If –12

Question

If –12 < x < –2 and 3 < y < 6, which of the following could equal xy ?

I. -72
II. -71
III. -6

A. I only
B. II only
C. III only
D. I and III only
E. None

CrackverbalGMAT · Accepted Answer

This question tests you on the max/min concept of inequalities. Knowing this process will help you avoid falling for obvious traps and give a structured process of working. The two explanations above do not seem to be right as they assume that x and y here are integers. This is a very obvious trap that any test taker will need to avoid.

Let us first discuss the when and how to use the max/min concept of inequalities:

When to use the Max/Min Concept of Inequalities:

Whenever you encounter a question with two finite ranges (x and y in this case) and the question asks us to find the sum (x+y), difference (x-y) and product (xy) of the two ranges, then this concept needs to be used

How to use the Max/Min Concept of Inequalities:

1. Place the two finite ranges one below the other
2. Make sure the inequality signs are the same. If they are not the same then we make them the same by flipping one finite ranges inequality sign. This can be done by reversing the inequality or multiplying throughout by -1
3. Perform the mathematical operation only between the extreme values of the finite ranges.

The question here clearly has two finite ranges and asks us information about the product xy, so we can definitely use the Max/Min concept.

Going step by step

1. Place the two finite ranges one below the other

-12 < x < -2
 3 < y < 6

2. Make sure the inequality signs are the same.

The inequality signs are the same here, so we can directly proceed to step 3

3. Perform the mathematical operation only between the extreme values of the finite ranges

-12 < x < -2
 3 < y < 6

Multiplying all extreme values in a straight line and cross pattern we get:

-12 * 3 = -36
-2 * 6 = -12
-12 * 6 = -72 (min)
-2 * 3 = -6 (max)

The advantage of the Max/Min concept is that it helps us get the maximum and minimum possible products, hence giving us a range for xy.

Since -6 is the max value and -72 is the min value, the range of xy will be  -72 < xy < -6. 
 
Notice here that we are not including -72 and -6 in the range of xy as the original ranges of x and y only have the less than sign and not the less than or equal to.

Now since -72 < xy < -6, the only possible value here for xy will be -71.

Answer: B

For more such Inequality properties, you can go through the following blog

https://www.crackverbal.com/gmat-inequalities/

Hope this helps!

Aditya
CrackVerbal Academic Team

m1033512 · Answer

IMO E

-72 = -12*6 but here can not be because we do not have = sign with > or <

71 is prime

-6 again can not be as explained earlier

Posted from my mobile device

Archit3110 · Answer

value of x = -12...-2
y = 3,6
so xy ; -36,-6 and -72 -11
so range -72 to -6
IMO B..

ScottTargetTestPrep · Answer

The largest possible value of xy is less than -2 x 3 = -6.

The smallest possible value of xy is greater than -12 x 6 = -72.

Thus:

-72 < xy < -6

Answer: B

Abhigmat2019 · Answer

Aditya, 
71 is a prime no., how it can be the product of x and y . Pls explain. Examples will be appreciated.

periyar22 · Answer

Hi Abhigmat,

Reading the question carefully and not making assumptions are two skills that you will need to develop to score well on the quant section.

X and Y are not integers here. Your assumption here is a prime cannot be obtained from a product of two numbers. It can if the numbers are fractions.

X can be -71/5.9999 and y can be 5.9999

Posted from my mobile device

MHIKER · Answer

Very Tricky Question. 
The Multiplications are 
-36,-12,-6,-72
We will take the extremes are as upper and lower limit of xy 
so, xy=
-72<xy<-6
-71 only option given within the range. 
The Answer is B.

Fdambro294 · Answer

the key is that X must be a (-)Neg. Value and Y must be a (+)Pos. Value

Thus, the Range of (XY) will be only (-)Neg. Values

MAXIMUM Boundary of XY:

the Highest Value that (XY) can not take and must be just beneath will be the LOWEST Magnitude of a (-)Neg. Product that we can find.

when X = (-)2

and

when Y = +3

(XY) = -6

this is the Upper Boundary that XY can NOT take

(XY) < -6

MINIMUM Boundary of (XY)
now we need to find the HIGHEST Magnitude of the (-)Neg. Product to find the Lowest Value that (XY) must be greater than.

when X = -12

and

Y = +6

(XY) = -72

(XY) must be greater than > -72

the Range of possible (XY) Values are:

-72 < (XY) < -6

only II. fits within the range

-B- II only

imslogic · Answer

How would we solve this question if it were x/y using the Min-Max method? Would we flip the signs per the rule of dividing inequalities?

Posted from my mobile device

BrushMyQuant · Answer

↧↧↧ Detailed Video Solution to the Problem Series ↧↧↧

Given that –12 < x < –2 and 3 < y < 6 and we need to find the value of xy

Lets find all possible values of Min and Max of xy by using Min and Max values of x and y

\(X_{Min} * Y_{Min}\) = -12 * 3 = -36
\(X_{Min} * Y_{Max}\) = -12 * 6 = -72
\(X_{Max} * Y_{Min}\) = -2 * 3 = -6
\(X_{Max} * Y_{Max}\) = -2 * 6 = -12

=> Smallest value of xy = -72 and Largest value of xy = -6
=> -72 < xy < -6

=> Only xy = -71 is possible as xy cannot be -72 and -6

So, Answer will be B
Hope it helps!

Watch the following video to MASTER Inequalities

bumpbot · Answer

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If –12 < x < –2 and 3 < y < 6, which of the following could equal xy ?

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If –12 < x < –2 and 3 < y < 6, which of the following could equal xy ?

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