How to multiply negative numbers - GRE Quantitative Reasoning
Card 1 of 32
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
Tap to reveal answer
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
← Didn't Know|Knew It →
and 
Quantity A: 
Quantity B: 
Quantity A:
Quantity B:
Tap to reveal answer
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
← Didn't Know|Knew It →
Simplify:
$-(-6)^{2}$(-1)-(-3)
Simplify:
$-(-6)^{2}$(-1)-(-3)
Tap to reveal answer
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
← Didn't Know|Knew It →
If 
and 
are both less than zero, which of the following is NOT possible?
If
Tap to reveal answer
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
is possible because two negative numbers added together will always equal a negative number.
is possible because xy and -yx are inverses of each other, so they will combine to make 0.
is possible because you don't know what the values of x and y are. If y is sufficiently larger than x, then subtracting the negative number resulting from 2y (aka adding 2y) to the negative number 3x could be a positive number, including 5.
is possible because a negative (2x) times a negative (y) will always be positive.
Which, of course, means that 
is impossible, because a negative times a negative will never equal a negative.
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
Which, of course, means that
← Didn't Know|Knew It →
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
Tap to reveal answer
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
← Didn't Know|Knew It →
and
Quantity A:
Quantity B:
Quantity A:
Quantity B:
Tap to reveal answer
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
← Didn't Know|Knew It →
Simplify:
$-(-6)^{2}$(-1)-(-3)
Simplify:
$-(-6)^{2}$(-1)-(-3)
Tap to reveal answer
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
← Didn't Know|Knew It →
If and are both less than zero, which of the following is NOT possible?
If
Tap to reveal answer
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
is possible because two negative numbers added together will always equal a negative number.
is possible because xy and -yx are inverses of each other, so they will combine to make 0.
is possible because you don't know what the values of x and y are. If y is sufficiently larger than x, then subtracting the negative number resulting from 2y (aka adding 2y) to the negative number 3x could be a positive number, including 5.
is possible because a negative (2x) times a negative (y) will always be positive.
Which, of course, means that is impossible, because a negative times a negative will never equal a negative.
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
Which, of course, means that
← Didn't Know|Knew It →
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
Tap to reveal answer
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
← Didn't Know|Knew It →
and
Quantity A:
Quantity B:
Quantity A:
Quantity B:
Tap to reveal answer
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
← Didn't Know|Knew It →
Simplify:
$-(-6)^{2}$(-1)-(-3)
Simplify:
$-(-6)^{2}$(-1)-(-3)
Tap to reveal answer
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
← Didn't Know|Knew It →
If and are both less than zero, which of the following is NOT possible?
If
Tap to reveal answer
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
is possible because two negative numbers added together will always equal a negative number.
is possible because xy and -yx are inverses of each other, so they will combine to make 0.
is possible because you don't know what the values of x and y are. If y is sufficiently larger than x, then subtracting the negative number resulting from 2y (aka adding 2y) to the negative number 3x could be a positive number, including 5.
is possible because a negative (2x) times a negative (y) will always be positive.
Which, of course, means that is impossible, because a negative times a negative will never equal a negative.
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
Which, of course, means that
← Didn't Know|Knew It →
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
Tap to reveal answer
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
← Didn't Know|Knew It →
and
Quantity A:
Quantity B:
Quantity A:
Quantity B:
Tap to reveal answer
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
← Didn't Know|Knew It →
Simplify:
$-(-6)^{2}$(-1)-(-3)
Simplify:
$-(-6)^{2}$(-1)-(-3)
Tap to reveal answer
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
← Didn't Know|Knew It →
If and are both less than zero, which of the following is NOT possible?
If
Tap to reveal answer
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
is possible because two negative numbers added together will always equal a negative number.
is possible because xy and -yx are inverses of each other, so they will combine to make 0.
is possible because you don't know what the values of x and y are. If y is sufficiently larger than x, then subtracting the negative number resulting from 2y (aka adding 2y) to the negative number 3x could be a positive number, including 5.
is possible because a negative (2x) times a negative (y) will always be positive.
Which, of course, means that is impossible, because a negative times a negative will never equal a negative.
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
Which, of course, means that
← Didn't Know|Knew It →
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
x, y and z are negative numbers.
A
---
x + y + z
B
---
xyz
Tap to reveal answer
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
Recognize the rules of negative numbers: if two negative numbers are multiplied, the result is positive. However if three negative numbers are multiplied, the result is negative. As such, we know B must be negative.
Since there are no restrictions on the values of x, y and z beyond being negative, lets check low values and high values: if every value was -1, multiplying the values would equal -1 while adding them would equal -3. However, if every value was -5, multiplying them would equal -125 while adding them would equal a mere -15. As such, we would need additional information to determine whether A or B would be greater.
← Didn't Know|Knew It →
and
Quantity A:
Quantity B:
Quantity A:
Quantity B:
Tap to reveal answer
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
Imagine two different scenarios when x equals either extreme: –1 or 1. If x equals –1, then x squared equals 1 and x cubed equals –1 (a negative times a negative times a negative is a negative), and thus Quantity A is greater. The other scenario is when x equals 1: x squared equals 1 and x cubed also equals 1. In this scenario, the two quantities are equal. Because both scenarios are possible, the relationship cannot be determined without more information.
← Didn't Know|Knew It →
Simplify:
$-(-6)^{2}$(-1)-(-3)
Simplify:
$-(-6)^{2}$(-1)-(-3)
Tap to reveal answer
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
$-(-6)^{2}$(-1)-(-3)
-(36)(-1)+(3)
(36)+(3)=39
Remember, the product of two negatives is positive. Also note that subtracting a negative is equivalent to adding its absolute value.
← Didn't Know|Knew It →
If and are both less than zero, which of the following is NOT possible?
If
Tap to reveal answer
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
is possible because two negative numbers added together will always equal a negative number.
is possible because xy and -yx are inverses of each other, so they will combine to make 0.
is possible because you don't know what the values of x and y are. If y is sufficiently larger than x, then subtracting the negative number resulting from 2y (aka adding 2y) to the negative number 3x could be a positive number, including 5.
is possible because a negative (2x) times a negative (y) will always be positive.
Which, of course, means that is impossible, because a negative times a negative will never equal a negative.
This question tests your familiarity with the mathematical principles behind how negative numbers operate.
Which, of course, means that
← Didn't Know|Knew It →