SAT Sample Test

This is typical SAT question which is not only testing on the... also on the ability of test taker to mark the correct answer.

The test taker’s needs to consciously remove the extraneous s...duced due to squaring the expression let us explain in detail.

Given that

To find the solutions, we typically simplify the equation by squaring both the sides

Since is a quadratic equation, hence it has two solutions, 18 and 3.

Most test takers stop at this step and mark option C. which is wrong.

In a challenging question like this we need to be conscious that

is not a quadratic equation. Hence, it will not have two solutions. We need to remove the extraneous solution.

So, plug-in both the values to check whether they satisfy the equation

or not.

By plugging in = 3 in , we get

=

=> = , which is not true as square root of a number is always nonnegative.

Hence, cannot be equal to 3.

By plugging in = 18 in , we get

=

=> 8 = , which is true as square root of a number is always nonnegative.

Hence, = 18.

Therefore, the only solution to the given equation is 18, which is choice B.

Note: In the above method, we are solving it by converting the initial equation into a quadratic equation, but the initial equation is not quadratic. So, we need to be careful about plugging in the values back in the initial equation.

To find the coordinates of the vertex (p, q), let us find the roots of the quadratic equation, y = a (x - 2) (x - 6).

Putting a (x - 2) (x - 6) = 0, we get

x = 2 and x = 6.

Next, we need to find the line of symmetry which is a vertical line passing through the mid-point of the x-intercepts.

A line of symmetry divides the parabola in two equal parts and passes through the vertex.

That implies,

mid-point of the x-intercepts = (2 + 6)/2 = 4

Hence, the equation of line of symmetry is x = 4.

We know that the vertex lies on the line of symmetry.

Hence, the x-coordinate of the vertex (p, q) is 4.

Thus, p = 4.

To find the y-coordinate of the vertex, substitute x = 4 in the equation

y = a (x - 2)(x - 6).

That implies,

y = a (4 - 2) (4 - 6) = -4a.

Hence, p = 4 and q = -4a.

Therefore, the correct answer is choice C.

There are multiple ways to solve this question. As per our analysis most of the questions on absolute value on SAT can be conveniently solved through the distance approach.

Let’s understand the concept of distance approach through this question.

It is given that the annual yield of a mango farm, Y, varies from 270 tons to 350 tons.

First, let us find the mid-point of 270 and 350 which is 310 which is the point of reference from which the distance of Y will be measured.

As 270 ≤ ≤ 350, so can be anywhere on the left side of 310 up to 270 or on the right side of 310 up to 350 as shown in the figure above.

can be 310 as well.

Hence, the distance of  from 310 is less than or equal to 40.

Let’s understand the concept further with the help of an example.

Now, the mathematical equation to express all the values of that are at the distance of 5 units from 2 is

Here, the minus sign signifies the distance.

Hence, implies the distance of from 2 is equal to 5 units.

In the question at hand, 310 is the mid-point of 270 and 350.

The distance of Y from 310 is less than or equal to 40. Hence, we will put less than or equal to inequality.

|Y - 310| ≤ 40.

Thus, 270 ≤ ≤ 350 is equivalent to .

Therefore, the correct answer is choice C.

Correct Answer: B

Explanation: The sentence contains a very important Past Coming into Present tense Time Clue “Ever since,” which clearly indicates that the only tense that can be marked is Past Coming into Present. Only B is in Past Coming into Present tense.

Correct Answer: A

Explanation: The text states despite multiple tense international confrontations (that earlier led to the Second World War), no large-scale conflict has resulted. The historians argue that fear of enormous destruction has had a deterrent effect. To counter the argument and prove that destruction was not a deterrent, we need evidence that the Second World War happened despite the destruction in the First World War. Only A achieves this.

B: Incorrect. Out of Scope.
Fear of retaliation is not the agenda, destruction as a deterrent of war is.

C: Incorrect. Out of Scope.
Comparing the destruction in the two wars is not the agenda, destruction as a deterrent of war is.

D: Incorrect. Opposite.
This option supports the argument not weaken it.

Correct Answer: A
Explanation: Divide the options and the text into two halves. Read the first half of the text and eliminate the option choice based on it. Then read the second half of the text to eliminate the remaining options. Only A describes the structure well.

B: Incorrect. Out of Scope.
The text does talk about social behavior but does not validate it.

C: Incorrect. Out of Scope.
The text does not describe different perspectives of a technological aspect.

D: Incorrect. Out of Scope.
There is no debate mentioned in the text.

Correct Answer: D
Explanation: Make brackets.
[Lupita Nyong’o had already won an Academy Award for her role in Twelve Years a Slave when she landed the lead in Eclipsed, an off-Broadway play] = C
[successfully launching her stage career] = IC

A Complete and Incomplete sentence can only be joined with a comma, hence option D.

Correct Answer: C
Explanation: The goal is to explain the origin of the site's name. Only C explicitly states that the site was named to recognize the professor who led the team that discovered it.

A: Incorrect.
This option only talks about the description but does not explain the origin of the site’s name.

B: Incorrect.
This option focuses on how old the site is and nothing on the origin of site’s name.

D: Incorrect.
This option tells us that the ruins were named MaríaRuins but does not explain why it was named so.