All GRE Math Resources
Example Questions
Example Question #1 : Basic Squaring / Square Roots
Which quantity is greater? When
Quantity A
Quantity B
1
Quantity A is greater.
Quantity B is greater.
The two quantities are equal.
The relationship cannot be determined from the information given.
Quantity B is greater.
X must equal a number between 0 and 1.
If you square any decimal number in this range you will get an answer less than 1. Try = 0.998.
Therefore Quantity B is always larger.
Example Question #1 : How To Square A Decimal
Which is greater, when
Quantity A
Quantity B
Quantity B is greater
Quantity A is greater
The two quantities are equal
The relationship cannot be determined from the information given
The relationship cannot be determined from the information given
When ,
must be a decimal. Therefore it will decrease when it is squared. To find this answer we can substitute two values for
.
and
When
But when
Therefore we cannot tell which is greater based on the information given.
Example Question #3 : Basic Squaring / Square Roots
Which is greater, when
Quantity A
Quantity B
Quantity A is greater
The two quantities are equal
Quantity B is greater
The relationship cannot be determined from the information given
The relationship cannot be determined from the information given
When ,
must be a decimal. Therefore it will decrease when it is squared. To find this answer we can substitute two values for
.
and
When
But when
Therefore we cannot tell which is greater based on the information given.
Example Question #21 : Decimals
Which is greater, when
Quantity A
Quantity B
The relationship cannot be determined from the information given
Quantity A is greater
Quantity B is greater
The two quantities are equal
Quantity A is greater
When ,
must be a negative decimal. Therefore it will decrease when it is squared and become positive. The first quantity
is the distance to 0 from
, in other words the positive value of
. The second quantity
will always be positive, but because it is a decimal it will always be less than
, if
was a positive quantity. Since
, then
wiill always be greater than
.
Quantity A is greater.
Example Question #1 : How To Square A Decimal
Which is greater, when
Quantity A
Quantity B
The two quantities are equal
The relationship cannot be determined from the information given
Quantity A is greater
Quantity B is greater
Quantity B is greater
When ,
must be a negative decimal. Therefore it will decrease when it is squared and become positive. Because
must be a decimal,
will also be a decimal. Therefore
will never be greater than 1.
Quantity B is greater.
Example Question #1 : Basic Squaring / Square Roots
Find the square root of the following decimal:
The easiest way to find the square root of a fraction is to convert it into scientific notation.
The key is that the exponent in scientific notation has to be even for a square root because the square root of an exponent is diving it by two. The square root of 9 is 3, so the square root of 8.1 is a little bit less than 3, around 2.8
Example Question #1 : Basic Squaring / Square Roots
Find the square root of the following decimal:
To find the square root of this decimal we convert it into scientific notation.
Because has an even exponent, we can divide the exponenet by 2 to get its square root.
Example Question #1 : How To Find The Square Root Of A Decimal
Find the square root of the following decimal:
This problem can be solve more easily by rewriting the decimal into scientific notation.
Because has an even exponent, we can take the square root of it by dividing it by 2. The square root of 4 is 2, and the square root of 1 is 1, so the square root of 2.5 is less than 2 and greater than 1.
Example Question #2 : Basic Squaring / Square Roots
Find the square root of the following decimal:
This problem becomes much simpler if we rewrite the decimal in scientific notation
Because has an even exponent, we can take its square root by dividing it by two. The square root of 4 is 2, and because 3.6 is a little smaller than 4, its square root is a little smaller than 2, around 1.9
Example Question #1341 : Act Math
Find the square root of the following decimal:
To find the square root of this decimal we convert it into scientific notation.
Because has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, and the square root of 4 is two, so the square root of 6.4 is between 3 and 2, around 2.53
All GRE Math Resources
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