LOWER limit of xy: -42.
The GREATEST result gives us the UPPER limit of xy: 24.
Thus:
-42 < xy < 24.

The correct answer is B.

Another example:
If -4<x<7 and -6<y<3, which of the following specifies all the possible values of x-y?
Here, the given operation is SUBTRACTION.
Calculating the value of x-y using every combination of endpoints, we get:
-4 - (-6) = 2.
-4 - 3 = -7.
7 - (-6) = 13.
7 - 3 = 4.
Thus:
-7 < x-y < 13.
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by beatgmatny1 » Tue Mar 18, 2014 2:48 pm
Thank you! I realized that forgot to consider fractions!
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