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Example Questions
Example Question #1561 : Gre Quantitative Reasoning
(b * b4 * b7)1/2/(b3 * bx) = b5
If b is not negative then x = ?
1
7
–1
–2
–2
Simplifying the equation gives b6/(b3+x) = b5.
In order to satisfy this case, x must be equal to –2.
Example Question #1561 : Gre Quantitative Reasoning
If〖7/8〗n= √(〖7/8〗5),then what is the value of n?
5/2
√5
1/5
2/5
25
5/2
7/8 is being raised to the 5th power and to the 1/2 power at the same time. We multiply these to find n.
Example Question #1561 : Gre Quantitative Reasoning
Quantity A:
(0.5)3(0.5)3
Quantity B:
(0.5)7
Quantity B is greater.
The two quantities are equal.
Quantity A is greater.
The relationship cannot be determined from the information given.
Quantity A is greater.
When we have two identical numbers, each raised to an exponent, and multiplied together, we add the exponents together:
xaxb = xa+b
This means that (0.5)3(0.5)3 = (0.5)3+3 = (0.5)6
Because 0.5 is between 0 and 1, we know that when it is multipled by itself, it decreases in value. Example: 0.5 * 0.5 = 0.25. 0.5 * 0.5 * 0.5 = 0.125. Etc.
Thus, (0.5)6 > (0.5)7
Example Question #1562 : Gre Quantitative Reasoning
For the quantities below, x<y and x and y are both integers.
Please elect the answer that describes the relationship between the two quantities below:
Quantity A
x5y3
Quantity B
x4y4
Quantity B is greater.
Quantity A is greater.
The quantities are equal.
The relationship cannot be determined from the information provided.
The relationship cannot be determined from the information provided.
Answer: The relationship cannot be determined from the information provided.
Explanation: The best thing to do here is to notice that quantity A is composed of two complex terms with odd exponents. Odd powers result in negative results when their base is negative. Thus quantity A will be negative when either x or y (but not both) is negative. Otherwise, quantity A will be positive. Quantity B, however, has two even exponents, meaning that it will always be positive. Thus, sometimes Quantity A will be greater and sometimes Quantity B will be greater. Thus the answer is that the relationship cannot be determined.
Example Question #21 : Exponential Operations
Simplify: (x3 * 2x4 * 5y + 4y2 + 3y2)/y
10x11 + 7y3
10x7 + 7y3
10x7y + 7y2
None of the other answers
10x7 + 7y
10x7 + 7y
Let's do each of these separately:
x3 * 2x4 * 5y = 2 * 5 * x3 * x4 * y = 10 * x7 * y = 10x7y
4y2 + 3y2 = 7y2
Now, rewrite what we have so far:
(10x7y + 7y2)/y
There are several options for reducing this. Remember that when we divide, we can "distribute" the denominator through to each member. That means we can rewrite this as:
(10x7y)/y + (7y2)/y
Subtract the y exponents values in each term to get:
10x7 + 7y
Example Question #1561 : Gre Quantitative Reasoning
Quantitative Comparison
Quantity A: x3/3
Quantity B: (x/3)3
The two quantities are equal.
Quantity A is greater.
Quantity B is greater.
The relationship cannot be determined from the information given.
The relationship cannot be determined from the information given.
First let's look at Quantity B:
(x/3)3 = x3/27. Now both columns have an x3 so we can cancel it from both terms. Therefore we're now comparing 1/3 in Quantity A to 1/27 in Quantity B. 1/3 is the larger fraction so Quantity A is greater.
However, if , then the two quantities would both equal 0. Thus, since the two quantities can have different relationships based on the value of
, we cannot determine the relationship from the information given.
Example Question #1 : How To Multiply Exponents
Quantitative Comparison: Compare Quantity A and Quantity B, using additional information centered above the two quantities if such information is given.
Quantity A Quantity B
(23 )2 (22 )3
The relationship cannot be determined from the information given.
Quantity B is greater.
Quantity A is greater.
The two quantities are equal.
The two quantities are equal.
The two quantites are equal. To take the exponent of an exponent, the two exponents should be multiplied.
(23 )2 or 23*2 = 64
(22 )3 or 22*3 = 64
Both quantities equal 64, so the two quantities are equal.
Example Question #21 : Exponential Operations
Compare and
.
The answer cannot be determined from the information given.
To compare these expressions more easily, we'll change the first expression to have in front. We'll do this by factoring out 25 (that is,
) from 850, then using the fact that
.
When we combine like terms, we can see that . The two terms are therefore both equal to the same value.
Example Question #1562 : Gre Quantitative Reasoning
Which of the following is equal to ?
is always equal to
; therefore, 5 raised to 4 times 5 raised to 5 must equal 5 raised to 9.
is always equal to
. Therefore, 5 raised to 9, raised to 20 must equal 5 raised to 180.
Example Question #21 : Exponents
Which of the following is equal to ?
First, multiply inside the parentheses: .
Then raise to the 7th power: .
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