How to evaluate algebraic expressions - GRE Quantitative Reasoning

The answer is 2.

First solve for the constant x:

3_x_ + 2 = 32

x = 10

Now plug in x = 10 and b = 12:

a(10) + 12 = 32

a = 2

Substitute the values into equation: 3(-4) - 5(7) = -12 - 35 = -47.

The answer is 2.

First solve for the constant x:

3_x_ + 2 = 32

x = 10

Now plug in x = 10 and b = 12:

a(10) + 12 = 32

a = 2

Since both values are negative, in both situations the final result of the fraction will be positive regardless of the absolute value sign. Additionally, the definition of the exponent "–1" means the value is becoming its reciprocal. Thus, "x" → "1/x" and "1/y" → "y", equating to y/x.

Since A is a fraction with an exponential term in the denominator, its maximum value is when x is at a minimum. In B, the maximum value is when x approaches its maximum. Therefore, we can check whether there is overlap between the two quantities: No matter how close to either 0 or 1 x reaches, A will always be greater than B. (In fact, the minimum value for A is ~7, while the maximum value of B is ~5)

Be sure to keep your value of x consistent when plugging between the two fractions! The question asks for when they have the same x-value, not for when they are solved independently.

Since we know the mean is 7, and the number of terms is 5, we can first find the value of x:

((x – 2)+ (x) + (x + 1) + (x + 4) + (x + 7))/5 = (5x + 10)/5 = 7

x = 5

Since the terms are already listed in order, we can simpy plug in x = 5 to the middle value to get 5 + 1 = 6 as the median term.

For a quantitative comparison question such as this one, it is best to first plug in the numbers 0, 1, and –1. Plugging in 0 gets the same answer for both columns. Plugging in 1 makes Quantity B bigger. Plugging in –1 makes Quantity A bigger. Therefore the answer cannot be determined.

The answer is 7.

Write two independent equations that represent the problem.

x + y = 17 and 12_x_ + 7_y_ = 169

If we solve the first equation for x, we get x = 17 – y and we can plug this into the second equation.

12(17 – y) + 7_y_ = 169

204 – 12_y_ + 7_y_ =169

–5_y_ = –35

y = 7

The answer is 98.

If the area of each square tile is 49 then each side of the tile is 7. The width of the floor is 98 so 14 tiles would fit across. The length of the floor is 49 so 7 tiles would fit down.

14 tiles * 7 tiles = 98 tiles total

The answer is 7.

Let us first write down three equations that represent the problem:

n + d + q = 22

2_q_ = n

5_n_ + 10_d_ + 25_q_ = 245

Lets plug the second equation into the first and third equations:

(2_q)_ + d + q = 22

5(2_q_) + 10_d_ + 25_q_ = 245

Solve the first equation for d and plug into the last equation:

d = 22 – 3_q_

10q + 10(22 – 3_q_) + 25_q_ = 245

Solve for q.

220 – 30_q_ + 25_q_ + 10_q_ = 245

5_q_ = 25

q = 5

Therefore, n = 10 and d = 7

The answer is $11.55

The original cost is $29.99 but we are going to discount 30%, meaning we will only pay 70%. The new prices is 29.99 x 0.70 = $20.99.

The new price is then dicounted an additional 45%, meaning we will only pay 55% of the new price. The final price is 20.99 x 0.55 = $11.55.

When picking numbers, we should always try to plug in the numbers 0, 1, and –1 first.

First try 0:

(0 + 1)2 = 1

(0 – 1)2 = 1

Here the two quantities are equal.

Now try 1:

(1 + 1)2 = 4

(1 – 1)2 = 0.

Here Quantity A is greater.

Therefore the relationship cannot be determined.

squats: 10 squats * 60 minutes = 600 squats

situps: 6 situps * 30 minutes = 180 situps

total = 600 + 180 = 780

If x = 0, (x – 5)2 = 25 and (x + 5)2 = 25, so the quantities are equal.

If x = 1, (x – 5)2 = (–4)2 = 16 and (x + 5)2 = 62 = 36, so B is greater.

This is a contradiction, so the answer cannot be determined.

Set up two different equations:

and

Note the importance in the second equation of accounting for the exchange of 2 chickens for both quantities: Jan loses the two that she gives to Fran, and Fran gains the two that she receives.

Solve for by substituting for in the second equation:

Solving for results in .

The quantity produces a minimum of and a maximum of 4, which are less than and greater than 0, respectively. Therefore, the answer cannot be determined from the information given.

The third prime integer is 5, since 1 is not considered a prime number.

Working backwards,

You don't actually need to solve for the values of x and y. You just want to know the sum of x and y. Adding the two equations together you get

If we set the quantities equal, and the units digit of is 4, then the thousands digit which is three times the units digit would be 12, which doesnt make sense at all because a digit must be one of the integers 0 through 9. So 4 is too big to be the units digit of . Therefore Quantity B is greater.